ლ.ფერაძე, მ.სორდია maTematikuri sistema M athcad

saqarTvelos teqnikuri universiteti 

ლ.ფერაძე, მ.სორდია 

maTematikuri sistema 

M a t h c a d 

Tbilisi 

2008 

damtkicebulia stu_s 

saredaqcio-sagamomcemlo 

sabWos mier

uak. 621 397 

winamdebare saxelmZRvaneloSi pirvelad qarTulad sruli saxiT aRwerilia 

Mathcad maTematikuri sistema (Mathcad 11.0 versia), romlis meSveobiTac sruldeba 

yvela saxis maTematikuri gamoTvlebi da miiReba amocanebis amoxsna rogorc 

analizuri, aseve ricxviTi saxiT – saWiroebis SemTxvevaSi maTi grafikuli 

warmodgeniT. wignSi ganxilulia Mathcad–is ZiriTadi cnebebi da gansazRvrebebi, 

aRwerilia menius brZanebebi, instrumentTa panelebi, funqciebi da operatorebi, 

daprogramebis SesaZleblobebi. 

naSromi gankuTvnilia mkiTxvelTa farTo wrisaTvis: sxvadasxva specialobis 

studentebisaTvis, doqtorantebisa da mecnier muSakebisaTvis. SesaZlebelia misi 

rogorc TviTmaswavleblis gamoyeneba. 

avtorebi madlobas uxdian prof. T. kupataZes da asoc. prof. d. beriaSvils 

Rirebuli rCevebisaTvis masalis momzadebis procesSi. 

recenzentebi: 

telekomunikaciis departamentis 

sruli profesori, t.m.d. s. SavguliZe, 

saqarTvelos maTematikosTa 

kavSiris prezidenti, f/m.m.d. j. SariqaZe. 

2

s a r C e v i 

თavi I sawyisi cnebebi 7 

1.1 maTematikuri sistema Mathcad_is zogadi mimoxilva 7 

1.2 Mathcad–is instalireba 9 

1.3 Mathcad_is gaSveba 10 

1.4 Mathcad–is dokumentis fanjris struqtura 10 

1.5 ZiriTadi cnebebi da gansazRvrebebi 11 

1.6 kursoris formebi 12 

1.7 maTematikuri gamosaxulebebis Seqmna 13 

1.8 monacemTa ZiriTadi tipebi 16 

Tavi II menius punqti File (faili) 21 

2.1 mTavari menius File punqtis Semadgenloba 21 

2.2 Mathcad–is dokumentis Seqmna, Senaxva, gaxsna da daxurva 21 

2.3 gverdebis parametrebis dayeneba, beWdviswina daTvalierebis 24 

da beWdvis reJimebi 

Tavi III dokumentis redaqtirebis meTodebi 27 

3.1 redaqtirebis zogadi xerxebis mokle mimoxilva 27 

3.2 maTematikuri gamosaxulebebis redaqtirebis magaliTebi 28 

3.3 mTavari menius Edit (redaqtireba) punqtis Semadgenloba 32 

3.4 redaqtirebis operaciis gauqmeba_aRdgena 33 

3.5 dokumentis fragmentebTan muSaoba 33 

3.6 teqstis an gamosaxulebis fragmentis Zebna da Secvla 35 

3.7 dokumentis sasurvel gverdze gadasvla 36 

Tavi IV menius punqti View (xedi) 37 

4.1 mTavari menius View punqtis Semadgenloba 37 

4.2 instrumentTa panelebi 37 

4.3 saxazavi, mdgomareobis striqoni da areebi 38 

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4.4 masStabis Secvla da ganaxleba 38 

4.5 gverdis kolontitulebis Seqmna da gaformeba 39 

Tavi V menius punqti Insert (Casma) 41 

5.1 mTavari menius Insert punqtis Semadgenloba 41 

5.2 grafikis Casma 41 

5.3 organzomilebiani X_Y grafikis ageba da redaqtireba 42 

5.4 polaruli grafikis ageba da redaqtireba 46 

5.5 3_ganzomilebiani zedapiris grafikis ageba da redaqtireba 48 

5.6 konturuli grafikis Seqmna 52 

5.7 wertilovani da svetovani grafikebis Seqmna 54 

5.8 veqtoruli velis grafikis Seqmna 55 

5.9 grafikebis Seqmna ostatis meSveobiT 55 

5.10 matricis Casma dokumentSi 57 

5.11 funqciebis Casma 58 

5.12 sazomi erTeulis Casma 58 

5.13 naxatis Casma 59 

5.14 ubnis formireba da gverdis gawyveta 60 

5.15 maTematikuri da teqsturi areebis Casma 60 

5.16 komponentebis Casma 61 

5.17 monacemebis Casma 63 

5.18 mmarTveli komponentebis Casma 66 

5.19 Mathcad_is dokumentSi sxva obieqtis Casma 67 

5.20 miTiTebebis Casma 69 

5.21 hipermimarTvis damyareba 70 

Tavi VI simboluri operaciebi Mathcad_Si 72 

6.1 Symbolics menius da Symbolic panelis Semadgenloba 72 

6.2 maTematikuri gamosaxulebebis warmodgena analizuri saxiT 74 

6.3 maTematikuri gamosaxulebebis gamartiveba (simplify) 76 

6.4 maTematikuri gamosaxulebis gaSla (expand) 78 

6.5 maTematikuri gamosaxulebebis da ricxvebis martiv mamravlebad 79 

daSla (factor) 

6.6 maTematikuri gamosaxulebis mwkrivad gaSla msgavsi 80 

wevrebis SeerTebiT (collect) 

6.7 polinomis koeficientebis gansazRvra miTiTebuli 81 

cvladis mimarT (coeffs) 

6.8 gantolebebis da utolobebis amoxsna miTiTebuli 82 

cvladis mimarT (solve) 

4

6.9 gamosaxulebis Casma miTiTebuli cvladis magivrad (substitute) 83 

6.10 maTematikuri gamosaxulebebis diferencireba da integreba 85 

6.11 maTematikuri gamosaxulebebis teiloris mwkrivad gaSla (series) 86 

6.12 maTematikuri gamosaxulebebis warmodgena elementaruli 88 

wiladebis jamis saxiT (parfrac) 

6.13 matricebis transponireba, Sebruneba da determinantis gansazRvra 89 

6.14 maTematikuri gamosaxulebebis gardaqmnebi 91 

6.15 simboluri gamoTvlebis Sedegebis gamotanis stilis dayeneba 93 

6.16 cvladebis mniSvnelobebis SezRudva da instrumentTa 93 

paneli Modifier (modificikacia) 

6.17 simboluri gamoTvlebis Sedegebis warmodgena kompleqsuri ricxvis 95 

saxiT da mcocavi wertiliT (complex, float) 

Tavi VII daformateba Mathcad_Si 97 

7.1 Format menius da Formatting panelis Semadgenloba 97 

7.2 maTematikuri gamosaxulebebis daformateba 98 

7.3 ricxviTi Sedegebis daformateba 100 

7.4 teqstisa da abzacis daformateba 104 

7.5 tabulaciis poziciebis dayeneba 106 

7.6 stilis daformateba 106 

7.7 obieqtis Tvisebebis dayeneba 108 

7.8 grafikebis daformateba 110 

7.9 ferebis dayeneba 112 

7.10 ubnebis daformateba 113 

7.11 areebis gancalkeveba da sworeba. gverdebis xelmeore numeracia 114 

Tavi VIII mTavari menius Tools (instrumentebi) punqti 115 

8.1 mTavari menius Tools punqtis Semadgenloba 115 

8.2 marTlweris Semowmeba da koreqtireba 115 

8.3 animaciuri klipebis Seqmna da aRwarmoeba 116 

8.4 samuSao furclis dacva 119 

8.5 gamoTvlebis reJimebi 120 

8.6 calkeuli maTematikuri aris gaangariSebis procesidan gamoricxva 121 

8.7 gamoTvlebis optimizacia 121 

8.8 Secdomis wyaros gamovlineba 122 

8.9 samuSao furclis ofciebi 124 

8.10 parametrebis momarTva 125 

5

Tavi IX mTavari menius Window (fanjara) punqti 127 

9.1 mTavari menius Window punqtis Semadgenloba 127 

9.2 fanjrebis kaskaduri ganlageba (Cascade) 127 

9.3 fanjrebis horizontaluri da vertikaluri ganlageba 128 

(Tile Horizontal, Tile Vertical) 

9.4 dokumentebis fanjrebis marTva 129 

Tavi X sainformacio resursebi. mTavari menius Help punqti 131 

10.1 mTavari menius Help (daxmareba) punqtis Semadgenloba 131 

10.2 Mathcad_is sacnobaro sistema 131 

10.3 sainformacio resursebis gamoyeneba (Resource Center) 133 

10.4 daxmarebis sxva saSualebebi 136 

Tavi XI funqciebi Mathcad_Si 137 

11.1 momxmareblis mier funqciebis Seqmna 137 

11.2 CaSenebuli funqciebis mimoxilva 137 

11.3 momxmareblis mier operatoris Seqmna 147 

Tavi XII daprogrameba Mathcad_Si 149 

12.1 Programming instrumentTa panelis operatorebis aRwera 149 

12.2 miniWebisa da striqonis Casmis operatorebi 150 

12.3 pirobiTi gadasvlis iperatori 151 

12.4 ciklis operatorebi 153 

12.5 Break, Continue da Return operatorebi 155 

12.6 operatori on error 155 

gamoyenebuli literatura 157 

6

თavi I sawyisi cnebebi 

1.1 maTematikuri sistema Mathcad_is zogadi mimoxilva 

maTematikuri gamoTvlebis avtomatizirebis aucileblobam ganapiroba 

kompiuteris Seqmna. eleqtronul milakebze agebulma pirveli Taobis 

kompiuterebma farTo gamoyeneba ver hpova sxvadasxva mizezebis gamo. 

mikroeleqtronikis ganviTarebasTan erTad gamoCnda specializirebuli, 

maTematikuri gamoTvlebisTvis gankuTvnili miniaturuli kompiuteri – 

programirebuli kalkulatori, romelic amJamadac gamoiyeneba. bolo wlebSi 

masiuri gavrceleba hpova ufro mZlavrma, swrafma da universalurma 

personalurma kompiuterma, romelsac gaaCnia grafikebis agebis, logikuri da 

analizuri gamoTvlebis SesaZleblobanic. 

Tavdapirvelad kompiuterze maTematikuri gamoTvlebis SesrulebisaTvis 

aucilebeli iyo romelime daprogramebis enis, rogoricaa: fortrani, beisiki, 

paskali da sxva, Seswavla. es aucilebloba Tavidan acilebuli iqna bolo dros 

farTo masebSi gavrcelebul iseT maTematikur sistemebSi rogoricaa: Mathcad, 

Mercury, Matlab, Mathematica, Maple da sxv. 

maTematikuri sistema Mathcad–i warmoadgens amerikuli firmis MathSoft–is 

produqcias. igi muSaobs grafikuli garsis mqone operaciuli sistema Windows–is 

marTvis qveS, rac ganapirobebs am ukanasknelis tipiuri da farTo 

SesaZleblobebis Mathcad–Si gamoyenebas: dokumentis redaqtireba, yvela tipis 

printeris, yvelaze metad gavrcelebuli simboloebis gamoyenebis SesaZlebloba, 

Sriftebis mravalferovneba, mausis moxerxebuli manipulireba, amomwuravi 

eleqtronuli cnobari, OLE meqanizmis gamoyeneba da sxv. 

Mathcad–s, teqsturi redaqtoris msgavsad, gaaCnia WYSIWYG (What you see is what 

you get – rasac xedav, imas iReb) interfeisi, rac iTvaliswinebs dokumentis 

dabeWdvas imave saxiT, rogori saxec mas displeis ekranze aqvs. Mathcad–Si 

SesaZlebelia rogorc urTulesi maTematikuri gamoTvlebis, aseve martivi 

simboluri gardaqmnebis Catareba. mas gaaCnia maTematikur simboloebze 

orientirebuli interfeisi da grafikebis agebis saSualebani, aseTive saxe aqvs 

gamoTvlebis Sedegebsac, rac sruliad amarTlebs misi saxelis abreviaturas 

(cad _ Computer Aided Design – kompiuteris meSveobiT proeqtireba). 

iseve, rogorc eleqtronul cxril Excel–Si, Mathcad–is dokumentSic 

cvlilebebis Setana moaxdens arsebuli dokumentis formulebis Sesabamis 

gadaangariSebas, aseve avtomaturad cvlilebebs ganicdis agebuli grafikebic. 

eleqtronul wignSi Tavmoyrilia gamoyenebiTi formulebi da grafikebi, romlis 

kopireba da Casma momxmareblis dokumentSi martivad sruldeba. aseve 

7

SesaZlebelia gamoviyenoT ukve gamzadebuli, konkretuli amoxsnili magaliTebi, 

romlebic moTavsebulia e.w. standartul biblioTekebSi (Quick Sheets). 

Mathcad–Si dokumentis Seqmnis procesSi daSvebuli Secdomebis aRmofxvra 

advilad xdeba, radgan masSi sruldeba sintaqsuri da semantikuri Semowmeba. 

daSvebuli Secdomebi gamoiyofa wiTeli simboloebiT. masze amomwurav pasuxs 

gvaZlevs eleqtronuli cnobari, romlis gamoZaxebac xdeba klaviaturidan F1 

Rilakis gamoyenebiT. 

Mathcad–Si formulis Cawera advilad xorcieldeba grafikuli 

maTematikuri simboloebiT. formulebi Caiwereba analizuri saxiT da ar 

moiTxoveba sayovelTaod miRebul maTematikur simboloebTan (mag.,, ! , , ) 

dakavSirebuli gamoTvlebis proceduris dawvrilebiTi aRwera. aseTi midgoma 

aadvilebs maTematikur moqmedebaTa arsis aRqmas da momxmarebels acilebs 

daprogramebis enis (mag: fortrani, beisiki, paskali da a.S.) gamoyenebis 

aucileblobas. 

ra Tqma unda, es ar niSnavs imas, rom sistemas ar gaaCnia misi daprogramebis 

ena. sinamdvileSi igi arsebobs – algoriTmuli, maRali donis daprogramebis ena, 

romelic maTematikur simboloebze orientirebulia da gvexmareba sistemasTan 

dialogis damyarebaSi. am daprogramebis enis meSveobiT SesaZlebelia dasmuli 

amocanis amoxsna da Sedegis miReba sasurveli formiT. 

imis mixedviT Tu romel obieqts (teqsti, formula an grafiki) qmnis 

momxmarebeli Mathcad–Si, sistema Tavad aformirebs programas daprogramebis enis 

meSveobiT, romelic inaxeba operatiul mexsierebaSi manam, sanam ar iqneba 

Senaxuli diskze failis saxiT, romlis tipia .mcd. momxmareblisaTvis Mathcad–is 

gamosayeneblad sakmarisia masSi obieqtze orientireba. yvela operators gaaCnia 

maTematikuri simboloebis saxe, romlis arCevac advilad SesaZlebelia mausis 

meSveobiT, xolo maTematikuri funqciebi (mag: sin, cos da a.S.) SegviZlia 

klaviaturidan avkriboT ise, rogorc gviweria, an avirCioT instrumentTa 

panelidan, specialuri siidan, rac funqciis Seyvanisas SecdomaTa albaTobas 

amcirebs. 

Mathcad 11.0 Pro versiaSi wina versiebidan gansxvavebiT damatebulia axali 

SesaZleblobani rogoricaa: dokumentis feradi gaformeba, animaciuri (moZravi) 

grafikebis ageba da xmovani gaformeba, teqsturi, formulebis da grafikuli 

redaqtorebis gaerTianeba. aseve SesaZloa sxva simbolur maTematikur mZlavr 

sistemebTan gaerTianeba urTulesi gamoTvlebisaTvis. aqedan gamomdinareobs aseTi 

sistemebis saxelic _ integrirebuli sistemebi. 

bolo dros mniSvnelovan interess iwvevs kompiuteruli algebris 

sistemebis unari Seasrulos ara mxolod cifruli, aramed analoguri 

gamoTvlebic. 

IBM PC–Tvis SemuSavda simboluri maTematikuri (kompiuteruli algebra) 

sistemebi, iseTebi rogoricaa: Mathcad, Matlab, Derive [10], Maple V da Mathematica2 da 

3. maTi gamoyeneba aadvilebs yvelaze rTul maTematikur, statistikur da 

8

finansur–ekonomikur gamoTvlebs, romlis CatarebisaTvis manamde saWiro iyo 

maRali donis maTematikos_analitikosebis Careva. 

aRsaniSnavia, rom liderebad kompiuteruli algebris sistemebSi iTvlebian 

kompania Waterloo Maple Software–is produqcia Maple V da firma Wolfram–is 

Mathematica3. am sistemebs gaaCniaT simboluri maTematikis amomwuravi 

SesaZleblobani, rac mosaxerxebelia maTematikosebisaTvis, magram ara farTo 

masebisaTvis. am ukanasknelTaTvis ufro moxerxebul maTematikur sistemad rCeba 

Mathcad–i, romelSic SesaZlebelia rTuli maTematikuri ricxviTi gamoTvlebis da 

agreTve simboluri operaciebis Catareba. amisaTvis firma Maple–is licenziiT 

Mathcad–Si gamoyenebulia ramodenime ZiriTadi simboluri operacia Maple–dan. maTi 

raodenoba SezRudulia im minimumamde, romelic saWiroa masiuri 

momxmareblisaTvis. amis dasadastureblad sakmarisia moviyvanoT statistikuri 

Sedareba. Maple VR4 Seicavs 2800 (!) funqcias, rodesac Mathcad-11.0 Pro–Si maTi 

ricxvi 300 umniSvnelod aRemateba da aqedan simboluri maTematikis funqciebi 

sul raRac or aTeuls utoldeba. 

amrigad, Mathcad–is ZiriTadi ganmasxvavebeli Tvisebebia: 

Mathcad–i maTematikuri amocanebis amoxsnis universaluri sistemaa, farTo 

momxmarebelze orientirebuli; 

maTematikuri amocanebis Cawera Mathcad–Si sxva sistemebTan SedarebiT 

miaxloebulia Cveulebriv Caweras, rac aadvilebs mis gamoyenebas; 

Mathcad–i ramdenjerme iafia Tavis analogebTan SedarebiT. 

1.2 Mathcad–is instalireba 

Mathcad 11.0–is instalirebisaTvis aucilebelia garkveuli aparaturuli da 

programuli uzrunvelyofa. 

kompiuters. 

aparaturul uzrunvelyofaSi vgulisxmobT IBM firmis personalur 

kompaqt_diskze (CD_ROM) arsebuli maTematikuri sistema MathCAD–is 

pirdapiri kopireba vinCesterze yovlad dauSvebelia. misi instalirebisaTvis 

aucilibelia: 

1. movaTavsoT diski kompakt–diskis diskur mowyobilobaSi; 

2. avirCioT ZiriTadi menius punqti Start Run... ; 

3. mivuTiToT kompakt–diskis saxeli (mag. D:\setup.exe). 

instalirebis procesi umtkivneulod mimdinareobs, magram Tu warmoiqmneba 

raime problema, SegviZlia misi gadaWra, Tu gavecnobiT detalur instruqcias 

instalirebis Sesaxeb readme failSi. 

9

1.3 Mathcad–is gaSveba 

Mathcad–is CatvirTva SesaZlebelia yvela im wesiT, romelic miRebulia 

operaciuli sistemaMAWindows –is garemoSi: 

samuSao magidaze Mathcad–is niSnakze Tagvis marcxena RilakiT orjeradi 

dawkapunebiT; 

sastarto menius Start → Programs → MathSoft Apps → Mathcad brZanebiT; 

Sesabamisi katalogis sarCevSi Mathcad.exe failze orjeradi dawkapunebiT; 

Start → Search dialogur fanjaraSi .mcd gafarToebis mqone failebis 

moZebniT da ormagi wkapuniT erT-erT aseT failze (am dros programa 

avtomaturad CaitvirTeba Sesabamisi dokumentis fanjarasTan erTad); 

saqaRaldis sarCevSi Mathcad–is dokumentze orjer dawkapunebiT (am dros 

programa avtomaturad gaiSveba da gaixsneba Sesabamisi dokumentis fanjara); 

Start → Run… brZanebis dialogSi Mathcad.exe failze mimarTvis gzis 

miTiTebiT an Mathcad–is dokumentis failis saxelis miTiTebiT; 

Tu Mathcad–is piqtograma gadatanilia swrafi gaSvebis (Quick Launch) 

panelze, am piqtogramaze dawkapunebiT. 

1.4 Mathcad–is dokumentis fanjris struqtura 

Mathcad–is gaSvebis Semdeg ekranze gaixsneba misi fanjara (nax.1.1). 

nax.1.1. Mathcad–is fanjara 

10

Mathcad–is fanjris stრuqturaa: 

Mathcad–is fanjris pirveli striqonia saTauris striqoni – marcxniv 

miTiTebulia dokumentis saTauri, xolo marjvniv ganlagebulia sami 

Rilaki: dakecvis, mTel ekranze gaSlisa (Tu fanjara gaSlilia, am adgilas 

gvaqvs aRdgenis Rilaki, romelic aRadgens fanjris zomas, romelic mas 

hqonda mTel ekranze gaSlamde) da daxurvis. 

meore striqonia menius striqoni, sadac Tavmoyrilia menius punqtebi: 

File (faili) – failebTan muSaoba; 

Edit (redaqtireba) – dokumentis redaqtireba; 

View (xedi) – fanjris struqturis dayeneba; 

Insert (Casma) – obieqtebis Casma; 

Format (formati) – obieqtebis daformateba; 

Tools (instrumentebi) – programis zogi parametris da reJimis dayeneba; 

Symbolics (simbolika) – simboluri operaciebi; 

Windows (fanjrebi) – sistemis fanjrebs Soris marTva; 

Help (daxmareba) – damxmare eleqtronuli cnobari. 

menius striqonis Semdeg gvaqvs instrumentTa panelebis striqonebi. 

mizanSewonilia ekranze Candes Standard, Formatting, Math panelebi, romelTa 

moxsna_dayeneba menius View → Toolbars brZanebis CamonaTvalidan xdeba. 

danarCeni panelebi rogorebicaa Boolean, Symbolics, Calculus da sxv. SegviZlia 

ganvalagoT samuSao areSi moTxovnilebis Sesabamisad View → Toolbars 

brZanebis CamonaTvalidan an Math panelze Sesabamis Rilakze dawkapunebiT. 

fanjris ZiriTadi nawili ukavia samuSao ares (WorkSheet), sadac xdeba 

maTematikuri amocanebis amoxsna. 

fanjris qveda nawili ukavia mdgomareobis striqons (Status Bar), romlis 

moxsna_dayeneba xdeba menius View → Status Bar brZanebiT. 

fanjris standartuli saxe iTvaliswinebs agreTve vertikaluri da 

horizontaluri gadafurcvlis zolebs – dokumentis im ubnebis 

dasaTvaliereblad, romlebic ekranze ar Cans. 

1.5 ZiriTadi cnebebi da gansazRvrebebi 

Mathcad_is dokumenti Sedgeba sxvadasxva tipis (formulebi, teqstebi, 

grafikebi, cxrilebi da a.S.) calkeuli blokebisagan. TiToeul bloks uWiravs 

marTkuTxedis formis garkveuli are. 

blokebis ganlagebas dokumentSi (teqsturi blokis garda) principialuri 

mniSvneloba aqvs. isini sruldeba marcxnidan marjvniv da zemodan qveviT, amitom 

blokebma ar unda gadafaron erTmaneTi, Tumca umniSvnelo gadafarvas 

mniSvneloba ara aqvs. 

11

lokebis konstruirebisaTvis Mathcad–Si CaSenebulia sami redaqtori: 

teqsturi, formuluri da grafikuli (Sesabamisad teqsturi komentarebis, 

maTematikuri gamosaxulebebis da grafikebis Seqmnis saSualebebi). 

maTematikuri are – es aris are maTematikuri gamosaxulebiT an grafikiT. 

masSi Setanili nebismieri cvlileba aisaxeba mis qvemoT da marjvniv ganlagebul 

yvela danarCen maTematikur areSi. 

teqsturi are – es aris marTkuTxedis formis teqstis gansaTavseblad 

gankuTvnili are. teqstur ares xmaroben komentarebisaTvis. teqsturi aris 

Sesaqmnelad arsebobs ramdenime xerxi: 

menius striqonidan Insert → Text Region brZanebiT; 

klaviaturidan “ simbolos gamoyenebiT; 

sityvis an Tundac erTi simbolos Setanis Semdeg klaviaturidan “hari” 

klaviSis akrebiT. 

zemoTCamoTvlili SesaZlo variantebis gamoyenebisas gamoCndeba 

marTkuTxedi, sadac standartuli wesiT Seitaneba teqsti, amasTan SesaZloa 

sasurveli Sriftis, misi zomisa da maxasiaTeblebis dayeneba. teqstur areSi Enter 

klaviSze dawkapunebiT gadavalT axali abzacis pirvel striqonze, xolo Enter + 

Shift–iT mimdinare abzacis Semdeg striqonze. teqsturi aris marTkuTxeds aqvs 

markerebi, romelTa meSveobiT SeiZleba teqsturi aris gadideba–dapataraveba. 

1.6 kursoris formebi 

kursorma SeiZleba miiRos Semdegi formebi: 

+ jvaredini wiTeli feris kursori _ viziri _ miuTiTebs samuSao areSi 

pozicias, sadac SeiZleba formulis, teqstisa da grafikis blokebis ageba; 

misi gadaadgileba SesaZlebelia klaviaturidan kursoris gadaadgilebis 

klaviSebis gamoyenebiT an mausiT – sasurvel poziciaze dawkapunebiT; 

kursoris wiTeli vertikaluri xazi miuTiTebs teqstur blokebSi 

simboloTa Casmis an waSlis adgils; 

kursoris lurji kuTxis forma miuTiTebs maTematikur blokSi morigi 

simbolos Casmis pozicias da agreTve gamoyofil calkeul nawils an mTli- 

an gamoyofil ares. misi saxe damokidebulia simboloebis Setanis 

mimarTulebaze. klaviaturidan am mimarTulebis Secvla SesaZlebelia Insert 

Rilakis gamoyenebiT. maTematikur areSi saxelis an ricxvis redaqtirebisas 

kursori Seicvleba da miiRebs Semdeg formas: . 

12

1.7 maTematikuri gamosaxulebebis Seqmna 

maTematikuri gamosaxulebebis Sesaqmnelad ZiriTadad viyenebT Math 

instrumentTa panelze arsebul maTematikur palitras. misi yoveli RilakiT Tavis 

mxriv gamoiZaxeba maTematikur simboloTa da moqmedebaTa esa Tu is paneli. Math 

instrumentTa panelis Rilakebia: 

– Calculator panelis gamoZaxeba. am panelze ganlagebulia ariTmetikuli 

operaciebis niSnebi da xSirad gamoyenebadi funqciebi; 

– Graph panelis gamoZaxeba, romelzec moTavsebulia or an samganzomi- 

lebiani grafikebis Sablonebi; 

– Matrix panelis gamoZaxeba, romelzec moTavsebulia matricebis da 

veqtorebis operatorebi; 

– Evaluation panelis gamoZaxeba. am panelze ganlagebulia miniWebis, 

tolobis, simboluri gardaqmnebis da momxmareblis mier operatoris 

ganmsazRvreli niSnebi; 

– Calculus (maTanalizis) panelis gamoZaxeba, romelSic ganlagebulia 

diferencialebis, integralebis, zRvrebis, jamis da namravlis Sablonebi; 

– Boolean panelis gamoZaxeba, romelSic ganlagebulia Sedarebis niSnebi da 

logikuri algebris operatorebi; 

– Programming panelis gamoZaxeba. am panelze ganlagebulia operatorebi, 

romlebic gvaZleven daprogramebis saSualebas; 

asoebi; 

– Greek panelis gamoZaxeba, romelzec ganlagebulia berZnuli anbanis 

– Symbolic panelis gamoZaxeba. am panelze ganlagebulia simboluri 

gamoTvlebis operatorebi. 

vTqvaT, gvinda gamovTvaloT Semdegi gamosaxulebis mniSvneloba: 

amisaTvis: 

3 

 

 

 

 

x 

2 

13 

1 

 

2xy 

 

 

1) Calculator panelze avirCioT (Tagvis marcxena Rilakze dawkapunebiT) 

niSnuli n (an davaWiroT Ctrl + \ ). gamoCndeba fesvis Setanis 

Sabloni. Savi marTkuTxedebiT naCvenebia, Tu sad unda aucileblad 

moTavsdes garkveuli maTematikuri informacia; 

2 

.

2) klaviaturis klaviSis meSveobiT an Shift + Tab–is daWeriT 

gadavalT poziciaSi, sadac iwereba fesvis xarisxi (gamosaxulebis 

nebismier adgilze kursoris dayeneba xdeba agreTve am adgilze 

TagviT dawkapunebiT); 

3) SevitanoT klaviaturidan an Calculator panelidan cifri 3. ekranze 

gveqneba 3 ; 

4) klaviSis meSveobiT an Tab–is daWeriT gadavalT poziciaSi, 

sadac unda SevitanoT fesvisqveSa gamosaxuleba; 

5) Calculator panelze avirCioT ( ), ekranze gamoCndeba 3 ( ) ; 

6) imave panelze avirCioT /, gveqneba 

7) mricxvelSi avkriboT 1; 

3 

1 

x 2 

 

warmoadgens koeficients). miviRebT ; 

2x y 

 

12) mimarTulebis klaviSis orjer gamoyenebis Semdeg avkriboT 

14 

3 

 

 

; 

8) Tab klaviSis gamoyenebiT aRmovCndebiT mniSvnelSi; 

9) Calculator panelidan gamoviZaxoT kvadratuli fesvis Sabloni (an 

davaWiroT klaviaturaze \ ), gveqneba 

10) Calculator panelze avirCioT 2 

x . gamoCndeba kvadratSi ayvanis Sabloni 

3 

 

 

 

1 

2 

 

 

. markeris adgilas SevitanoT x ; 

11) klaviSis gamoyeneba dagvayenebs sasurvel poziciaSi, sadac 

gavagrZeloT mniSvnelis Setana – klaviaturidan Tanmimdevrulad 

avkriboT simboloebi +2x*y (2–isa da x–is Soris gamravlebis niSnis 

Setana ar aris aucilebeli; sistema TviTon mixvdeba, rom 2 

klaviaturaze ^2 . 

gamosaxulebis Seqmnis procesi damTavrebulia. maTematikuri aridan 

gamosasvlelad davawkapunoT aris gareT an davaWiroT Enter klaviSs. 

gamosaxulebis gamosaTvlelad movniSnoT is anu lurji kuTxis kursoriT 

movicvaT is mTlianad da SevitanoT tolobis niSani (klaviaturidan, Evaluation an 

Calculator panelebidan). Tu x–isa da y–is mniSvnelobebi winaswar ar iyo 

gansazRvruli, ekranze wavikiTxavT informacias amis Sesaxeb da Sesabamisi 

cvladi iqneba gaferadebuli wiTlad. Tu Setanili formulis zeviT an marcxniv 

3 

 

 

 

1 

 

 

 

;

x–s da y–s mivaniWebT mniSvnelobebs, Cvens mier Seqmnil maTematikur gamosaxulebas 

miewereba Mathcad–is mier gamoTvlili pasuxi. 

aRvniSnoT, rom maTematikuri gamosaxulebis Seqmnisas da 

klaviSebis meSveobiT xdeba gadaadgileba erTi poziciiT marjvniv an marcxniv, 

xolo Tab–isa da Shift + Tab klaviSebiT Sablonis erTi marTkuTxedidan meoreze – 

Sesabamisad win da ukan. gamosaxulebis nebismier adgilze kursoris dayeneba 

SesaZlebelia agreTve am adgilze Tagvis dawkapunebiT. 

axarisxebis, fesvis amoRebis da gayofis operatorebs aqvT Semdegi Tviseba: 

yvelaferi, rac Seitaneba am operatorebis Semdeg, aRiqveba Sesabamisad xarisxis 

maCveneblad, fesqveSa gamosaxulebad da mniSvnelad. imisaTvis, rom es SevwyvitoT, 

davaWiroT an Space (hari) an klaviSs. 

nax.1.2–ze moyvanilia sxvadasxva maTematikuri gamosaxulebebi. 

nax.1.2. maTematikuri gamosaxulebebis magaliTebi 

miniWebis operatoris niSania : = , xolo = niSani gamoiyeneba maTematikuri 

gamosaxulebis ricxviTi mniSvnelobis gamosatanad. Evaluation (an Symbolic) panelis 

→ (simboluri tolobis niSani) punqtiT miviRebT gamosaxulebis mniSvnelobas 

analizuri saxiT. 

15

miniWebis operaciebis pirveladi Setanis dros SesaZlebelia gamoviyenoT = 

niSani. sistema TviTon gardaqmnis mas miniWebis niSnad (: =), magram Tu SemdgomSi 

viyenebT igive cvlads gansxvavebuli mniSvnelobiT, aucilebelia miniWebis niSnis 

gamoyeneba rogorc klaviaturidan : simbolos akrebis meSveobiT, aseve Calculator an 

Evaluation panelebis : = punqtze dawkapunebiT. 

1.8 monacemTa ZiriTadi tipebi 

Mathcad–Si monacemTa ZiriTadi tipebi aris mudmivebi (konstantebi), 

cvladebi, masivebi da failebi. 

konstanta es aris saxelis mqone obieqti, romlis mniSvneloba ar icvleba. 

konstantebi SeiZleba iyos sxvadasxva tipis. 

ricxviTi konstantebis magaliTebia: –682, 86.4, 5.281x10 +2 . ricxviTi 

konstantebis modulebis mniSvnelobebis diapazoni MathcadD–Si aris 10 307 –dan 10 -307 – 

mde (manqanuri usasruloba da manqanuri nuli). 

Mathcad_is konstantebi SeiZleba iyos agreTve mocemuli orobiT, rvaobiT 

da teqvsmetobiT sistemebSi. orobiTi ricxvebis bolos miewereba laTinuri aso b 

(binary niSnavs orobiTs), rvaobiTi ricxvebis bolos – laTinuri aso O (Octal 

niSnavs rvaobiTs), xolo TeqvsmetobiTi ricxvebis bolos – aso h an HH (hexagonal 

niSnavs TeqvsmetobiTs). mag., 11110001b warmoadgens aTobiTi sistemis 241. orobiTi, 

rvaobiTi da TeqvsmetobiTi sistemiT warmodgenili ricxvi unda iyos 2 31 _ze 

naklebi. 

Mathcad–s SeuZlia muSaoba rogorc namdvil, ise kompleqsur ricxvebTan. 

kompleqsuri ricxviTi konstantebis magaliTebia: 2+i x 3 an 3–j x 10 , sadac i da j 

simboloebiT aRniSnulia warmosaxviTi erTiani. kompleqsur ricxvebTan muSaobis 

win rekomendirebulia mivaniWoT i–s an j–s 1 mniSvneloba an SevamowmoT, am ori 

simboloTagan romels xmarobs sistema warmosaxviTi erTianis aRsaniSnavad. 

Mathcad–i muSaobs agreTve iseT konstantebTan, romlebsac ricxviTi 

mniSvnelobebis garda gaaCniaT miTiTeba fizikur sidideze (droze, sigrZeze, 

masaze, muxtze da a.S.). amisTana konstantebis Cawerisas iyeneben gamravlebis 

niSans ricxviTi mniSvnelobis da sididis aRmniSvnel simboloebs Soris. 

ricxviTi konstantebis garda, Mathcad–i agreTve muSaobs striqonuli tipis 

monacemebTan, romlebic warmoadgenen striqons brWyalebSi, mag., "Insert Matrix", 

"The rezult is valid". striqonuli tipis konstanta SeiZleba Sedgebodes erTi an 

ramdenime simbolosagan an sityvisagan. 

arsebobs agreTve sistemuri konstantebi (, e, ∞), romelTa mniSvnelobebi 

winaswar gansazRvrulia. 

cvladi – es aris saxelis mqone obieqti, romelsac gaaCnia mniSvneloba da 

es mniSvneloba SeiZleba Seicvalos programis Sesrulebis msvlelobisas. 

16

cvladis tipi ganisazRvreba misi mniSvnelobiT. igi SeiZleba iyos ricxviTi 

tipis, striqonuli da a.S. 

identifikatori warmoadgens mudmivis, cvladis an sxva obieqtis saxels. 

identifikatoris sigrZe praqtikulad ar aris SezRuduli. is warmoadgens 

laTinuri an berZnuli asoebis, cifrebis da zogi specialuri simbolos 

mimdevrobas, romelic asoTi iwyeba. mag: a, x1, alfa,YY_coordinate. identifikatoris 

CanawerSi dauSvebelia haris gamoyeneba. zogi specialuri simbolo, (mag.,@_ ) 

daSvebulia identifikatorebSi, zogi (mag., ariTmetikuli moqmedebis niSnebi) 

akrZalulia. sistema ganasxvavebs nusxur asoebs da asomTavrulebs. aRvniSnoT 

agreTve, rom identifikatori unda iyos unikaluri anu ar SeiZleba, magaliTad, 

identifikatorad vixmaroT sin, radgan es aris CaSenebuli funqciis saxeli. 

Mathcad–Si agreTve gvaqvs e.w. sistemuri cvladebi, romelTa mniSvnelobebs 

gansazRvravs sistema. mag., Tol cvladis mniSvneloba (es cvladi gansazRvravs 

ricxviTi meTodebis cdomilebas) winaswari SeTanxmebiT udris 0.001 . saWiroebis 

SemTxvevaSi sistemuri cvladis mniSvneloba SeiZleba SevcvaloT da mivaniWoT mas 

sxva mniSvneloba. 

rogorc ukve vTqviT, cvladisaTvis mniSvnelobis misaniWeblad iyeneben 

niSans : = . : = niSniT gansazRvrul miniWebas hqvia lokaluri miniWeba. pirvel 

miniWebamde cvladi ar aris gansazRvruli da sistema, cxadia, ver Seasrulebs 

gamoTvlebs am cvladis monawileobiT. miniWebisaTvis iyeneben aseve niSans. am 

miniWebas hqvia globaluri miniWeba. is SeiZleba Caiweros dokumentis nebismier 

adgilas. magaliTad, Tu Cven CavwereT globaluri miniWeba dokumentis bolos, 

Sesabamisi cvladis mniSvneloba iqneba igive dokumentis dasawyisSic. ra Tqma 

unda, globaluri miniWebis Semdeg dasaSvebia cvladis mniSvnelobis Secvla 

lokaluri miniWebiT. 

Mathcad–i orjer kiTxulobs dokuments, orivejer marcxnidan marjvniv da 

zevidan qveviT. pirveli wakiTxvis dros sruldeba globaluri miniWebis 

operatoriT nakarnaxevi yvela SesaZlo moqmedeba. meore wakiTxvisas Sesruldeba 

lokaluri miniWebis operatorTan dakavSirebuli moqmedebebi. 

Mathcad–s aqvs bevri CaSenebuli funqcia. Ffunqciis saxelis Semdeg 

frCxilebSi Caiwereba argumentebis sia. Mathcad–Si SesaZlebelia momxmareblis 

funqciebis Seqmna. 

maTematikuri gamosaxulebis calkeuli elementebi erTmaneTTan 

operatorebiT dakavSirebulia. operatorebis saxeobebia: ariTmetikuli 

operatorebi ( + , – , / , ! , n , da sxv.), logikuri operatorebi ( < , > , ≤ , ≥ 

, = da sxv.), maTanalizis operatorebi ( , b 

 

a 

17 

n 

, X , 

i 

m 

n 

X , 

i 

m 

X da sxv.), 

gamoTvlebis operatorebi ( = , : = , da sxv. ), daprogramebis operatorebi ( if, 

otherwise, for, while, break, continue, return ), veqtorebis da matricebis operatorebi, 

simboluri gamoTvlebis operatorebi. Mathcad–Si momxmarebels SeuZlia Seqmnas 

axali operatorebic.

diskretuli (ranJirebuli) cvladi es aris cvladi, romelsac gaaCnia 

ramdenime fiqsirebuli mniSvneloba. diskretuli cvladis mniSvnelobebi icvleba 

fiqsirebuli bijiT sawyisi mniSvnelobidan bolo mniSvnelobamde. nax.1.3–ze 

moyvanilia diskretuli cvladebis magaliTebi. ranJirebuli cvladis Sesatanad 

virCevT Matrix panelze m..n Sablons an viyenebT klaviaturis ; niSans. 

masivi aris ricxviTi an simboluri elementebis sasruli simravlis 

mowesrigebuli erToblioba. Mathcad–Si xmaroben erTganzomilebian masivebs 

(veqtorebs) da organzomilebian masivebs (matricebs). veqtorisa an matricis 

elementebis indeqsebi axasiaTeben elementis adgilmdebareobas. qveda indeqsi 

SeiZleba iyos 0–is an 1–is toli. misi mniSvneloba mocemulia sistemuri cvladiT 

ORIGIN da winaswari SeTanxmebiT udris 0–s. Tu gvsurs, SeiZleba SevcvaloT 

ORIGIN cvladis mniSvneloba da gavxadoT is 1–is toli. 

veqtori da diskretuli cvladi arsebiTad ar gansxvavdeba erTimeorisagan. 

nax.1.3. diskretuli (ranJirebuli) cvladebis magaliTebi 

veqtorebis da matricebis Sesatanad Mathcad–Si gaTvaliswinebulia 

ramdenime xerxi: 

Insert → Matrix... brZanebiT; 

swrafmoqmedebis klaviSebiT Ctrl + M; 

18

Matrix panelze matricis Sablonze dawkapunebiT. 

yvela aRniSnul SemTxvevaSi gamoCndeba dialoguri fanjara Insert Matrix 

(matricis Casma), sadac unda mivuTiToT matricis striqonebisa (Rows) da svetebis 

(Columns) raodenoba. veqtorebis SemTxvevaSi erT-erTi am parametrebisgan 1–is 

tolia. Tu svetebis raodenoba udris 1, saqme gvaqvs veqtor–svetTan, xolo Tu 

striqonebis raodenoba udris 1, veqtor–striqonTan. 

Insert Matrix dialogur fanjaraSi striqonebisa da svetebis raodenobis 

miTiTebis Semdeg ekranze gamoCndeba matricis Sabloni markerebiT. pirveli 

elementis Setanis Semdeg davaWiroT an Tab klaviSebs, gadavalT Semdeg 

markerze da a.S. nebismier markerze gadasvla SesaZlebelia agreTve masze 

dawkapunebiT an kursoris gadaadgilebis klaviSebiT. 

matricis elementi warmoadgens indeqsirebul cvlads. indeqsi SeiZleba 

iyos mxolod mTeli ricxvi. 

ganvixiloT magaliTis saxiT zogierTi moqmedeba matricaze. vTqvaT, gvaqvs 

Semdegi A matrica: 

A 

 

 

 

 

1 

5.6 

9.1 

2 

6.88 

10 

19 

3 

7.1 

11 

4 

8 

12.45 

matricis elementi Mathcad–Si Caiwereba Semdegnairad: A1,3 – me_2 striqonisa 

da me_4 svetis gadakveTaze myofi elementi (radgan winaswari SeTanxmebiT 

elementebis indeqsebis Tvla iwyeba 0_dan). misi mniSvnelobis gamosatanad: 

1) A simbolos akrebis Semdeg qveda indeqsis poziciaSi gadasasvlelad 

avirCioT [ simbolo (igives mivaRwevT Matrix panelidan Xn Sablonis 

gamoZaxebiT); 

2) avkriboT 1,3; 

3) gamoviyenoT klaviSi; 

4) avkroboT = . 

ekranze vnaxavT A1,3=-–8. 

Tu ORIGIN cvladis mniSvneloba gvqonda Secvlili 1–iT, ekranze 

vnaxavT A1,3=-–3 . 

matricis nebismieri svetis amosaRebad viqceviT Semdegnairad: 

1) avkriboT A; 

2) davaWiroT Ctrl + 6 klaviSebs an Matrix panelze avirCioT M < > punqti; 

3) gamoCndeba 

A 

, Savi markeris adgilas SevitanoT svetis nomeri; 

4) gamovyoT kursoriT akrebili gamosaxuleba mTlianad da avkriboT = . 

Tu ORIGIN iyo 0–is toli, miviRebT: 

A 1 

 

 

 

 

 

2 

6.88 

10 

 

 

 

 

. 

 

 

 

 

.

sxva SemTxvevaSi (rodesac ORIGIN udris 1–s) : 

A 1 

 

 

 

 

 

20 

1 

5.6 

9.1 

 

 

 

 

imisaTvis rom miviRoT A matricis romelime striqoni, saWiroa A–s Setanis 

Semdeg jer Ctrl + 1 klaviSebis meSveobiT movaxdinoT matricis transponireba, mere 

Ctrl + 6 klaviSebiT miviRoT kuTxis PfrCxilebi da Savi markeris adgilas 

mivuTiToT striqonis nomeri. igives mivaRwevT Matrix panelze M < > da M T punqtebis 

Tanmimdevruli SerCeviT da miRebuli Sablonis SevsebiT (ix. nax.1.4). 

nax.1.4_ze naCvenebia matricebi da operaciebi matricebze. 

nax.1.4. matricebi da operaciebi matricebze 

monacemTa faili Mathcad–Si arsebiTad warmoadgens igive veqtorebs da 

matricebs, romelTa elementebi Cawerilia failebSi maT bunebriv formatSi – 

mimdevrobiTi teqsturi failebis saxiT. es aris failebis tipi, romelic 

miRebulia sxva programebSic, rac gvaZlevs monacemTa gacvlis saSualebas 

Mathcad–sa da sxva programebs Soris. 

.

Tavi II menius punqti File (faili) 

2.1 mTavari menius File punqtis Semadgenloba 

menius punqti File (faili) emsaxureba dokumentis failebTan muSaobas. 

faili – es aris monacemTa mowesrigebuli erToblioba, romelsac gaaCnia 

saxeli da gafarToeba. Mathcad–is dokumentis failebs aqvs gafarToeba .mcd , 

romelic iwereba uSualod failis saxelis Semdeg. 

avirCioT menius punqti File (an davaWiroT klaviSebis kombinacias Alt + F). is 

Sedgeba Semdegi qvepunqtebisagan: 

New... (axali) Ctrl + N – axali dokumentis gaxsna; 

Open... (gaxsna) Ctrl + O – arsebuli failis gaxsna; 

Close (daxurva) – aqtiuri dokumentis daxurva; 

Save (Senaxva) Ctrl + S – dokumentis Senaxva; 

Save As... (Senaxva rogorc) – failis saxelis an adgilmdebareobis Secvla; 

Save as Web Page... – Senaxva Web gverdis saxiT; 

Page Setup… – gverdebis parametrebis dayeneba; 

Print Preview – beWdviswina daTvalierebis reJimi; 

Print… (beWdva) Ctrl + P – beWdvis parametrebis dayeneba; 

Send… (gagzavna) – aqtiuri failis gagzavna eleqtronuli fostis meSveobiT; 

gagzavnisas saWiroa gvqondes romelime damxmare programa, iseTi rogoricaa 

Microsoft Exchange, Microsoft Mail an Eudora; 

Exit – programidan gamosvla. 

2.2 Mathcad–is dokumentis Seqmna, Senaxva, gaxsna da daxurva 

File → New… brZanebis an Standard instrumentTa panelis New Rilakis 

arCevisas gamoCndeba dialoguri fanjara New. 

nax.2.1. dialoguri fanjara New 

21

movniSnoT Blank Worsheet (sufTa samuSao furceli) punqti da davawkapunoT 

Rilak OK–ze. gamoCndeba axali samuSao furceli, romelsac jer saxeli ar 

gaaCnia Untitled: 1. 

menius punqt File–s gaaCnia Senaxvis ori qvepunqti: Save da Save As... . 

dokumentis pirveladi Senaxvis dros SesaZlebelia nebismieri maTganis 

arCeva, ris Sedegad gamova Save As dialoguri fanjara (nax.2.2). 

nax.2.2. dialoguri Ffanjara Save As 

Save in: siisebur velSi mivuTiToT adgili, sadac gvsurs Cveni dokumentis 

ganTavseba da File name: kombinirebul velSi mivaniWoT mas saxeli. 

winaswari SeTanxmebiT (by Default) Mathcad–i Seinaxavs fails .mcd gafarToebiT 

anu Mathcad–is formatSi, magram Tu saWiroa, SeiZleba avirCioT sxva gafarToeba 

Save as type: velSi miTiTebuli siidan. imisaTvis, rom movaxdinoT dokumentis 

Senaxva Web gverdis saxiT anu HTML formatSi, avirCioT File menius Save as Web 

Page... brZaneba. 

dokumentSi Semdgomi cvlilebebis Sesanaxad viyenebT File →Save brZanebas (an 

klaviaturis F6 klaviSs an Standard instrumentTa panelis Save Rilaks ). 

ukve arsebuli failis saxelis an mdebareobis Sesacvlelad (an orivesi 

erTdroulad) viyenebT brZanebas Save As... . gamova failis Senaxvis dialoguri 

fanjara, sadac SevitanT sasurvel cvlilebebs. Cancel RilakiT xdeba Setanili 

cvlilebebis gauqmeba da dialoguri fanjris daxurva, xolo OK RilakiT 

fanjara daixureba da daiwyeba brZanebis Sesruleba. 

22

arsebuli dokumentis gaxsnisaTvis: 

1) avirCioT menius File → Open... brZaneba an davaWiroT Standard instrumentTa 

panelis Open Rilaks , SesaZlebelia agreTve klaviaturis F5 funqcionaluri 

Rilakis an Ctrl + O klaviSebis gamoyeneba.OgamoCndeba dialoguri fanjara Open , 

nax.2.3. dialoguri fanjara Open 

romlis zeda Look in: velSi miTiTebulia im diskos an saqaRaldis saxeli, sadac 

Sesruldeba failis moZebna. CamonaTvalSi vnaxavT qvesaqaRaldeebis da .mcd 

gafarToebis mqone failebis saxelebs. Tu Look in: velSi miTiTebuli disko an 

saqaRalde ar gvawyobs, gavxsnaT siiseburi velis diskoTa da katalogTa xe da 

avirCioT sasurveli. 

2) dialoguri fanjris CamonaTvalSi movniSnioT failis saxeli an avkriboT 

is File name: velSi; 

3) davaWiroT Open Rilaks. gaixsneba dokumentis fanjara. 

dokumentis fanjris gaxsna SesaZlebelia agreTve mis saxelze mausiT 

orjeradi dawkapunebiT. 

dokumentis swrafad gaxsna SesaZlebelia menius File punqtis qvemeniudan, 

sadac Exit punqtis zemoT moTavsebulia bolos gaxsnili dokumentebis 

CamonaTvali, an sastarto menius Start → Documents kaskadSi moTavsebuli 

dokumentebis siidan. 

23

File → Close brZaneba daxuravs aqtiur (mimdinare) fanjaras da sistema daiwyebs 

muSaobas wina dokumentTan. amasTan Tu mimdinare dokumenti iyo muSaobis seansis 

msvlelobisas modificirebuli, gamova dialoguri fanjara kiTxviT gvsurs Tu 

ara modificirebuli dokumentis Senaxva. 

nax.2.4. SekiTxvis dialoguri fanjara 

Tu dokumenti ar iyo modificirebuli, Sesabamisi fanjara daixureba 

SekiTxvis gareSe. 

Tu Cven vmuSaobT erTdroulad ramdenime fanjarasTan da gvsurs yvela 

fanjris daxurva, mosaxerxebelia Close punqtis nacvlad visargebloT Exit 

brZanebiT. am dros yvela aramodificirebuli fanjara daixureba avtomaturad, 

xolo modificirebuli – dokumentebis Senaxvis Sesaxeb kiTxvis Semdeg. 

aRvniSnoT, rom Save As da Open dialogur fanjrebSi gvaqvs instrumentTa 

paneli Semdegi RilakebiT: 

Go To Last Folder Visited – gadasvla im saqaRaldeSi, romelSic bolos 

vimyofebodiT; 

Up One Level – erTi doniT zeviT gadaadgileba; 

Create New Folder – axali saqaRaldis Seqmna; 

View Menu – CamonaTvalSi miTiTebuli failebis warmodgena sxvadasxva 

saxiT. 

2.3 gverdebis parametrebis dayeneba, 

beWdviswina daTvalierebis da beWdvis reJimebi 

gverdebis parametrebis dasayeneblad viyenebT File → Page Setup… brZanebas. 

gamoCndeba dialoguri fanjara (nax.2.5), sadac Size: velSi SeirCeva furclis 

zomebi, Source: (wyaro) velSi qaRaldis miwodebis xerxi, Orientation areSi SeirCeva 

furcelze teqstis ganlagebis wesi: grZivi (Portrait) an ganivi (Landscape), Margins 

(mindvrebi) areSi misaTiTebelia marcxena (Left:), marjvena (Right:), zeda (Top:) da 

qveda (Bottom:) mindvrebis mniSvnelobebi. SesaZlebelia davayenoT alami Print single 

page width – erTi gverdis siganis dokumentis dabeWdva. 

24

nax.2.5. dialoguri fanjara Page Setup 

File → Print Preview brZanebis SerCeviT an Standard instrumentTa panelze 

Rilakis daWeriT SevdivarT dokumentis beWdviswina daTvalierebis reJimSi, 

romlis fanjaraSi (nax.2.6) naCvenebi iqneba dokumentis mimdinare gverdi. am 

nax.2.6. dialoguri fanjara Print Preview 

25

dialoguri fanjris zeda nawilSi ganlagebulia Semdegi Rilakebi: Print… – 

beWdvis reJimSi gadasvla, Next Page – Semdegi gverdis daTvaliereba, Prev Page – wina 

gverdis daTvaliereba, Two Pages – ori gverdis erTdrouli daTvaliereba, Zoom 

In – gamosaxulebis gadideba, Zoom Out – gamosaxulebis dapataraveba, Close – 

dialoguri fanjris daxurva da beWdviswina daTvalierebis reJimidan gamosvla. 

File → Print... brZanebiT an Standard instrumentTa panelze Print 

Rilakze dawkapunebiT gamoiZaxeba Print dialoguri fanjara (nax.2.7), 

nax.2.7. dialoguri fanjara Print 

romelSic SeirCeva printeri da beWdvis parametrebi. Print range (beWdvis diapazoni) 

areSi All gadamrTvelis CarTva gamoiwvevs mTeli dokumentis dabeWdvas, Selection 

gadamrTveli gamoiyeneba winaswar gamoyofili fragmentis dasabeWdad, Current 

Page – aqtiuri furclis dasabeWdad, xolo Pages gadamrTveli gamoiyeneba 

dasabeWdi gverdebis konkretuli diapazonis misaTiTeblad. am SemTxvevaSi from: 

velSi Seitaneba diapazonis pirveli gverdis nomeri, xolo to: velSi – bolo 

gverdis nomeri. Copies areSi Number of copies: velSi misaTiTebelia dasabeWdi 

egzemplarebis raodenoba. erTze meti egzemplaris dabeWdvisas Collate almis 

dayeneba–moxsniT ganisazRvreba maTi miRebis wesi, romelic iqve nimuSze aisaxeba. 

Tu printeri mzadyofnaSia, sakuTriv beWdvis procedura daiwyeba OK 

Rilakze daWeriT. 

Mathcad–is dokuments SeiZleba hqondes ormagi sigane da erT gverdze meti 

sigrZe, maSin jer ibeWdeba marcxena nawilis yvela gverdi, Semdeg ki marjvena 

nawilis. 

26

Tavi III dokumentis redaqtirebis meTodebi 

3.1 redaqtirebis zogadi xerxebis mokle mimoxilva 

gamosaxulebis calkeuli elementebis, misi nawilis an mTlianad 

gamosaxulebis gamosayofad viyenebT Semdeg klaviSebs: 

klaviSi gadaitans kursors zeviT; gamoTvliT blokSi Sesvlisas viziri 

gardaiqmneba lurj kuTxed, romelic moicavs mTel gamosaxulebas; 

klaviSi moqmedebs analogiurad, mxolod kursoris gadatana xdeba 

qveviT; 

klaviSebi da moqmedeben analogiurad, magram maTematikuri aris 

SigniT lurji kuTxis markeris gadatanisas icvleba misi forma; 

Shift + , Shift + , Shift + , Shift + klaviSebis kombinaciebiT 

gamosaxuleba gamoiyofa Setanis markeris adgilidan Sesabamisad zeviT, 

qveviT, marcxniv da marjvniv. amasTan Tu vimyofebiT maTematikur an teqstur 

areSi, moxdeba Sesabamisi fragmentis gamoyofa da gamoyofili nawilis 

gaferadebuli marTkuTxedis saxiT Cveneba. 

ganvmartoT marTvis klaviSebis daniSnuleba redaqtirebis procesSi: 

Tab – gadaaqvs kursori: SablonSi – mimdinare Wdidan (markeridan) 

momdevnoze, Tu yvela Wde Sevsebulia, xdeba kursoris gadatana blokis 

gareT da is aRmoCndeba blokis Semdeg; 

Shift + Tab – gadaaqvs kursori: SablonSi – mimdinare Wdidan wina Wdeze, Tu 

yvela Wde Sevsebulia, xdeba kursoris gadatana blokis gareT, ris Sedegad 

is aRmoCndeba blokis win; 

Page Up – naxevari fanjriT zeviT gadaadgileba; 

Page Down – naxevari fanjriT qveviT gadaadgileba; 

Ctrl + Page Up – erTi fanjriT zeviT gadaadgileba; 

Ctrl + Page Down – erTi fanjriT qveviT gadaadgileba; 

Home – teqstur areSi Setanis markeris teqsturi striqonis dasawyisSi 

dayeneba; 

End – teqstur areSi Setanis markeris teqsturi striqonis boloSi 

dayeneba; 

Ctrl + Home – dokumentis dasawyisSi gadaadgileba anu kursoris dayeneba 

pirveli obieqtris dasawyisSi; 

Ctrl + End – dokumentis boloSi gadaadgileba anu kursoris dayeneba 

dokumentis bolo oboeqtis dasawyisSi. 

teqsturi blokebis redaqtireba ar gansxvavdeba im xerxebisagan, romlebic 

miRebulia teqstur redaqtorebSi (WordPad, Word). 

27

maTematikuri blokebis redaqtireba detalurad ganxilulia 3.2–Si. aq 

aRvniSnoT, rom Insert klaviSis meSveobiT xdeba kursoris gadatana gamoyofili 

fragmentis dasawyisSi an bolos, imisda mixedviT Tu saiTken iyo mimarTuli 

lurji kuTxis markeri. imisaTvis, rom SevcvaloT ricxvi an aso maTematikur 

gamosaxulebaSi, saWiroa davayenoT Setanis markeri Sesabamis adgilas da jer 

wavSaloT Sesacvleli simbolo Backspace klaviSis meSveobiT (Tu lurj Setanis 

markers aqvs forma) an Delete klaviSiT (Tu lurj Setanis markers aqvs forma), 

Semdeg avkriboT axali simbolo. Secvla SesaZlebelia agreTve wasaSleli 

fragmentis gamoyofiT Tagvis Cavleba–gadaTrevis (Drag and Drop) teqnikiT da axali 

simboloebis akrebiT.DA 

qvemoT moyvanilia klaviSebi da maTi kombinaciebi, romelTa meSveobiT 

SesaZloa redaqtirebis procesis gamartiveba: 

Shift + F5 – Replace dialoguri fanjris gamoZaxeba; 

Alt + Backspace – redaqtirebis bolo operaciis gauqmeba; 

Ctrl + Insert – gamoyofili obieqtis kopireba monacemTa gacvlis buferSi 

(monacemTa gacvlis buferi warmoadgens operatiuli mexsierebis 

specialur ares, romelic ixmareba programebs Soris monacemebis 

gacvlisaTvis); 

Shift + Delete – gamoyofili obieqtis buferSi gadatana; 

Insert – Casmis reJimis CarTva; 

Shift + Insert – monacemTa kopireba buferidan dokumentSi. 

ganvixiloT dokumentebis da fanjrebis marTvis klaviSebi: 

Ctrl + Esc – Windows operaciuli sistemis mTavari menius gamoZaxeba (igivea, 

rac Start Rilakze dawkapuneba); 

Ctrl + F 4 – dokumentis daxurva; 

Ctrl + P – Print dialoguri fanjris gamoZaxeba; 

Alt + F4 – sistemidan gamosvla (Quit); 

F1 – daxmarebis (Help) fanjris gaxsna. 

3.2 maTematikuri gamosaxulebebis redaqtirebis magaliTebi 

maTematikur gamosaxulebaze dawkapunebiT SevdivarT redaqtirebis reJimSi, 

romelSic SesaZlebelia saWiro cvlilebebis Setana. 

saxelis an ricxvis redaqtireba 

1) davawkapunoT maTze TagviT. gamoCndeba formis redaqtirebis niSani; 

2) da klaviSebiT gadavaadgiloT redaqtirebis niSani saWiro 

adgilas; 

28

3) klaviaturidan Setanili simbolo gamoCndeba redaqtirebis kursoris 

marcxniv. Backspace klaviSis daWeriT waiSleba kursoris marcxniv mdgomi 

simbolo, xolo Delete klaviSiT marjvniv mdgomi simbolo. 

operatoris Casma 

I. vTqvaT, identifikatorSi ori simbolos an mudmivSi ori cifris Soris 

Casasmelia operatori. mag., gvaqvs ab da gvinda miviRoT a + b. amisTvis: 

1) davawkapunoT TagviT a da b simboloebs Soris; 

2) avkriboT klaviaturidan + an SevirCioT + operatori Calculator panelidan. 

miviRebT sasurvel Sedegs. 

a 

II. gvaqvs ab+1. gvinda miviRoT 1 . amisTvis: 

b 

1) davayenoT redaqtirebis xazi a da b simboloebs Soris. ekranze vnaxavT 

ab+1; 

2) klaviaturidan an Calculator panelidan gamoviyenoT / niSani. ekranze 

a 

miviRebT redaqtirebis Sedegs: 1 . 

b 

III. vTqvaT, x gvsurs gadavaqcioT x _ad. 

1) davawkapunoT gamosaxulebaze da miviyvanoT kursori x_Tan Semdegnairad: x; 

2) davaWiroT \ klaviSs. davinaxavT x . 

Tu 1 punqtSi kursori moicavda x sxva mxridan _ x , \ klaviSis gamoyeneba 

mogvcems Sedegad x . 

a b 

( a b) 

c 

IY. gvaqvs . gvinda miviRoT . amisTvis: 

x d 

x d 

1) davawkapunoT gamosaxulebaze da Semdegnairad davayenoT kursori: 

a b 

x d 

; 

a b 

a b 

x d 

x d 

c 

( a b) 

c 

2) avriboT *c . miviRebT . 

x d 

a b 

Y. gvaqvs . gvsurs miviRoT (an c ). 

 

x d 

a b 

1) davayenoT lurji kuTxe ise, rom is wilads moicavdes srulad: ; 

x d 

a b 

2) avkriboT *c . miviRebT . 

x d 

c 

aRvniSnoT, rom Tu meore punqtSi jer davaWerT Insert klaviSs (ekranze 

a b 

a b 

vnaxavT ), xolo Semdeg davbeWdavT *c , miviRebT c . 

x d 

 

x 

d 

29

operatoris waSla 

I. gvaqvs a b . wavSaloT operatori da miviRoT ab. amisTvis: 

1) davayenoT kursori b_s win: a b; 

2) davaWiroT Backspace klaviSs. miviRebT ab 

. 

a 

II. gvaqvs . gadavaqcioT ab _d. 

b 

a 

1) davayenoT redaqtirebis lurji kursori Semdegnairad: ; 

b 

2) davaWiroT Backspace klaviSs, miviRebT ab . 

III. gvaqvs erTi operandis mqone operatori, mag., x . wavSaloT operatori da 

miviRoT x . amisTvis: 

1) davayenoT kursori x_is win x ; 

2) davaWiroT Backspace klaviSs, miviRebT x. 

operatoris Secvla 

a c 

a c 

I. vTqvaT, gvaqvs , gvsurs miviRoT . amisTvis: 

b d 

b d 

a c 

1) davayenoT redaqtirebis kursori Semdegnairad: ; 

b d 

a c 

2) davaWiroT Backspace klaviSs, miviRebT 

b d 

, anu operatoris adgilas 

gamoCndeba marTkuTxedi, romelSic Casasmelia sxva operatori; 

a c 

3) SevitanoT gamoklebis niSani. miviRebT . 

b d 

2 x x 2 

2 x x 2 

 

2 x x 2 

II. gvaqvs Setanili . gvinda miviRoT . 

1) miviRoT ekranze ; 

2 x 2 

2) davaWiroT Delete klaviSs. Sedegad moiniSneba da mTlianad gaferaddeba |x| ; 

3) davaWiroT Delete klaviSs. miviRebT ; 

4) avkriboT x . miviRebT 2 x x . 

2 

 

Tu kidev erTxel SevirCevT |x| punqts Calculator panelze, miviRebT: 

. 

2 x x 

ra Tqma unda, SesaZlebelia es amocana gadavwyvitoT 1_l punqtSi 

2 

 

miRebiT da me_2 punqtSi Backspace klaviSis daWeriT (me_3 da me_4 punqtebi 

ucvlelia). 

gamosaxulebis dasawyisSi minusis Casma 

gvaqvs sin(a). gvsurs miviRoT _sin(a). 

1) davawkapunoT sin(a)_ze da Tu saWiroa gamoviyenoT Space klaviSi. miviRebT 

sin(a) . davaWiroT Insert klaviSs. miviRebT sin(a); 

2) davbeWdoT gamoklebis niSani. miviRebT sasurvel Sedegs. 

a b 

a b 

c 

a b 

 

a b c 

frCxilebis Casma 

I. vTqvaT, gvaqvs . gvsurs miviRoT . 

a b 

1) davayenoT kursori Semdegnairad: ; 

a b 

c 

30 

2 x x 2

2) davbeWdoT apostrofis niSani ‘ an davawkapunoT Calculator panelis ( ) 

Rilakze . miviRebT a b 

. 

a b c 

II. gvaqvs a_b+c. miviRoT a_(b+c): 

1) davayenoT redaqtirebis kursori b_s win: a_b+c ; 

2) davbeWdoT ( ; 

3) davawkapunoT c_ze da davayenoT redaqtirebis xazi c_s ukan a_(b+c ; 

4) davbeWdoT ) . 

frCxilebis waSla 

vTqvaT, gvaqvs a_(b+c) . frCxilebis wasaSlelad: 

1) davayenoT redaqtirebis kursori b_s win a_( b+c); 

2) davaWiroT Backspace klaviSs. miviRebT a_ b+c. 

anda: 

1) davayenoT redaqtirebis kursori c_s ukan a_( b+c ); 

2) davaWiroT Delete klaviSs. miviRebT a_b+c . 

da bolos aRvniSnoT, rom gamosaxulebaze ormagi wkapuni gamoyofs rogorc 

mTel obieqts, aseve Sesabamis obieqts mis SigniT. 

amrigad, gamosaxulebebis redaqtirebisas redaqtirebis kursoris poziciis 

SerCevas principuli mniSvneloba aqvs. unda gvaxsovdes, rom obieqtze 

dawkapunebis Semdeg: 

Insert klaviSis daWera Secvlis lurji kuTxis formis redaqtirebis niSnis 

mimarTulebas: _dan _ze da piriqiT, ase rom Tu lurji kuTxis 

kursori moicavda simbolos, gamosaxulebis nawils an mTel 

gamosaxulebas, vTqvaT, marjvnidan, Insert klaviSis daWeris Sedegad igive 

simbolo, gamosaxulebis nawili an mTeli gamosaxuleba iqneba moculi 

marcxnidan ; 

da klaviSebiT xdeba erTi simbolodan meoreze gadasvla da 

agreTve redaqtirebis kursoris gadaadgileba; 

Space (hari) klaviSis gamoyenebis Sedegad lurji kuTxiT iqneba moculi 

gamosaxulebis ufro didi nawili. ase rom Space–ze zedized daWeriT 

lurji kuTxiT iqneba moculi mTeli gamosaxuleba. Tu kidev davaWerT 

Space_s, redaqtirebis kursori dabrundeba Tavdapirvel poziciaSi, 

saidanac daviwyeT redaqtirebis procesi. Space klaviSis moqmedeba 

ilustrirebulia nax.3.1_Si; 

Tab da Shift + Tab klaviSebis daniSnuleba redaqtirebisas ukve iyo 

miTiTebuli 3.1_Si; 

cvlilebebis Setana SesaZlebelia agreTve wasaSleli fragmentis 

DA 

gamoyofiT Tagvis Cavleba–gadaTrevis (Drag and Drop) teqnikiT da axali 

simboloebis akrebiT. am meTodiT gamoyofili obiqti Delete klaviSze 

dawkapunebiT waiSleba. 

31

nax.3.1. Space klaviSis moqmedebis principi 

3.3 mTavari menius Edit (redaqtireba) punqtis Semadgenloba 

mTavari menius Edit punqti emsaxureba dokumentis redaqtirebas. 

avirCioT mTavari menius Edit punqti (an davaWiroT klaviSebis kombinacias 

Alt + E). is Sedgeba Semdegi qvepunqtebisagan: 

Undo (gauqmeba) Ctrl+Z _ bolo Sesrulebuli operaciis gauqmeba; 

Redo (aRdgena) Ctrl+Y _ gauqmebuli operaciis gameoreba; 

Cut (amoWra) Ctrl+X _ gamoyofili fragmentis amoWra da buferSi 

moTavseba; 

Copy (kopireba) Ctrl+C _ gamoyofili fragmentis aslis buferSi 

moTavseba; 

Paste (Casma) Ctrl+V _ buferis SigTavsis dokumentSi Casma; 

Paste Special… _ specialuri Casma; 

Delete (waSla) Ctrl+D _ gamoyofili fragmentis waSla; 

Select All (yvelafris gamoyofa) Ctrl+A _ yvela obieqtis moniSvna; 

Find… (Zebna) Ctrl+F _ teqstis da gamosaxulebis fragmentis Zebna; 

Replace… (Secvla) Ctrl+H _ teqstis da gamosaxulebis fragmentis 

Secvla; 

Go to Page... (gverdze gadasvla) _ sxva gverdze gadasvla; 

Links... (kavSirebi) _ dokumentSi Casmul obieqtTan kavSirebis 

redaqtireba; * 

Object (obieqti) _ dokumentSi Casmuli obieqtis redaqtireba. 

* Links... da Object punqtebi iqneba ganxiluli 5.21 da 5.19_Si. 

32

3.4 redaqtirebis operaciis gauqmeba_aRdgena 

Edit → Undo brZaneba auqmebs bolo Sesrulebuli operaciis Sedegs. igives 

mivaRwevT Standard instrumentTa panelze Undo Rilakze daWeriT. 

bolo operaciis gauqmebis Semdeg SesaZlebelia ekranis wina saxis aRdgena, 

rasac emsaxureba Edit → Redo brZaneba an Redo Rilaki Standard instrumentTa 

panelze. Redo operacia gvaZlevs saSualebas xelmeored SevasruloT bolo 

gauqmebuli brZaneba. 

3.5 dokumentis fragmentebTan muSaoba 

redaqtirebis procesSi xSirad gvesaWiroeba ukve Setanili obieqtis, 

obieqtTa jgufis an obieqtis nawilis erTi adgilidan meore adgilze gadatana, 

kopireba, waSla an formatis Secvla. amisTvis saWiroa winaswar miTiTebuli iyos 

Tu raze unda Catardes moqmedeba anu saWiroa movaxdinoT egreT wodebuli 

fragmentis gamoyofa (moniSvna). 

ganvixiloT fragmentis gamoyofis wesebi: 

calkeuli obieqtis gamoyofa xdeba Tagvis marcxena RilakiT masze 

dawkapunebiT. obieqti moiqceva marTkuTxedSi, xolo kursori 

aRmoCndeba SigniT da miiRebs saTanado formas (teqstur areSi wiTeli 

vertikaluri xazi , maTematikur areSi – lurji kuTxe an ). 

calkeuli obieqtis gamoyofa SesaZlebelia aseve obieqtze orjer 

dawkabunebiT. is moiqceva marTkuTkuTxedSi, amasTan iqneba gamoyofili da 

gaferadebuli obieqtis Sesabamisi nawili. Tu obieqti grafikia, erTi 

wkapuni gamoyofs mas, xolo ori _ gamoiZaxebs daformatebis dialogur 

fanjaras; 

obieqtis an obieqtTa jgufis gamoyofa SesaZlebelia agreTve Tagvis 

gadaTrevis (Drag and Drop) teqnikis gamoyenebiT. amisTvis unda 

mivitanoT Tagvis maCvenebeli obieqtTan (magram ara mis 

SigniT), davaWiroT Tagvis marcxena Rilaks da gadavaTrioT 

Tagvi diagonalze. ekranze vnaxavT punqtiriT daxazul 

marTkuTxeds. rogorc ki am marTkuTxedSi moxdeba obieqti an 

obieqtis nawili, is moiniSneba _ gamoiyofa punqtiruli xazebiT. roca 

Tagvis Rilaks avuSvebT xels, ZiriTadi marTkuTxedi gaqreba ekranidan, 

magram yvela moniSnuli obieqti darCeba; 

taqstur areebSi da maTematikur gamosaxulebebSi SesaZlebelia nebismieri 

fragmentis moniSvna Drag and Drop teqnikiT; 

calkeuli obieqtebis gamosayofad davawkapunoT jer erT_erT obieqtze, 

Semdeg Ctrl klaviSTan erTad davawkapunoT danarCen obieqtebze. Tu 

33

daWerili iqneba Shift , sawyis obieqtTan erTad gamoiyofa yvela obieqti, 

romlebic mdebareoben sawyis da bolo dawkapunebul obieqtTa Soris. 

aRvniSnoT, rom Tu moniSvnisas obieqti gamoyofilia markerebiani 

marTkuTxediT, markerTan Tagvis maCveneblis mitanisas ukanaskneli miiRebs 

ormxrivi isris formas. TagviT isris gadaweva gamoiwvis obieqtis zomebis 

Secvlas. 

Edit → Cut brZanebiT an Standard instrumentTa panelze Cut Rilakze 

daWeriT xdeba gamoyofili fragmentis amoWra da gadatana buferSi. 

Edit → Copy brZanebiT an Standard instrumentTa panelze Copy Rilakze 

daWeriT xdeba gamoyofili fragmentis aslis moTavseba buferSi, amasTan TviTon 

fragmenti rCeba dokumentSi Tavis adgilze. 

Edit → Paste brZanebiT an Standard instrumentTa panelze Paste Rilakze 

daWeriT xdeba buferSi mdebare obieqtis dokumentSi Casma kursoris adgilas. 

am dros buferis SigTavsi SenarCundeba da SesaZlebelia Casmis operaciis 

gameoreba. 

gamoyofili obieqtis gadatana da kopireba SesaZlebelia gacvlis buferis 

gamouyenebladac _ Drag and Drop meTodiT anu im dros, rodesac Tagvis maCvenebels 

xelisgulis forma aqvs, xdeba obieqtis TagviT Cavleba da gadaTreva erTi 

adgilidan meoreze (kopirebisas – Ctrl klaviSze erTdrouli daWeriT). 

Cut, Copy da Paste brZanebebiT fragmentis gadatana da kopireba 

SesaZlebelia ara mxolod erTi dokumentis farglebSi, aramed erTi dokumentidan 

meoreSic. fragmentis gadanacvleba erTi fanjridan meoreSi xorcieldeba agreTve 

Tagvis meSveobiT uSualod erTi fanjridan meore fanjris sasurvel adgilas 

fragmentis gadaTreviT (kopirebisas erTdroulad vaWerT Ctrl klaviSs). 

Edit → Paste Special... brZaneba gvaZlevs dokumentSi sxvadasxva formatis 

nax.3.2. dialoguri fanjara Paste Special 

34

(teqsturi, Mathcad, RTF, Bitmap) failebis Casmis saSualebas. gamoCndeba dialoguri 

fanjara (nax.3.2), sadac amoirCeva saWiro formati. 

Edit → Delete brZanebiT xdeba gamoyofili fragmentis waSla anu iseTi 

moSoreba, romlis dros ar xdeba misi gadatana buferSi. 

Edit → Select All brZanebiT xdeba yvela obieqtis gamoyofa punqtiruli 

marTkuTxedebiT. am dros Cven naTlad vxedavT Tu rogor arian 

urTierTganlagebuli blokebi da saWiroebisamebr vaxdenT maT gadanacvlebas. 

ra Tqma unda, brZanebebi SeiZleba SeirCes konteqsturi meniudanac. 

3.6 teqstis an gamosaxulebis fragmentis Zebna da Secvla 

Edit → Find... brZanebiT xdeba Zebnis dialoguri fanjris gamoZaxeba (nax3.3). 

am fanjris Find what: teqstur velSi unda SevitanoT teqstis an 

gamosaxulebis saZebni fragmenti. Zebnis gasagrZeleblad davaWiroT Find Next 

Rilaks, xolo operaciis gasauqmeblad – Cancel Rilaks. 

areebSi. 

nax.3.3. Zebnis dialoguri fanjara 

winaswari SeTanxmebiT Mathcad_i axorcielebs Zebnas mxolod teqstur 

Tu saWiroa, SegviZlia CavrToT almebi: Match whole word only (am dros saZebni 

fragmenti calkeul sityvas warmoadgens), Match case (zeda da qveda registrebis 

gaTvaliswineba anu am almis dayenebiT Mathcad–i gansxvavebulad aRiqvams mcire 

da mTavrul asoebs Zebnis procesSi), Find in Text Regions (teqstur areebSi Zebna), 

Find in Math Regions (maTematikur areebSi Zebna). 

(Down). 

Zebnis mimarTuleba (Direction) SeiZleba iyos kursoris zeviT (Up) an qvevviT 

Edit → Replace… brZanebiT xdeba Secvlis dialoguri fanjris gamoZaxeba 

(nax.3.4), romelsac Find what: teqsturi velis garda gaaCnia teqsturi veli 

Replace with: , sadac Caiwereba Semcvleli fragmenti. 

35

nax.3.4. Secvlis dialoguri fanjara 

Secvlis dialoguri fanjris Replace All Rilaks viyenebT, Tu gvsurs Find 

what: velSi miTiTebul yvela saZebni monacemis Secvla Replace with: velSi 

Cawerili monacemiT; Replace da Find Next Rilakebs viyenebT, Tu Secvla gvsurs 

amorCeviT. Secvlis dialogur fanjaraSi gvxvdeba igive gadamrTvelebi, rac Find 

dialogSi. 

3.7 dokumentis sasurvel gverdze gadasvla 

Edit → Go to Page… brZanebiT gamoiZaxeba Go to Page dialoguri fanjara 

(nax.3.5), sadac unda mivuTiToT, romel gverdze gvsurs gadasvla: pirvelze (First 

Page), boloze (Last Page) Tu gverdze, romlis nomers mivuTiTebT Page Number: 

gadamrTvelis cifrul velSi. am dialoguri fanjris qveda nawilSi Cans ori 

Setyobineba: Number of Pages: (gverdebis raodenoba) da Current Page: (mimdinare 

gverdis nomeri). 

nax.3.5. dialoguri fanjara Go to Page 

36

Tavi IV menius punqti View (xedi) 

4.1 mTavari menius View punqtis Semadgenloba 

avirCioT mTavari menius View punqti (an davaWiroT klaviSebis kombinacias 

Alt + V). davinaxavT qvemenius Semdeg punqtebs: 

Toolbars (instrumentTa panelebi) _ instrumentTa panelebis moxsna_dayeneba; 

Ruler (saxazavi) _ saxazavis Cveneba_damalva ekranze; 

Status Bar (mdgomareobis striqoni) _ mdgomareobis striqonis 

Cveneba_damalva ekranze; 

Header and Footer… (zeda da qveda kolontitulebi) _ kolontitulebis 

Seqmna da gaformeba; 

Regions (areebi) _ areebis TeTri foniT gamoyofa; 

Refresh (ganaxleba) Ctrl + R _ samuSao furclis ganaxleba; 

Zoom... (masStabi) _ masStabis Secvla. 

4.2 instrumentTa panelebi 

View → Toolbars brZanebiT, rogorc ukve viciT, xdeba ama Tu im panelis 

moxsna_dayeneba. 

Toolbars CamonaTvalSi Sedis: 

Standard _ standartuli paneli; 

Formatting _ daformatebis paneli; 

Math _ maTematikuri paneli; 

Controls _ marTvis paneli; 

Resources _ resursebis paneli; 

Calculator _ gamoTvlebis Catarebis operatorebis paneli; 

Graph _ grafikebis agebis paneli; 

Matrix _ matricebTan muSaobisaTvis gankuTvnili operatorebis paneli; 

Evaluation _ miniWebis, tolobis, simboluri gardaqmnebis operatorebis 

paneli. aq agreTve ganlagebulia momxmareblis mier operatoris 

ganmsazRvreli punqtebi; 

Calculus _ maTanalizis operatorebis paneli; 

Boolean _ bulis algebris operatorebis paneli; 

Programming _ daprogramebis paneli; 

Greek _ berZnuli anbanis paneli; 

Modifier _ modifikaciis paneli. 

37

4.3 saxazavi, mdgomareobis striqoni da areebi 

View menius Ruler da Status Bar punqtebiT xdeba saxazavisa da mdgomareobis 

striqonis Cveneba_damalva ekranze. es punqtebic, iseve rogorc panelebis saxelebi 

Toolbars CamonaTvalSi, arsebiTad alams warmoadgenen. 

Mathcad_is dokumenti Sedgeba calkeuli blokebisagan, romelTa Soris 

sazRvrebi Cveulebrivad ar Cans ekranze. View → Regions brZaneba yvela ares 

TeTrad gamoyofs, xolo maT Soris Sualedebs – ruxad, rac mogvcems saSualebas 

naTlad davinaxoT maTi urTierTganlageba. Tu saWiroa, Format → Separate Regions 

brZanebiT xdeba areebis urTierTgadafarvis mocileba. 

4.4 masStabis Secvla da ganaxleba 

View menius Zoom... punqti gamoitans ekranze Zoom dialogur fanjaras 

(nax.4.1). am fanjaraSi gadamrTvelis ama Tu im poziciaSi dayenebiT (200%, 100%, 

75%, 50%, 25%) xdeba Sesabamisi masStabis dafiqsireba da OK Rilakze 

daWeris Semdeg am masStabiT gamosaxulebis danaxva. Custom punqtis arCevisas 

misawvdomi xdeba mis marjvniv mdebare veli, sadac SegviZlia mivuTiToT 

sasurveli masStabi. 

nax.4.1. masStabis Secvlis fanjara 

View → Refresh brZanebiT xdeba mimdinare samuSao furclis ganaxleba. saqme 

imaSia, rom obieqtebTan muSaobis dros, mag., maTi zomebis Secvlisas, gamoyofisas, 

gadaadgilebisas da a.S., ekranze xandaxan Cndeba arasasurveli obieqtebi (mag., 

jvaredini wiTeli kursori SeiZleba Candes ramdenime adgilas an teqsturi aris 

nawili ar Candes, radgan is nawilobriv maTematikuri ariT aris gadafaruli). 

Refresh brZaneba moiSorebs am zedmet obieqtebs, amasTan dokumentis obieqtebi 

xeluxlebeli darCeba. 

38

4.5 gverdis kolontitulebis Seqmna da gaformeba 

zeda (Header) da qveda (Footer) kolontitulebi (TavsarTi da qvesarTi) es 

aris teqsti, romelic avtomaturad gameordeba yvela gverdze Sesabamisad zeda da 

qveda mindvris areSi. es SeiZleba iyos dokumentis saTauri, organizaciis 

dasaxeleba, avtoris gvari da sxv. aq SeiZleba agreTve moTavsdes gverdis nomeri, 

TariRi, dro da a.S. 

View → Header and Footer brZanebiT ekranze gamoitaneba kolontitulebis 

dialoguri fanjara (nax.4.2) ori CanarTiT: Header da Footer, romlebSic xdeba 

Sesabamisad TavsarTis da bolosarTis Seqmna da gaformeba. 

nax.4.2. kolontitulebis dialoguri fanjara 

avirCioT romelime, vTqvaT, Header CanarTi. fanjris zeda nawilSi davinaxavT 

sam seqcias: Left (marcxena), Center (centraluri), Right (marjvena). blokebSi 

klaviaturidan SeiZleba SevitanoT sasurveli teqsti. teqstis garda, blokebSi 

survilisamebr Seitaneba sxva informaciac Tools (instrumentebi) ganyofilebis 

Rilakebis meSveobiT: 

– Insert File Name (failis saxelis Casma); 

_ Insert File Path (failis sruli misamarTis Casma); 

_ Insert Page Number (mimdinare gverdis nomris Casma); 

_ Insert Number of Pages (gverdebis raodenobis Casma); 

_ Insert Date Last Saved (failis bolo Senaxvis TariRis Casma); 

_ Insert Time Last Saved (failis bolo Senaxvis drois Casma); 

39

_ Insert Date (mimdinare TariRis Casma); 

_ Insert Time (mimdinare drois Casma). 

Tools ganyofilebaSi aris agreTve Rilakebi Format… , romelic gaxsnis 

daformatebis dialogur fanjaras, da Image... (gamosaxulebis Casma), romelic 

gaxsnis naxatebis Casmis dialogur fanjaras. 

Format dialogur fanjaraSi (nax.4.3) SesaZlebelia Sriftis, misi stilis da 

zomis dayeneba. am fanjris Alignment ganyofilebaSi SeiZleba mivuTiToT sworebis 

tipi, xolo Effects ganyofilebaSi efeqtebi: Strikeout (gadaxazva), Underline (xazgasma) 

da Color: (feri). 

nax.4.3. dialoguri fanjara Format 

kolontitulebis dialogis Options (parametrebi) ganyofilebaSi SeiZleba 

mivuTiToT Tu romeli cifriT gvsurs numeraciis dawyeba da davayenoT alami 

Different header and footer on first page – pirveli gverdisaTvis gansxvavebuli TavsarTis 

da qvesarTis Seqmna. Frame (CarCo) ganyofilebaSi SegviZlia davayenoT almebi 

mTeli gverdis (Page), zeda (Header) da qveda (Footer) kolontitulebis CarCoSi 

mosaTavseblad. 

Use full width for each section almis dayenebiT kolontituli daikavebs Sesabamisi 

seqciis (marcxena, centraluri da marjvena) mTel siganes da mxolod Semdeg 

gadaitaneba Tavisi seqciis Semdeg striqonze. 

OK Rilakze daWeris Semdeg kolontituli Caismeba dokumentSi, magram 

Cveulebriv reJimSi Cven mas ver davinaxavT. misi danaxva SesaZlebelia Print Preview 

reJimSi da rasakvirvelia, is daibeWdeba beWdvisas. 

40

Tavi V menius punqti Insert (Casma) 

5.1 mTavari menius Insert punqtis Semadgenloba 

avirCioT mTavari menius Insert punqti (an davaWiroT klaviSebis kombinacias 

Alt + I). davinaxavT qvemenius Semdegi punqtebiT: 

Graph (grafiki) _ sxvadasxva tipis grafikebis Casma; 

Matrix... (matrica) Ctrl + M _ matricis Casma; 

Function... (funqcia) Ctrl + E – funqciis Casma; 

Unit... (sazomi erTeuli) Ctrl + U – sazomi erTeulis Casma; 

Picture (naxati) Ctrl + T – naxatis Casma; 

Area (ubani) _ ubnis formireba; 

Page Break – gverdis gawyveta; 

Math Region (maTematikuri are) _ maTematikuri aris Casma; 

Text Region (teqsturi are) “ _ teqsturi aris Casma; 

Component... (komponenti) _ komponentis Casma; 

Data (monacemebi) _ monacemebis Casma; 

Control (marTva) _ mmarTveli komponentebis Casma; 

Object... (obieqti) _ obieqtis Casma; 

Reference... (miTiTeba) _ sxva dokumentze miTiTebis Casma; 

Hyperlink... (hipermimarTva) Ctrl + K _ hipermimarTvis damyareba. 

5.2 grafikis Casma 

Insert → Graph brZaneba Seicavs Semdeg qvepunqtebs: 

X_Y Plot (X_Y grafiki) Shift + @ – dekartis koordinatTa sistemaSi 

grafikis ageba; 

Polar Plot (polaruli grafiki) Ctrl + 7 – polaruli grafikis ageba; 

Surface Plot (zedapiris grafiki) Ctrl + 2 – zedapiris grafikis ageba; 

Contour Plot (konturuli grafiki) Ctrl + 5 – konturuli grafikis ageba; 

3D Scatter Plot (samganzomilebiani wertilovani grafiki) – samganzomilebiani 

wertilovani grafikis ageba; 

3D Bar Plot (samganzomilebiani svetovani grafiki) – samganzomilebiani 

svetovani grafikis ageba; 

Vector Field Plot (veqtoruli velis grafiki) – veqtoruli velis grafikis 

ageba; 

41

Plot Wizard... (grafikis ostati) – grafikis agebis ostatis dialoguri 

fanjris gamoZaxeba. 

grafikebis asagebad iyeneben agreTve Graph instrumentTa panels (nax.5.1) 

Semdegi RilakebiT: X_Y Plot, Zoom(masStabi), Trace(trasa), Polar Plot, Surface Plot, Contour 

Plot, 3D Bar Plot, 3D Scatter Plot, Vector Field Plot. 

nax.5.1. Graph instrumentTa paneli 

5.3 organzomilebiani X_Y grafikis ageba da redaqtireba 

Insert → Graph → X_Y Plot brZanebiT (an Graph instrumentTa panelze 

Sesabamisi Rilakis daWeriT) viziris adgilas Seiqmneba organzomilebiani X_Y 

grafikis Sabloni dekartis koordinatTa sistemaSi (nax.5.2). 

grafikis asagebad: 

nax.5.2. X_Y grafikis Sabloni 

1) davawkapunoT markerze, romelic mdebareobs ordinatTa RerZis marcxniv da 

SevitanoT funqcia, cvladi an gamosaxuleba; 

2) davawkapunoT markerze, romelic mdebareobs abscisTa RerZis qveS da 

SevitanoT funqcia, cvladi an gamosaxuleba. 

markeridan markerze gadasasvlelad SeiZleba visargebloT agreTve 

klaviaturis kursoris gadaadgilebis klaviSebiT. 

3) gadavitanoT kursori grafikuli obieqtis gareT da davawkapunoT an 

davaWiroT Enter klaviSs, grafiki aigeba gamoTvlebis avtomatur reJimSi. Tu 

gamoTvlebis avtomaturi reJimi gamorTulia, grafikis asagebad saWiroa F9 

funqcionaluri klaviSis gamoyeneba. 

42

grafikis agebisas Mathcad_i TviTon irCevs X da Y RerZebis zRvrul 

mniSvnelobebs. saWiroebisamebr momxmarebels SeuZlia sxva mniSvnelobebis 

miTiTeba. 

erT grafikul areSi SesaZlebelia miviRoT ramdenime wiri. am SemTxvevaSi X 

da Y RerZebis markerebis adgilas Setanili funqciebi, cvladebi an 

gamosaxulebebi gamovyoT erTimeorisagan mZimiT. 

Tagvis marcxena RilakiT dawkapuneba grafikze gamoyofs mas. davinaxavT 

marTkuTxeds, romelic moicavs mTel grafiks. mivitanoT Tagvis kursori 

CarCosTan da rodesac is miiRebs xelisgulis formas, gadavaadgiloT grafiki 

sasurvel adgilas. 

grafikis zomis Sesacvlelad gamovyoT grafiki da mivitanoT Tagvis 

maCvenebeli CarCoze mdebare marTkuTxedis formis patara Sav markerebTan. roca 

Tagvis maCvenebeli miiRebs ormimarTuliani isris formas, Tagvis gadaTreviT 

SesaZlebelia grafikis dapataraveba_gadideba. zomis Secvla xdeba vertikaluri, 

horizontaluri da diagonaluri mimarTulebiT. 

grafikis parametrebis Sesacvlelad SevasruloT mis areSi ormagi wkapuni 

Tagvis marcxena RilakiT. gamoCndeba organzomilebiani grafikis parametrebis 

Secvlis dialoguri fanjara (nax.5.3). igives mivaRwevT konteqsturi meniudan 

Format... punqtis arCeviT an Format → Graph → X_Y Plot... brZanebiT. 

nax.5.3. X_Y grafikis daformatebis dialoguri fanjara 

X_Y grafikis daformatebis dialogur fanjaraSi X_Y Axes (X_Y RerZebi) 

CanarTis X_Axis da Y_Axis ganyofilebebSi gvaqvs almebi: 

Log Scale – logariTmuli skalis dayeneba; 

43

Grid Lines (badis xazebi) – RerZidan gamomavali xazebis dayeneba grafikis 

badiT dafarvisaTvis; 

Numbered – RerZis numeracia; 

Autoscale – RerZis masStabis avtomaturi dayeneba; 

Show Markers – markerebis Cvenebis reJimis dayeneba; 

Auto Grid _ RerZidan gamomavali xazebis avtomaturi dayeneba; 

Number of Grids: – RerZidan gamomavali xazebis raodenobis miTiTeba. 

es almebi SeiZleba davayenoT cal_calke X da Y RerZebisaTvis. 

Axis Style ganyofilebaSi Boxed gadamrTveli gamoiyvans grafiks CarCoSi da 

RerZebis gareSe, Crossed _ uCarCod, magram RerZebiT, xolo None – uCarCod da 

RerZebis gareSe. alami Equal Scales daayenebs erTnair masStabs orive RerZisaTvis. 

Grid Color… Rilakis meSveobiT dayendeba badis xazebis sasurveli feri. 

amave dialoguri fanjris Traces CanarTSi miTiTebulia wirebis parametrebi 

(mag., xazis feri, stili da a.S.), romlebic SegviZlia survilisamebr SevcvaloT. 

dialoguri fanjris Labels (warwerebi) CanarTSi Title ganyofilebis teqstur 

velSi SeiZleba SevitanoT grafikis saTauri. aqve gadamrTveli Above an Below 

aCvenebs, grafikis zeviT Tu qveviT gvsurs saTauris ganlageba. Show Title alami 

daayenebs saTauris Cvenebis reJims. amave CanarTis Axis Labels ganyofilebaSi 

davayenoT, Tu gvsurs, almebi X_Axis da Y_Axis RerZebze warwerebis Sesaqmnelad da 

SevitanoT es warwerebi Sesabamis teqtur velebSi. 

Formatting Currently Selected X_Y Plot dialoguri fanjris Defaults CanarTSi 

SeiZleba davayenoT alami Use for Defaults, ris Sedegad grafikis mimdinare 

parametrebi iqneba damaxsovrebuli rogorc winaswari SeTanxmebis (by Default) 

parametrebi, xolo alami Change to Defaults winaswari SeTanxmebis parametrebs 

Secvlis mimdinare parametrebiT am dokumentisaTvis. 

grafiki: 

nax.5.4_ze naCvenebia dekartis koordinatTa sistemaSi agebuli sxvadasxva 

1. grafikis SablonSi X RerZis markerSi Setanilia x, Y RerZis – 2x 2 +5x_6. 

redaqtirebisas Setanilia saTauri, dayenebulia alami Show Title da 

miTiTebulia saTauris adgilmdebareoba Above (zeviT). 

2. grafikis agebamde gansazRvrulia diskretuli cvladi z, romelic 

miuTiTebs z–is zRvrul mniSvnelobebs da Secvlis bijs, da y(z) funqcia. 

grafikis SablonSi abscisTa RerZis markeris adgilas Setanilia z , xolo 

ordinatTa RerZis _ y(z). redaqtirebisas dayenebulia gadamrTveli Crossed. 

3. grafikis SablonSi abscisTa RerZis markerSi Setanilia r , ordinatTa sin(r). 

Setanilia agreTve ordinatis zRvruli mniSvnelobebi: _0.5 da 1. 

4. grafikis SablonSi abscisTa RerZis markerSi Setanilia sin(a), xolo 

ordinatTa – cos(a). miRebulia e.w. parametruli grafiki anu grafiki, 

romelic aCvenebs erTi funqciis (gamosaxulebis) damokidebulebas meore 

funqciaze (gamosaxulebaze). 

44

nax.5.4. dekartis sakoordinato sistemaSi agebuli grafikebi 

5. grafikis SablonSi abscisTa RerZis markerSi Setanilia , xolo 

ordinatTa – sin( ) , sin( ) + 1. dayenebulia gadamrTveli Crossed. Sedegad erT 

koordinatTa sistemaSi miRebulia ori wiri, romelTa ordinatebi erT 

cvladze arian damokidebuli. 

6. grafikis SablonSi abscisTa RerZis markerSi Setanilia c, d, xolo 

ordinatTa RerZis markerSi sin(c) 2 , d + 3. dayenebulia gadamrTveli Crossed. 

Sedegad erT koordinatTa sistemaSi miRebulia ori wiri, romelTa 

ordinatebis mniSvnelobebi sxvadasxva cvladebze arian damokidebuli. 

7. Seqmnilia matrica N da veqtorebi X da Y , romlebic warmoadgenen 

Sesabamisad matricis pirvel da meore svets. grafikis SablonSi abscisTa 

RerZis markeris adgilas miTiTebulia X , xolo ordinatTa _ Y. miRebulia 

erTi veqtoris meoreze damokidebuleba. 

yvela grafiks aqvs warwera: graph.1 , graph.2 da a.S. warwerebi Seqmnilia 

calke da Drag and Drop tenikiT ganlagebulia sasurvel adgilze. 

45

5.4 polaruli grafikis ageba da redaqtireba 

Insert → Graph → Polar Plot brZanebiT (an Graph instrumentTa panelze 

Sesabamisi Rilakis daWeriT) viziris adgilas Seiqmneba polaruli grafikis 

Sabloni koordinatTa polarul sistemaSi (nax.5.5). 

nax.5.5. polaruli grafikis Sabloni 

koordinatTa polarul sistemaSi wertili moicema Tavisi kuTxis da R 

radius_veqtoris mniSvnelobebiT. grafiki aigeba kuTxis sxvadasxva 

mniSvnelobebisaTvis, yvelaze xSirad icvleba 0–dan 2 –mde. saWiroebisamebr 

momxmarebels winaswar SeuZlia sxva mniSvnelobebis miTiTeba (vTqvaT, kuTxes 

diskretuli cvladis saxiT gamosaxviT: ). SesaZlebelia agreTve 

uSualod grafikis Sablonze radius_veqtoris minimaluri da maqsimaruri 

mniSvnelobebis miTiTeba. 

polaruli grafikis daformatebisaTvis gamoiZaxeba dialoguri fanjara 

Formatting Currently Selected Polar Plot, sadac Polar Axes CanarTis Radial (radialuri 

RerZi) da Angular (kuTxis RerZi) ganyofilebebSi gvaqvs almebi: radialuri 

RerZisaTvis _ Log Scale, Grid Lines, Numbered, Show Markers, Auto Grid, Number of Grids: 

da kuTxisaTvis _ Grid Lines, Numbered, Auto Grid, Number of Grids:. almebis 

daniSnuleba ar gansxvavdeba X_Y grafikis daformatebis fanjris analogiuri 

almebis daniSnulebisagan. 

Axes Style ganyofilebaSi gadamrTveli Perimeter gamoiyvans wrewiriT 

SemosazRvrul grafiks, Crossed _ wrewiris gareSe da RerZebiT, None _ wrewiris da 

RerZebis gareSe. 

Grid Color... RilakiT dayendeba badis xazebis sasurveli feri. 

am dialoguri fanjris Traces, Labels da Defaults CanarTebs gaaCniaT igive 

datvirTva, rac X_Y grafikis daformatebisas. 

grafiki: 

nax.5.6_ze naCvenebia polarul koordinatTa sistemaSi Seqmnili ramdenime 

46

nax.5.6. polarul koordinatTa sistemaSi agebuli grafikebi 

1. polaruli grafikis SablonSi qveda markeris adgilas Setanilia , xolo 

marcxena markeris – sin ( ) + 1. dayenebulia bade kuTxis RerZisaTvis da 

miTiTebulia misi feri (Savi). 

2. polaruli grafikis SablonSi qveda markeris adgilas Setanilia , xolo 

marcxena markeris – 2sin( ), cos( ) 2 . redaqtirebisas dayenebulia bade kuTxis 

RerZisaTvis da miTiTebulia misi feri (Savi). Traces CanarTSi meore wiris 

feri Secvlilia lurjidan Savze, xolo misi moxazulobis stili 

Secvlilia dash_ze ( ). miRebulia erT polarul koordinatTa sistemaSi 

ori wiri. 

3. polaruli grafikis SablonSi qveda markeris adgilas Setanilia x, xolo 

marcxena markeris – sin(x), cos(x). redaqtirebisas dayenebulia Savi feris bade 

kuTxis RerZisaTvis da Traces CanarTSi _ dash moxazuloba kosinusoidasTvis. 

Sedegad erT polarul koordinatTa sistemaSi miRebulia ori wiri. isrebi 

Seqmnilia Word_Si da Casmulia Mathcad_is dokumentSi. 

4. polaruli grafikis SablonSi qveda markeris adgilas Setanilia y, xolo 

marcxena markeris – cos(2y), sin(2y). daformatebisas orive miRebuli 

wirisaTvis Traces CanarTSi miTiTebulia 4_is toli wona (Weight) da xazis 

tipi Solid. 

47

5.5 3_ganzomilebiani zedapiris grafikis ageba da redaqtireba 

3_ganzomilebiani zedapiris grafikis Sesaqmnelad saWiroa: 

1) ganvsazRvroT orcvladiani funqcia funqciis an matricis saxiT; 

2) Tu saWiroa, mivuTiToT cvladebis zRvruli mniSvnelobebi; 

3) mivceT brZaneba Insert → Graph → Surface an Graph panelze davaWiroT 

Sesabamis Rilakze. Seiqmneba zedapiris grafikis Sabloni (nax.5.7); 

nax.5.7. zedapiris grafikis Sabloni 

4) Sablonis qveda marcxena kuTxeSi ganlagebul markerSi SevitanoT 

funqciis an matricis saxeli; 

5) davaWiroT Enter klaviSs an davawkapunoT TagviT grafikis gareT. 

Tu 3_ganzomilebiani grafikis Sesaqmnelad viyenebT funqcias da ara 

matricas, aseT grafiks ewodeba swrafad miRebadi grafiki (Quick Plot). misi Seqmnisas 

Mathcad_i iyenebs winaswari SeTanxmebiT gansazRvrul damoukidebeli cvladebis 

mniSvnelobebs (isini icvlebian _5_dan 5_mde) da am mniSvnelobebis Secvlis bijs 

(0,5). Tu saWiroa, 3_ganzomilebiani grafikis daformatebis Sesabamis CanarTSi 

(Quick Plot Data) SeiZleba am parametrebis Secvla. 

funqcia SeiZleba iyos mocemuli sxvadasxvanairad, mag.: 

F( x, 

y) 

: sin( x) 

cos( y) 

an 

A( 

p, 

q) 

: 3p 

cos( q) 

. 

48 

p 3 

3p 

sin( q) 

pirveli funqciis grafikis Seqmnisas x da y cvladebis zRvruli 

mniSvnelobebi iqneba _5 da 5, xolo biji 0,5. Sablonis markerSi Sesatania F . 

meore funqcia A(p,q) warmoadgens veqtor_funqcias. grafikis Seqmnisas p da 

q cvladebi icvleba _5_dan 5_mde bijiT 0,5. x, y da z koordinatebi icvleba 

veqtor_funqciaSi mocemuli formulebis mixedviT. Sablonis markerSi Sesatania 

A.

funqcia SeiZleba agreTve ganvsazRvroT rogorc x, y da z koordinatebis 

damokidebuleba damoukidebel cvladebze, mag.: 

x( u, 

v) 

: 2v 

R( a) 

: a 

y( u, 

v) 

: u v 

an 

z u v u v 

2 

( , ) : 

S( a) 

: a 

2 

T ( a) 

: a 

3 

a 

2 

. 

aq pirvel SemTxvevaSi x, y da z warmoadgenen ori (u da v) cvladis funqcias, 

romelnic icvlebian _5_dan 5_mde bijiT 0,5; Sablonis gamoZaxebis Semdeg 

markerSi Sesatania (x, y, z). meore SemTxvevaSi R,S da T warmoadgenen erTi cvladis 

funqcias, damoukidebeli cvladi aseve icvleba _5_dan 5_mde bijiT 0,5, Sablonis 

markerSi unda SevitanoT (R,S,T). 

rodesac ori cvladis damokidebuleba mocemulia ara funqciiT, aramed 

matricis saxiT, saWiroa ganvsazRvroT x da y cvladebis zRvruli mniSvnelobebi 

da warmovidginoT Z(x,y) funqcia M matricis saxiT. mag.: 

i : 0.. 

50 , j : 0.. 

51, 

xi : 10 

2i 

, y j : 1 

4 j , 

Z( x, 

y) 

: x 

2 

y 

2 

, 

M i, 

j : Z( 

xi 

, y j ) . 

am magaliTSi x icvleba _10_dan 90_mde bijiT 2, y icvleba _4_dan 200_mde 

bijiT 4. Seiqmneba 51_striqoniani da 52_svetiani M matrica, romlis i-_uri 

striqonis da j_uri svetis gadakveTaze myofi elementi udris 

x 

2 

y 

2 

i j . 

aqve aRvniSnoT, rom 3_ganzomilebiani grafikic, rogorc 2_ganzomilebiani, 

SeiZleba iyos parametruli. 

gamovyoT grafiki. davaWiroT Tagvis marcxena Rilaks da aseT 

mdgomareobaSi gavwioT_gadmovwioT Tagvi grafikis areSi. davinaxavT, rom 

rakursi, romliT Cans grafiki, Tagvis moZraobisas icvleba. am xerxiT advilad 

SeirCeva CvenTvis sasurveli xedvis kuTxe. 

grafikis Seqmnis Semdeg SesaZlebelia misi daformateba. grafikze TagviT 

marcxena ormagi wkapuniT an konteqsturi meniudan Format... punqtis arCeviT an 

mTavari menius Format → Graph → 3D Plot... brZanebiT gamoitaneba 3_ganzomilebiani 

grafikis daformatebis dialoguri fanjara (nax5.8). 

aq General CanarTis Display As: ganyofilebaSi gvaqvs gadamrTveli, romelic 

iqneba CarTuli Surface Plot poziciaSi. Tu gadavrTavT gadamrTvels sxva poziciaSi 

(Data Points – wertilovani grafiki, Bar Plot – svetovani grafiki, Contour Plot – 

konturuli grafiki, Vector Field Plot – veqtoruli velis grafiki, Patch Plot – 

calkeuli elementebisagan Sedgenili grafiki), igive funqcia sxva saxis grafikad 

iqneba warmodgenili. 

General CanarTis View ganyofilebis pirvel sam velSi miTiTebuli ricxvebi 

aCveneben ra rakursiT Cans grafiki, xolo Zoom_Si miTiTebulia misi masStabi. 

49

nax.5.8. 3_ganzomilebiani 

grafikis daformatebis dialoguri fanjara 

Axes Style ganyofilebaSi aris gadamrTveli Semdegi SesaZlo poziciebiT: 

Perimeter (aCvenebs grafiks zomebiT perimetrze); Corner (aCvenebs grafiks zomebiT 

RerZebze); None (aCvenebs grafiks zomebis gareSe). alami Equal Scales daayenebs yvela 

RerZze erTnair masStabs. 

Frames ganyofilebaSi SeiZleba davayenoT ori alami: Show Border _ aCvenebs 

grafikis sazRvrebs, Show Box _ aCvenebs grafiks da marTkuTxa paralelepipeds, 

romelSic is moqceulia. 

Title CanarTis Graph Title ganyofilebis teqstur velSi SeiZleba SevitanoT 

grafikis saTauri, ris Semdeg davayenoT gadamrTveli poziciaSi Above (zemoT), 

Below (qvemoT) an Hide (damalva). 

Axes CanarTSi xdeba TiToeuli RerZisaTvis badis dayeneba xazebis 

raodenobis, sisqis da feris arCeviT. 

aRvniSnoT, rom Quick Plot grafikis ageba SesaZlebelia ara mxolod dekartis, 

aramed agreTve sferul da cilindrul koordinatTa sistemebSi. amisaTvis Quick 

Plot grafikis daformatebisas Quick Plot Data CanarTis Coordinate System 

ganyofilebaSi unda avirCioT ara Cartesian (dekartis koordinatTa sistema), 

romelic dayenebulia winaswari SeTanxmebiT, aramed Spherical (sferuli) an 

Cylindrical (cilindruli). 

nax.5.9_ze (a,b,c,d magaliTebi) naCvenebia 3_ganzomilebiani zedapiris 

grafikebi, xolo e magaliTSi moyvanilia 3_ganzomilebiani wertilovani grafiki, 

romelic miRebulia d_dan gadamrTvelis Display As: Sesabamis poziciaSi dayenebiT. 

50

nax.5.9. 3_ganzomilebiani grafikebis magaliTebi 

a da b grafikebi warmoadgenen Quick Plot tipis zedapiris grafikebs. a_Si 

gamoyenebulia winaswari SeTanxmebiT mocemuli zRvruli mniSvnelobebi, xolo 

b_Si es mniSvnelobebi da biji, romliTac icvleba damoukidebeli cvladebi, 

Secvlilia. amisaTvis Quick Plot grafikebisaTvis arsebobs Semdegi wesi: 

1. grafikze ormagi wkapuniT SevideT 3D Plot Format dialogur 

fanjaraSi, sadac avirCioT QuickPlot Data CanarTi; 

2. Range 1 (1_li diapazoni) velSi davayenoT X RerZisaTvis sawyisi da bolo 

mniSvnelobebi (Cven magaliTSi esaa Sesabamisad 0 da 5), xolo # of Grids 

(badis danayofTa raodenoba) velSi mivuTiToT sasurveli raodenoba 

(Cven magaliTSi 5); 

3. Range 2 (me_2 diapazoni) velSi davayenoT Y RerZisaTvis sawyisi da bolo 

mniSvnelobebi (0 da 5) da mivuTiToT badis danayofTa raodenoba (15). 

aqve aRvniSnoT, rom Mathcad_i “dagveTanxmeba” Cvens mier miTiTebul 

cvladebis zRvrul mniSvnelobebs mxolod im SemTxvevaSi, rodesac dekartis 

(Cartesian) koordinatTa sistemaSi asagebia grafiki, romelic asaxavs Cveulebriv 

orcvladian funqcias. danarCen SemTxvevebSi Mathcad_i TviTon airCevs zRvrul 

mniSvnelobebs X, Y da Z RerZebisaTvis, romlebic Seesabameba mocemul funqcias. 

51

c grafikis redaqtirebisas 3D Plot Format dialoguri fanjris Appearance 

CanarTis Fill Options (Sevsebis ofciebi) ganyofilebaSi dayenebulia Fill Surface 

(zedapiris Sevseba) gadamrTveli, ris Semdeg Color Options (ferebis ofciebi) 

ganyofilebaSi dayenebulia Solid Color gadamrTveli. marjvniv mdgom patara 

marTkuTxedze dawkapunebiT gamoZaxebulia ferTa palitra, sadac arCeulia 

stafilosferi; Line Options (wirebis ofciebi) ganyofilebaSi dayenebulia 

gadamrTveli Contour Lines da Weight_Si (wona) miTiTebulia wiris sisqe 2.0; Color 

Options ganyofilebaSi dayenebulia gadamrTveli Solid Color da datovebulia 

winaswari SeTanxmebiT mocemuli Savi feri. 

d grafikis redaqtirebisas 3D Plot Format dialoguri fanjris Axes CanarTSi X 

RerZisaTvis Grids (bade) velSi dayenebulia alami Draw Lines, xolo Line Color_Si 

badis xazebis ferad aRebulia ruxi. 

e grafikis redaqtirebisas 3D Plot Format dialoguri fanjris Appearance 

CanarTSi Points Options (wertilebis ofciebi) velSi, sadac winaswari SeTanxmebiT am 

tipis grafikisaTvis dayenebulia simboloebis Cvenebis reJimi anu dayenebulia 

alami Draw Points, Secvlilia simboloebis moxatuloba: winaswari SeTanxmebiT iyo 

dots (wertilebi), dayenda Boxes (yuTebi) zomiT 1.5. Color Options–Si CarTulia 

gadamrTveli Colormap (ferebis sqema), ris Sedegad miRebulia grafiki, romelSic 

funqciis sxvadasxva dones sxvadasxva feri aqvs. 

5.6 konturuli grafikis Seqmna 

Insert → Graph → Contour Plot brZanebiT an Graph panelze Sesabamisi Rilakis 

daWeriT Seiqmneba 3_ganzomilebiani konturuli grafikis Sabloni. konturuli 

grafiki – erTnairi donis wirebis ruka – farTod gamoiyeneba, magaliTad, 

kartografiaSi. is xSirad Seicavs met informacias, vidre zedapiris grafiki, 

romelSic zedapiris erTi nawili sakmaod xSirad dafarulia sxva nawilebiT. am 

grafikis Seqmnis da redaqtirebis procesi arsebiTad ar gansxvavdeba zedapiris 

grafikisagan. nax.5.10_is a magaliTSi moyvanilia konturuli grafiki. 

3_ganzomilebiani grafikebisTvisac SeiZleba erT grafikul areSi ramdenime 

funqciis grafikis ageba. praqtikuli gamoyeneba hpova mxolod konturuli (an 

veqtoruli velis) da zedapiris (wertilovani an svetovani) erTi da igive 

funqciis amsaxveli grafikebis erT grafikul areSi Seqmna. 

ganvixiloT konturuli da Data Points tipis erTi funqciis grafikebis erT 

sakoordinato sistemaSi warmodgena magaliTze: 

52

nax.5.10. konturuli, wertilovani, svetovani da veqtoruli velis grafikebi 

1) ganvsazRvroT funqcia: 

1 x 1 y 

P ( x, 

y) 

: 1 

; 

4 40 4 40 

2) Insert → Graph → Contour Plot brZanebiT miviRebT Sablons, sadac markerSi 

SevitanoT P,P; 

3) davaWiroT Enter klaviSs. Sedegad erT grafikul areSi miiReba ori 

grafiki: konturuli da meore – by Default – zedapiris (nax.5.11 a). 

4) SevideT daformatebis reJimSi; 

5) General CanarTis Display As: ganyofilebaSi avirCioT Plot2 da davayenoT 

grafikis tipebis gadamrTveli Data Plot_ze; 

6) davaWiroT OK Rilaks. 

miviRebT 2 grafiks erT sakoordinato sistemaSi: konturul da Data Plot 

tipis (nax.5.11 b). 

nax.5.11 c_zec agebulia 2 grafiki erT grafikul areSi: veqtoruli velis da 

zedapiris grafikebi. Tagvis gawev_gamoweviT Secvlilia xedvis rakursi. 

53 

2 

2

nax.5.11. erT sakoordinato sistemaSi ori grafikis agebis magaliTebi 

5.7 wertilovani da svetovani grafikebis Seqmna 

Insert → Graph → 3D Scatter Plot brZanebiT an Graph panelze Sesabamisi Rilakis 

daWeriT Seiqmneba 3_ganzomilebiani wertilovani grafikis Sabloni. wertilovani 

grafikis agebis da redaqtirebis procesi ar gansxvavdeba sxva tipis 

3_ganzomilebiani grafikebis Seqmnis da redaqtirebis procesisagan. aRvniSnoT, 

rom wertilovani grafikis redaqtirebisas SeiZleba SevcvaloT wertilebis zoma, 

maTi gamosaxuleba (mag., SevcvaloT wertilebi jvaredina formis simboloebiT, 

wrewirebiT, kvadratebiT da a.S.) da feri. nax5.10 b_ze moyvanilia wertilovani 

grafiki. redaqtirebis reJimSi Secvlilia gamoyenebuli simbolo (3D Plot Format 

dialogur fanjris Appearance CanarTis Points Options ganyofilebaSi miTiTebulia 

simbolo x’s da simboloebis feri – wiTeli). 

Insert → Graph → 3D Bar Chart brZanebiT an Graph panelze Sesabamisi Rilakis 

daWeriT Seiqmneba 3_ganzomilebiani svetovani grafikis (histogramis) Sabloni. 

histogramaSi svetebis simaRle X da Y RerZebis koordinatebis mniSvnelobebze 

damokidebulia. svetovani grafikis magaliTi moyvanilia nax.5.10 c_ze. 

54

5.8 veqtoruli velis grafikis Seqmna 

Insert → Graph → Vector Field Plot brZanebiT an Graph panelis igive 

saxelwodebis Rilakis daWeriT Seiqmneba veqtoruli velis grafikis Sabloni. es 

grafiki warmoadgens mokle isrebis – veqtorebis erTobliobas. isari mimarTulia 

zedapiris simaRlis zrdis mxares, xolo isrebis ganlagebis simkvrive zrdis 

siCqarezea damokidebuli. grafikis aseTi forma xSirad gamoiyeneba 

eleqtromagnituri, siTburi da gravitaciuli velebis warmodgenisaTvis. 

veqtoruli velis grafiki moyvanilia nax.5.10 d_ze. 

5.9 grafikebis Seqmna ostatis meSveobiT 

Insert → Plot Wizard brZanebiT gamoiZaxeba grafikis Seqmnis ostati. ostatis 

muSaobis pirvel safexurze Plot Type dialogSi xdeba grafikis tipis SerCeva 

(nax.5.12). 

nax.5.12. grafikis Seqmnis ostatis muSaobis pirveli safexuri 

ostats SeuZlia Seqmnas Semdegi tipis grafikebi: Surface Plot, Contour Plot, 

Vector Field Plot, Bar Plot an Scatter Plot. aqve vnaxavT SerCeuli tipis nimuSs. Rilak 

Next>_ze daWeriT xdeba me_2 safexurze gadasvla, sadac SeirCeva grafikis 

garegnuli saxe. 

nax.5.13_ze moyvanilia me_2 safexuris Appearance dialogi, sadac gvaqvs ga- 

damrTveli: Draw lines (xazebis Cveneba), Fill surface with color (zedapiris Sevseba feriT), 

Fill surface and draw lines (zedapiris Sevseba da xazebis Cveneba). marjvniv vnaxavT 

Sesabamis nimuSs. Rilakze daWeriT 

gadavdivarT bolo, me_3 safexurze. 

55

nax.5.13. grafikis Seqmnis ostatis muSaobis meore safexuri 

nax.5.14_ze naCvenebia me_3 safexuris Coloring dialogi, sadac gadamrTveli 

gvaZlevs gaferadebis stilis erT_erT Semdeg variants: Color by height (feris 

Secvla simaRlis cvlasTan erTad), Color using lighting (feri ganaTebiT), Solid color 

(feri ar icvleba). Tu arCeulia gaferadebis stili Solid color , marjvniv naCvenebi 

iqneba feri, romelzec dawkapunebiT gamoiZaxeba palitra, sadac SeiZleba 

SevarCioT sxva feri. Finish Rilakze daWeriT ostatis muSaoba dasruldeba. 

nax.5.14. grafikis Seqmnis ostatis muSaobis mesame safexuri 

samuSao furcelze davinaxavT grafikis Sablons, sadac markerSi Sesatania 

funqciis an matricis saxeli. Enter klaviSze daWeriT an grafikis gareT 

dawkapunebiT davinaxavT ostatis mier Seqmnil grafiks. 

56

5.10 matricis Casma dokumentSi 

rogorc ukve iyo naTqvami, Insert → Matrix... brZanebiT, Ctrl + M 

swrafmoqmedebis klaviSebiT Man Matrix panelze matricis Sablonze dawkapunebiT 

gamoiZaxeba matricis Casmis dialoguri fanjara Insert Matrix (nax.5.15), romelSic 

Rows: da Columns: velebSi misaTiTebelia matricis striqonebisa da svetebis 

raodenoba. 

nax.5.15. matricis Casmis dialoguri fanjara 

amis Semdeg Tu avirCevT Insert Rilaks (am dros dialoguri fanjara rCeba 

ekranze) an davaWerT OK Rilaks an klaviaturis Enter klaviSs (am dros dialoguri 

fanjara ixureba), viziris adgilas Caismeba matricis an veqtoris Sabloni. 

SablonSi Sesatania matricis (veqtoris) elementebis mniSvnelobebi. matricis 

(veqtoris) elementebi SeiZleba iyon ricxvebi, mudmivebi, cvladebi da 

maTematikuri gamosaxulebebi. 

Tu Cven davasrulebT matricis Sevsebas ise, rom yvela markeri ar iqneba 

Setanili, Seuvsebeli markerebi gawiTldebian. 

Insert Matrix dialoguri fanjris meSveobiT SeiZleba gavadidoT an 

SevamciroT matricis zoma. amisaTvis SevideT am dialogSi, roca kursori 

imyofeba matricis Sablonis an Sevsebuli matricis SigniT. Rows: da Columns: 

velebSi SevitanoT Casasmeli (wasaSleli) striqonebis da svetebis raodenoba. 

davaWiroT Insert (Delete) Rilaks. Mathcad_i Casvams striqonebs gamoyofili 

elementis qveviT, xolo svetebs _ gamoyofili elementis marjvniv. striqonebis 

(svetebis) waSlas Mathcad_i iwyebs gamoyofili elementis striqonidan (svetidan) 

da agrZelebs striqonebis waSlas qveviT, xolo svetebis marjvniv. 

mag., Tu gvsurs wavSaloT romelime sveti, davayenoT kursori am svetis 

romelime elementSi, SevideT Insert Matrix dialogSi, Rows: velSi SevitanoT 0, 

Columns: velSi _ 1 da davaWiroT Delete Rilaks. 

57

5.11 funqciebis Casma 

Insert → Function... brZanebiT an Ctrl + E swrafmoqmedebis klaviSebiT 

gamoiZaxeba Insert Function dialoguri fanjara (nax.5.16). 

nax.5.16. funqciis Casmis dialoguri fanjara 

fanjris marcxena nawilSi moyvanilia funqciebis kategoriebis CamonaTvali. 

saWiro kategoriaze dawkapunebis Semdeg fanjris marjvena nawilSi vnaxavT am 

kategoriis funqciebis sias. Tu Cven ar viciT, romel kategorias ekuTvnis 

funqcia, is moiZebneba All kategoriaSi, romelSic moyvanilia yvela funqcia 

alfabetis mixedviT. dialoguri fanjris Qqveda nawilSi mokled moyvanilia 

arCeuli funqciis aRwera. OK an Insert Rilakebis arCeviT an klaviaturis Enter 

klaviSze dawkapunebiT kursoris adgilas Caismeba funqciis Sabloni. 

5.12 sazomi erTeulis Casma 

Insert → Unit... brZanebiT an Ctrl + U swrafmoqmedebis klaviSebiT gamoiZaxeba 

sazomi erTeulebis Casmis dialoguri fanjara (nax.5.17). 

Insert Unit dialoguri fanjris Dimension (ganzomileba) ganyofilebaSi 

moyvanilia ganzomilebis mqone sidideebis CamonaTvali, xolo Unit ganyofilebaSi 

ganzomilebebi. winaswari SeTanxmebiT gamoyenebulia SI sistema. Tu Mathcad_i 

muSaobs ganzomilebis mqone sidideebTan, cvladebis mniSvnelobebi iqneba 

gamoTvlili da gamotanili saWiro ganzomilebebis miTiTebiT. 

58

nax.5.17. sazomi erTeulebis Casmis dialoguri fanjara 

5.13 naxatis Casma 

Mathcad_s SeuZlia moaxdinos sxva programebSi (AutoCAD, PCAD da a.S.) 

Seqmnili grafikuli failebis importireba. 

Insert → Picture brZanebiT an Matrix panelze Picture Rilakze dawkapunebiT an 

Ctrl + T swrafmoqmedebis klaviSebiT xdeba naxatis Sablonis Casma. Sablons aqvs 

erTaderTi markeri qveda marcxena kuTxeSi, sadac Tu Casasmeli faili mimdinare 

direqtoriaSi imyofeba, Sesatania failis saxeli, winaaRmdeg SemTxvevaSi ki _ 

failis sruli misamarTi. es monacemebi striqonuli tipisaa da amitom saWiroa 

maTi brWyalebSi Casma. amis Semdeg Tagvis marcxena RilakiT naxatis gareT 

dawkapunebiT moxdeba naxatis importireba. 

ra Tqma unda, SesaZlebelia agreTve movaxdinoT sxva programebiT Seqmnili 

naxatebis kopireba gacvlis buferidan (brZanebebiT Edit → Copy an Edit → Cut 

naxatis Semqmnel programaSi, Semdeg Edit → Paste an Edit → Paste Special Mathcad_Si). 

nebismier matricas SeiZleba SevusabamoT nacrisferi skalis gradaciebSi 

Sesrulebuli naxati. amisaTvis: 

1. davawkapunoT furclis cariel adgilas; 

2. Insert → Picture brZanebiT an Matrix panelze Picture Rilakze dawkapunebiT an 

Ctrl + T swrafmoqmedebis klaviSebiT SevqmnaT naxatis Sabloni; 

3. SevitanoT markerSi matricis saxeli. 

Sedegad miviRebT matricis amsaxvel naxats. matricis yoveli elementi 

Seesabameba naxatis erT piqsels, amasTan matricis 0_is toli elementi aisaxeba 

Sav ferad, xolo 255_is toli _ TeTr ferad. ricxvebs, romlebic ar Sedian 0 _ 

255 diapazonSi, Mathcad_i naxatis Sesaqmnelad “Secvlis” da “miiyvans” zRvrul 

mniSvnelobebamde, xolo ricxvebis wiladur nawilebs ar miiRebs mxedvelobaSi. 

59

Tu gvaqvs erTi da igive ganzomilebis mqone 3 matrica, Mathcad_s SeuZlia am 

matricebis safuZvelze Fferadi naxatis Seqmna, vTqvaT, erTi matricis wiTeli, 

meore – mwvane, xolo mesame – lurji komponentad warmodgeniT. 

naxatis konteqsturi meniudan Picture toolbar punqtis SerCeviT SesaZlebelia 

misi redaqtireba. redaqtirebisas SeiZleba SevcvaloT naxatis zomebi, masStabi, 

kontrastuloba, sikaSkaSe da a.S. 

5.14 ubnis formireba da gverdis gawyveta 

Insert → Area brZanebiT Mathcad_i Casvams dokumentSi wirebis wyvils, 

romlebic aCveneben ubnis sazRvrebs. 

Format menius punqtebis meSveobiT SeiZleba ubnisaTvis saxelis miniWeba, 

misi Caketva, gaReba, SekumSva da gafarToeba. ubnis sazRvari moiniSneba masze 

dawkapunebiT an Tagvis waTreviT mis gaswvriv. moniSnuli sazRvari SeiZleba 

gadavaadgiloT ubnis gasazrdelad an Sesamcireblad. 

ubnebis raodenoba dokumentSi ar aris SezRuduli, magram ar aris 

daSvebuli ubnis Casma arsebuli ubnis farglebSi. 

ubnis wasaSlelad gamovyoT misi orive sazRvari da mivceT Edit → Delete an 

Edit → Cut brZaneba an davaWiroT Standard panelis Cut Rilaks. 

gverdis gawyveta xdeba Insert → Page Break brZanebiT. es brZaneba gamoiyeneba 

im situaciaSi, rodesac Print Preview reJimSi gamoCndeba, rom gverdis qveda nawilSi 

ganlagebuli romelime grafiki an cxrili ar eteva am gverdze an paragrafis 

saTauri aRmoCndeba erT gverdze, xolo TviT paragrafi iwyeba meoreze. 

5.15 maTematikuri da teqsturi areebis Casma 

maTematikuri da teqsturi areebis Casma xdeba Insert → Math Region da Insert → 

Text Region brZanebebiT. 

rodesac teqsturi are aqtiuria, SesaZlebelia misi daformateba Format → 

Text... brZanebis meSveobiT, Tumca am dialogur fanjaraSi gvaqvs teqstur 

redaqtorebTan SedarebiT (mag., MSWord_Tan) mwiri SesaZleblobani. 

teqstur areSi teqstis Setanis Semdeg dokumentis cariel adgilze 

dawkapunebiT komentarebis Seqmnis procesi dasruldeba. 

Mathcad_Si SesaZlebelia teqstur areSi maTematikuri formulebis Casma. 

amisaTvis teqsturi markeri davayenoT teqsturi aris im adgilas, sadac unda 

CavweroT formula. brZaneba Insert → Math Region gamoiyvans am adgilas 

maTematikuri aris Sablons patara Savi kvadratis saxiT. am SablonSi SeiZleba 

CavweroT formulebi Mathcad_Si arsebuli Cveulebrivi xerxebiT. cxadia, teqsturi 

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aris formulebi ar gamoiTvlebian. arsebuli maTematikuri gamosaxulebebis Casma 

teqstur areSi SesaZlebelia Edit → Copy, Edit → Paste brZanebebiT. 

5.16 komponentebis Casma 

Insert → Component... brZanebiT gamoiZaxeba komponentebis Casmis ostati. 

ostati warmoadgens ramdenime safexurebian dialogs, romlis pirvel safexurze 

(nax.5.18) xdeba im komponentis anu sxva programis SerCeva, romelic gvsurs 

mivuerToT Mathcad_s. amasTan SerCeva xdeba mxolod arsebuli siidan. 

nax.5.18. komponentebis Casmis ostatis muSaobis pirveli safexuri 

avirCioT, vTqvaT, Microsoft Excel_i. Next> Rilakze dawkapunebiT gadavalT 

Semdeg safexurze – Excel Setup Wizard (Excel_is dayenebis ostati) dialogSi (nax.5.19). 

masSi gvaqvs gadamrTveli: Create an empty Excel worksheet (Excel_is carieli 

samuSao furclis Seqmna) an Create from file: (failidan Seqmna). avirCioT saWiro, 

vTqvaT, Create an empty Excel worksheet. aqve SegviZlia davayenoT alami Display as Icon 

(gamoaCine piqtogramis saxiT). Next> Rilakze dawkapunebiT gadavalT Semdeg 

safexurze (nax.5.20), xolo

nax.5.19. Excel_is dayenebis ostatis dialoguri fanjara (I) 

sawyisi ujredis nomeri. mag., Tu Input cvladi warmoadgens 44 _ ganzomilebian 

matricas da sawyis ujredad mivuTiTebT A1, matricis mniSvnelobebi daikaveben 

Excel_is A1 : B4 diapazons. Range areSi Sesatania ujredebis diapazoni, sadac 

moTavsdeba Output cvladebi. 

nax.5.20. Excel_is dayenebis ostatis dialoguri fanjara (II) 

davaWiroT Finish Rilaks. Mathcad_is samuSao furcelze davinaxavT Excel_is 

eleqtronuli cxrilis Sablons. Input cvladebis saxelebi SevitanoT qveda 

markerSi, xolo Output cvladebis _ miniWebis simbolos marcxniv mdebade markerSi. 

Tu davawkapunebT Casmuli komponentis gareT, Input cvladebi aRmoCndebian Excel_is 

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cxrilSi. komponentze ormagi wkapuniT moxdeba misi gaaqtiureba da davinaxavT 

komponentis meniusa da panelebs, ase rom Mathcad_idan gamousvlelad SevZlebT 

muSaobasK Excel_Si. Excel_Tan muSaobis damTavrebis Semdeg Mathcad_Si dafiqsirdeba 

Output cvladebis mniSvnelobebi. 

meSveobiT. 

komponentebis Casma xdeba aseve Insert → Data da Insert → Controls brZanebebis 

5.17 monacemebis Casma 

Insert → Data brZanebis qvebrZanebebia: 

Table _ eleqtronuli cxrilis Casma; 

File Input _ monacemTa failebis importireba; 

File Output _ monacemTa failebis eqsportireba. 

Casmuli eleqtronuli cxrilis monacemebis gamoyeneba Mathcad_Si 

Insert → Data → Table brZanebiT SesaZlebelia Mathcad_is samuSao furcelSi 

nax.5.21. Mathcad_is samuSao furcelSi Casmuli cxrilidan monacemTa 

gamoyenebis magaliTi 

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CavsvaT eleqtronuli cxrili, romelic arsebiTad masivs warmoadgens. marcxena 

zeda kideSi arsebuli markeris adgilas avkriboT sasurveli saxeli da SevavsoT 

cxrili monacemebiT. nax.5.21_ze mocemulia Mathcad_is samuSao furcelSi Casmuli 

cxrilidan monacemTa gamoyenebis magaliTi. 

Casmuli cxrilis ganzomilebis Sesacvlelad gamovyoT cxrili da 

mivitanoT Tagvis maCvenebeli marTkuTxedis formis patara Sav markerebTan. roca 

Tagvis maCvenebeli miiRebs ormimarTuliani isris formas, Tagvis gadaTreviT 

SesaZlebelia cxrilis dapataraveba_gadideba. 

monacemTa eqsportireba da importireba 

menius Insert → Data punqtiT SesaZlebelia monacemTa failebis importireba 

da eqsportireba. Insert → Data → File Input brZanebis gamoyenebis Semdeg gamodis File 

Options dialoguri fanjara (nax.5.22), romlis meSveobiT xdeba monacemTa 

importireba. 

monacemTa importirebisaTvis: 

nax.5.22. dialoguri fanjara File Options 

1. File Format: siisebur velSi moTavsebulia im programebis CamonaTvali, 

saidanac SesaZlebelia monacemebis importireba. avirCioT sasurveli 

programa am siidan; 

2. teqstur velSi avkriboT sasurveli failis sruli saxeli an gamoviyenoT 

Browse... Rilaki, romelic gadagviyvans Read from file dialogSi; am dialogis 

Look in: velSi avirCioT katalogi, sadac aris Cawerili Cveni faili, 

movZebnoT faili da movaxdinoT masze orjeradi wkapuni. teqstur velSi 

Caiwereba failis sruli saxeli; 

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3. Next Rilakis meSveobiT gadavideT meore safexurze, sadac xdeba 

importirebul monacemTa adgilis dakonkreteba (mag., Excel_is failis 

arCevisas samuSao furclis da ujredebis misamarTebis miTiTeba); 

4. Tu saWiroa, davayenoT alami Use comma as decimal symbol (aTobiT wiladebSi 

mTeli nawilis wiladuri nawilisagan mZimiT gamoyofa); 

5. davayenoT, Tu saWiroa, alami Use relative file path. amiT failis sxva misamarTze 

gadaadgilebis Semdegac Mathcad_i SeZlebs misi axali adgilmdebareobis 

gansazRvras. 

6. davaWiroT Finish Rilaks. 

Mathcad_is samuSao furclis moniSnul adgilas Caismeba piqtograma failis 

sruli saxeliT, romlis marcxena zeda kideSi, miniWebis operatoris win 

arsebuli markeris adgilas unda mivuTiToT sasurveli saxeli. Casmuli regionis 

gareT Tagvis dawkapunebis Semdeg Mathcad_i kiTxulobs Casmuli failis monacemebs 

da SesaZlebloba gveZleva es monacemebi gamoviyenoT Mathcad_is matricebSi an 

ricxviT diapazonebSi. nax.5.23_ze naCvenebia Casmuli failidan (Cven SemTxvevaSi 

aRebulia Excel_is faili) monacemebis gamoyenebis magaliTi. 

nax.5.23. importirebuli failidan monacemebis gamoyenebis magaliTi 

analogiurad sruldeba Mathcad_idan monacemTa eqsportireba, mxolod 

amisaTvis viyenebT Insert → Data → File Output brZanebas. 

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samuSao furcelze arsebuli monacemebis saxeli unda Caiweros Casmuli 

piqtogramis marcxena qveda kideSi arsebuli markeris adgilas. monacemebi 

dafiqsirdeba im failSi, sadac movaxdineT eqsportireba. nax.5.24_ze naCvenebia 

eqsportirebis magaliTi. 

nax.5.24. Mathcad_idan monacemTa eqsportirebis magaliTi 

5.18 mmarTveli komponentebis Casma 

Insert → Control brZanebiT SesaZlebelia Mathcad_is samuSao furcelSi Caisvas 

mmarTveli komponentebi rogoricaa: 

damoukidebeli gadamrTveli _ alami (Check Box); 

erTmaneTze damokidebuli gadamrTveli (Radio Button); 

Rilaki (Push Button); 

slaidi (Slider); 

teqsturi veli (Text Box); 

siiseburi veli (List Box). 

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igive moqmedebebis Sesruleba SesaZlebelia Controls panelis (nax.5.25) 

Rilakebis meSveobiT. 

nax.5.25. Controls panelis Rilakebi 

5.19 Mathcad_is dokumentSi sxva obieqtis Casma 

Mathcad_s aqvs SesaZlebloba gamoiyenos OLE (Object Link Embedding) meqanizmi 

sxva gafarToebis failebTan kavSiris damyarebisaTvis CaSenebuli (Embedding) an 

bmulis (Link) saxiT. Oobieqti warmoadgens ZiriTad dokumentSi gadatanil 

monacemTa nebismier tips anu es SeiZleba iyos teqstis fragmenti, formula an 

misi nawili, grafiki, eleqtronulo cxrili, videoklipi, faili da a.S. obieqtis 

Casma ZiriTad dokumentSi SesaZlebelia rogorc kopirebiT da specialuri 

CasmiT, aseve Insert → Object... brZanebiT. Aam ukanasknels xmaroben, rodesac 

romelime faili mTlianad Casasmelia ZiriTad dokumentSi. aRvniSnoT, rom 

dokuments, sadac xdeba obieqtis Casma, uwodeben klients, xolo obieqts, romlis 

CaSeneba an mibma xdeba, uwodeben servers. gansxvaveba am or operaciaTa Soris 

Semdegia: 

Mathcad_is dokumentSi sxva gafarToebis failis CaSenebisas masSi 

Semdgomi cvlilebebi ar aisaxeba Mathcad_is dokumentSi; 

Mathcad_is dokumentSi sxva gafarToebis failis mibmis SemTxvevaSi 

cvlilebebi (redaqtireba) aisaxeba rogorc Mathcad_is dokumentSi, aseve serverSi 

anu mibmul failSic. 

Mathcad_Si sxva obieqtis CaSeneba 

1. avirCioT menius Insert → Object... brZaneba. gamova dialoguri fanjara Insert 

Object (nax.5.26); 

2. dialoguri fanjris Create New gadamrTvelis arCevisas Object Type velidan 

sasurveli programis miTiTebiT Caismeba sruliad axali dokumenti, xolo 

Create from File gadamrTvelis arCeviT SesaZlebelia ukve arsebuli failis 

Casma. am ukanasknelis arCeviT Seicvleba dialoguri fanjris saxe (nax.5.27). 

Browse... Rilakis meSveobiT SesaZlebelia katalogTa da failebis xeze 

sasurveli failis moZebna; 

3. davaWiroT OK Rilaks. Sedegad im adgilas, sadac manamde iyo aqtiuri 

kursori, Mathcad_Si CaSendeba sxva obieqti. 

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nax.5.26. obieqtis Casmis dialoguri fanjara (I) 

nax.5.27. obieqtis Casmis dialoguri fanjara (II) 

Mathcad_Si sxva obieqtis mibma. 

1. avirCioT menius Insert → Object... brZaneba. gamova dialoguri fanjara Insert 

Object (nax.5.26); 

2. avirCioT gadamrTveli Create from File. obieqtis Casmis dialoguri fanjara 

Seicvleba (nax.5.27). Browse... Rilakis meSveobiT sasurveli failis miTiTebis 

Semdeg davayenoT Link alami, rac mogvcems bmuli kontaqtis damyarebis saSualebas. 

Tu ar gvsurs Mathcad_Si CaSenebuli an bmuli dokumentis srulad danaxva, 

Display As Icon almis dayenebiT SesaZlebelia obieqtis piqtogramis saxiT warmoCena. 

obieqtis Casma piqtogramis saxiT SesaZlebelia agreTve misi iarliyis TagviT 

gadaTreviT, vTqvaT, Windows Explorer_is fanjridan. 

CaSenebuli obieqtis redaqtireba. 

movniSnoT CaSenebuli obieqti masze TagviT erTjer dawkapunebiT. Mmenius 

Edit → Object brZaneba xelmisawvdomi gaxdeba. Mmisi saxe (Edit → Document Object, Edit 

→ Object Equation da a.S.) damokidebulia obieqtis tipze. mas gaaCnia Edit da Open 

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qvebrZanebebi. Edit qvebrZanebis gamoyenebiT SesaZlebelia Mathcad_is programaSive 

CaSenebuli failis redaqtireba. Open qvebrZanebis arCevisas gadavalT CaSenebuli 

failis programaSi da iq vaxdenT redaqtirebas. 

CaSenebuli obieqtis redaqtireba SesaZlebelia agreTve masze TagviT 

orjeradi dawkapunebiT, romelic faqtobrivad Edit → Document Object (an am punqtis 

sxva saxecvla) → Edit brZanebis tolfasia. 

aRsaniSnavia, rom redaqtireba, romelsac SevasrulebT CaSenebul obieqtze, 

ar aisaxeba mis wyaroze (igulisxmeba obieqti, romlis CaSenabac moxda). 

5.20 miTiTebebis Casma 

zog SemTxvevaSi saWiroa erTi da igive gansazRvrebebis da gamoTvlebis 

xSiri gameoreba. ra Tqma unda, amas advilad mivaRwevT Edit → Copy da Edit → Paste 

brZanebebiT an Sesabamisi areebis Drag and Drop teqnikiT kopirebiT erTi 

dokumentidan meoreSi, magram im SemTxvevaSi, roca ganmeorebadia mTeli 

dokumentis gansazRvrebebi da gamoTvlebi, umjobesia mTavar dokumentSi CavsvaT 

e.w. miTiTeba (Reference) meore dokumentze. am dros meore dokumenti misaRwevadi 

xdeba misi gaxsnis gareSe. 

miTiTebebis Casasmelad: 

1. davawkapunoT mTavari dokumentis Tavisufal adgilas – iq, sadac gvsurs 

miTiTebis Casma; 

2. mivceT Insert → Reference... brZaneba, gamoCndeba Insert Reference dialoguri 

fanjara (nax.5.28); 

nax.5.28. miTiTebis Casmis dialoguri fanjara 

3. Insert reference to file velSi CavweroT im failis misamarTi, romelzec miTiTeba 

xdeba. misamarTi Caiwereba klaviaturidan an Browse... Rilakis meSveobiT. am velSi 

SesaZlebelia agreTve Web_qselSi ganlagebul Mathcad_is failis saxelis Cawera. 

4. davaWiroT OK Rilaks. Sedegad Mathcad_i Casvams miTiTebas, rasac Cven 

davinaxavT marTkuTxedSi Casmuli patara Canaweris saxiT. am Canaweris marjvniv da 

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qveviT moqmedebs miTiTebuli dokumentis gansazRvrebebi da gamoTvlebi, xolo 

masze ormagi wkapuni gaxsnis miTiTebul dokuments Tavis fanjaraSi – 

redaqtirebisaTvis. nebismieri sxva obieqtis msgavsad, SesaZlebelia am Canaweris 

gadaadgileba an, vTqvaT, waSla. miTiTebis Casmis Semdeg Cven ver vxedavT 

miTiTebuli dokumentis obieqtebs da formulebs, magram mTavari dokumenti 

“xedavs” da muSaobs maTTan ise rogorc am dokumentSi Setanil monacemebTan. 

aRvniSnoT, rom winaswari SeTanxmebiT miTiTebuli dokumentis sxva 

misamarTze gadaadgilebis Semdeg Mathcad_i ver SeZlebs misi axali 

adgilmdebareobis gansazRvras. Tu gvsurs, rom Mathcad_ma SeZlos amis gakeTeba, 

saWiroa Insert Reference dialogur fanjaraSi Use relative path for reference almis 

dayeneba. 

Tu miTiTebuli dokumenti saWiroebs modifikacias, mTavari dokumentis 

ganaxlebisaTvis: 

1. movaxdinoT saWiro cvlilebebi miTiTebul dokumentSi; 

2. SevinaxoT miTiTebuli dokumenti; 

3. davawkapunoT mTavari dokumentis miTiTebaze da davaWiroT F9 klaviSs. 

5.21 hipermimarTvis damyareba 

hiperlinki (hipermimarTva) es aris moniSnuli sityva an sityvebis jgufi, 

romelzec orjer dawkapunebiT gadavdivarT sxva samuSao furcelze an sxva 

failSi. SesaZlebelia agreTve internetis sasurvel misamarTze gadasvla. 

hiperlinkis dasamyareblad: 

1. movniSnoT sasurveli regioni an sityvaTa jgufi; 

2. mivceT Insert → Hyperlink… brZaneba. Ggamova hiperlinkis Casmis dialoguri 


nax.5.29. hipermimarTvis Casmis dialoguri fanjara 

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3. Link to file or URL: velSi avkriboT im failis misamarTi, romelzec gadavalT 

hiperlinkis meSveobiT (mag., C:\David’s_documents\file1.mcd) an movZebnoT 

sasurveli faili katalogTa da failebis xeze Browse... Rilakis 

gamoyenebiT. arCeuli misamarTi Caiwereba Link to file or URL: velSi. Tu 

gvsurs internetis misamarTze hiperlinkis damyareba, unda avkriboT 

misamarTi srulad (mag., http://www.mathsoft.com/text.swk da ara 

www.mathsoft.com/text.swk); 

4. davayenoT, Tu gvsurs, alami Use relative path for hyperlink. amiT miTiTebuli 

failis sxva misamarTze gadaadgilebis Semdegac Mathcad_i moaxerxebs misi 

axali adgilmdebareobis gansazRvras. 

5. Message that appears on the status line when mouse is over link: velSi SegviZlia 

CavweroT raime teqsturi Setyobineba, romelic gamoCndeba moniSnul 

obieqtTan Tagvis miaxlovebisas; 

6. OK Rilakis gamoyeneba brZanebas gauSvebs Sesrulebaze. 

SesaZlebelia gamoZaxebuli dokumentis ara mxolod wakiTxva, aramed 

redaqtirebac. 

Tu gvsurs hiperlinkis waSla, movniSnoT sityva an sityvaTa jgufi, 

romelzec iyo ganxorcielebuli hiperlinki, da mivceT Insert → Hyperlink... brZaneba. 

gamoCndeba Edit Hyperlink dialoguri fanjara (nax.5.30). davaWiroT Remove Link 

Rilaks. hipermimarTva waiSleba. 

Nnax.5.30. hipermimarTvis redaqtirebis dialoguri fanjara 

Oobieqtis Casmis Semdeg (Edit → Paste Special... an Insert → Object... brZanebebis 

meSveobiT) menius Edit punqtis Links... qvepunqtiT gaixsneba dialoguri fanjara, 

romlis GRilakebi gvaZleven hipermimarTvis ganaxlebis da waSlis, obieqtis 

wyaros gaxsnis da Secvlis saSualebas. 

71

Tavi VI simboluri operaciebi Mathcad_Si 

6.1 Symbolics menius da Symbolic panelis Semadgenloba 

simboluri operaciebi – es iseTi operaciebia, romelTa Sedegi ZiriTadad 

moicema ara ricxobrivad, aramed simboloebis saxiT. 

avirCioT mTavari menius Symbolics punqti (an davaWiroT Alt + S klaviSebs). 

davinaxavT qvemenius: 

Evaluate – gamoTvla; 

Simplify (gamartiveba) – gamoyofili gamosaxulebis gamartiveba; 

Expand (gaSla) – gamoyofili gamosaxulebis gaSla; 

Factor (mamravli) – gamoyofili gamosaxulebis martiv mamravlebad daSla; 

Collect (Segroveba) – gamoyofili gamosaxulebis mwkrivad gaSla da msgavsi 

wevrebis dayvana (SeerTeba); 

Polynomial Coefficients (polinomis koeficientebi) – polinomis koeficientebis 

gansazRvra gamoyofil gamosaxulebaSi; 

Variable – cvladi; 

Matrix – matrica; 

Transform – transformireba; 

Evaluation Style... (gamoTvlebis stili) – gamoTvlebis stilis formireba. 

Symbolics → Evaluate brZanebis qvebrZanebebia: 

Symbolically (simbolurad) _ gamoyofili gamosaxulebis simboluri 

gardaqmna; 

Floating Point... (mcocavi wertili) – gamoTvlebis Sedegis mcocavi wertiliT 

warmodgena; 

Comlex (kompleqsuri) – gamoTvlebis Sesruleba kompleqsur areSi da 

Sedegis warmodgena kompleqsur formaSi. 

Symbolics → Variable brZanebis qvebrZanebebia: 

Solve (amoxsna) – amocanis amoxsna miTiTebuli cvladis mimarT; 

Substitute (Casma) – gamosaxulebis Casma miTiTebuli cvladis magivrad; 

Differentiate (diferencireba) – diferencireba miTiTebuli cvladis mimarT; 

Integrate (integreba) – integreba miTiTebuli cvladis mimarT; 

Expand to Series... (mwkrivad gaSla) _ teiloris mwkrivad gaSla; 

Convert to Partial Fraction (wiladebad gardaqmna) _ gamosaxulebis warmodgena 

elementaruli wiladebis jamis saxiT. 

Symbolics → Matrix brZanebis qvebrZanebebia: 

Transpose (transponireba) – matricis transponireba; 

Invert (Sebruneba) – matricis Sebruneba; 

Determinant (determinanti) – matricis determinantis gamoTvla. 

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Symbolics → Transform brZanebis qvebrZanebebia: 

Fourier – furies gardaqmna miTiTebuli cvladis mimarT; 

Inverse Fourier – furies Sebrunebuli gardaqmna miTiTebuli cvladis 

mimarT; 

Laplace – laplasis gardaqmna miTiTebuli cvladis mimarT; 

Inverse Laplace _ laplasis Sebrunebuli gardaqmna miTiTebuli cvladis 

mimarT; 

Z _ Z_gardaqmna miTiTebuli cvladis mimarT; 

Inverse Z – Sebrunebuli Z_gardaqmna miTiTebuli cvladis mimarT. 

nax.6.1_ze moyvanilia instrumentTa paneli Symbolic Semdegi punqtebiT: 

nax.6.1. instrumentTa paneli Symbolic 

→ _ simboluri tolobis niSani, sxvanairad mas simboluri gardaqmnebis 

operators eZaxian; gamoiZaxeba Sabloni maTematikuri gamosaxulebis Sesatanad da 

misi analizuri saxiT warmosadgenad; 

_ gafarToebuli simboluri gardaqmnebis operatori; gamoiZaxeba 

Sabloni maTematikuri gamosaxulebisa da simboluri operaciis saxelis 

Sesatanad; 

Modifiers _ gamoiZaxeba instrumentTa paneli Modifier; 

float _ gamoiZaxeba Sabloni Sedegis mcocavi wertilis formatSi 

warmosadgenad; 

complex _ am operatoriT xdeba gamoTvlebis Sesruleba kompleqsur areSi, 

Sedegic Caiwereba kompleqsur formaSi; 

assume _ gamoiZaxeba Sabloni cvladisaTvis SezRudvebis dasawesad; 

solve _ gamoiZaxeba Sabloni gantolebis da utolobis amosaxsnelad 

miTiTebuli cvladis mimarT; 

simplify _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis gasamartiveblad; 

substitute _ gamoiZaxeba Casmis Sabloni; 

73

factor _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis martiv mamravlebad 

dasaSlelad; 

expand _ gamoiZaxeba maTematikuri gamosaxulebis gaSlis Sabloni; 

coeffs _ gamoiZaxeba Sabloni polinomis koeficientebis gansazRvrelad 


collect _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis mwkrivad 

gasaSlelad (miTiTebuli cvladis mimarT) msgavsi wevrebis SeerTebiT; 

series _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis teiloris mwkrivad 

gasaSlelad miTiTebuli cvladis mimarT; 

parfrac _ gamoiZaxeba Sabloni maTematikuri gamosaxulebis elementaruli 

wiladebis jamis saxiT warmosadgenad miTiTebuli cvladis mimarT; 

fourier _ gamoiZaxeba Sabloni furies gardaqmnis Sesasruleblad miTiTebuli 

cvladis mimarT; 

laplace _ gamoiZaxeba Sabloni laplasis gardaqmnis Sesasruleblad miTiTebuli 


ztrans _ gamoiZaxeba Sabloni Z_gardaqmnis Sesasruleblad miTiTebuli 


invfourier _ gamoiZaxeba Sabloni furies Sebrunebuli gardaqmnis 

Sesasruleblad miTiTebuli cvladis mimarT; 

invlaplace _ gamoiZaxeba Sabloni laplasis Sebrunebuli gardaqmnis 

Sesasruleblad miTiTebuli cvladis mimarT; 

invztrans _ gamoiZaxeba Sabloni Sebrunebuli Z_gardaqmnis Sesasruleblad 


M T → _ gamoiZaxeba Sabloni matricis transponirebisaTvis; 

M _1 → _ gamoiZaxeba Sabloni matricis SebrunebisaTvis; 

|M |→ _ matricis determinantis gansazRvra. 

6.2 maTematikuri gamosaxulebebis warmodgena analizuri saxiT 

rogorc ukve iyo naTqvami, maTematikuri gamosaxulebis warmodgena 

analizuri saxiT SeiZleba miviRoT Evaluation an Symbolic panelebis → (simboluri 

toloba) operatoris meSveobiT. amisaTvis: 

davayenoT kursori maTematikur gamosaxulebaSi, gamoviyenoT → operatori 

(an Ctrl + . klaviSebis kombinacia) da Semdeg klaviaturis Enter klaviSi; 

gamoviyenoT simboluri tolobis operatori an klaviaturis Ctrl + . 

klaviSebi. ekranze gamoCndeba simboluri tolobis niSani da mis marcxniv markeri. 

markeris adgilas SevitanoT maTematikuri gamosaxuleba da Enter klaviSiT 

davadasturoT brZaneba. 

74

maTematikuri gamosaxulebis analizuri saxiT warmodgenis miReba 

SesaZlebelia agreTve Symbolics → Evaluate → Symbolically brZanebiT. amisaTvis jer 

gamovyoT maTematikuri gamosaxuleba anu Setanis markeri – lurji kuTxe – 

davayenoT ise, rom is moicavdes gamosaxulebas mTlianad, Semdeg ki mivceT 

Symbolics → Evaluate → Symbolically brZaneba (an Shift + F9). ekranze davinaxavT Sedegs. 

aRvniSnoT, rom maTematikuri gamosaxulebis analizuri saxiT warmodgenisas 

Mathcad_i Seecdeba miiRos pasuxi rac SeiZleba martivi formiT. aRsaniSnavia 

agreTve, rom Tu gamoyofili iyo maTematikuri gamosaxulebis nawili, Symbolics 

menius brZanebebi am nawils exeba. 

Tu Mathcad_ma ver SeZlo gamosaxulebis warmodgena analizuri saxiT, 

ekranze sawyisi gamosaxuleba gameordeba (nax.6.2_5), rac niSnavs, rom amocana 

dasmulia koreqtulad, magram misi warmodgena analizuri saxiT ver moxerxda. 

Nnax.6.2. maTematikuri gamosaxulebebis analizuri saxiT warmodgenis 

magaliTebi 

nax.6.2_ze (1,2,3,4,5 magaliTebi) marcxniv moyvanilia sxvadasxva saxis 

maTematikuri gamosaxulebebi, marjvniv (amisaTvis dialogur fanjaraSi Evaluation 

Style arCeulia gadamrTveli Horizontally) Symbolics → Evaluate → Symbolically brZanebiT 

75

miRebuli am gamosaxulebebis analizuri saxe. nax.6.2_ze (6,7,8,9,10,11) 

gamosaxulebebis analizuri saxe miRebulia Symbolic panelis → operatoris 

meSveobiT. 

6.3 maTematikuri gamosaxulebebis gamartiveba 

(simplify) 

maTematikuri gamosaxulebebis gasamartiveblad gamoiyeneba Symbolic panelis 

simplify operatori. 

amisaTvis arsebobs sami xerxi. 

I xerxi: 

1. avirCioT Symbolic panelis simplify punqti; 

2. miRebul SablonSi markeris adgilas SevitanoT gasamartivebeli 

gamosaxuleba; 

3. davaWiroT klaviaturis Enter klaviSs. 

II xerxi: 

1. avkriboT gasamartivebeli maTematikuri gamosaxuleba; 

2. avirCioT Symbolic an Evaluation panelebis punqti (an davaWiroT klaviSebis 

kombinacias Ctrl + Shift + . ). gamosaxulebis marjvniv Caismeba markeri da simboluri 

tolobis → niSani; 

3. markeris adgilas avkriboT klaviaturidan sityva simplify ; 


III xerxi: 

1. avirCioT Symbolic an Evaluation panelebis punqti (an davaWiroT klaviSebis 

kombinacias Ctrl + Shift + . ). Caismeba Sabloni ori markeriT → niSnis win; 

2. pirveli markeris adgilas SevitanoT gasamartivebeli maTematikuri 

gamosaxuleba; 

3. meore markeris adgilas avkriboT klaviaturidan sityva simplify ; 


aqve aRvniSnoT, rom Symbolic panelis sxva operatorebis arCevisas aseve am 

meTodebs viyenebT. pirvel meTodSi miRebuli Sablonis saxe operatorzea 

damokidebuli. umetes SemTxvevaSi Sabloni or markers Seicavs da me_2 punqtis 

Semdeg emateba Sablonis marjvena markeris waSlis aucilebloba (Tu cvladis 

miTiTeba ar aris saWiro) an marjvena markerSi cvladis (an gamosaxulebis) Setana, 

romlis mimarT gvsurs operaciis Sesruleba. xolo meore da mesame xerxSi me_3 

punqtSi sityva_gasaRebis dabeWdvis Semdeg, Tu saWiroa, aikribeba mZime da cvladi, 

romlis mimarT sruldeba operacia. 

76

Symbolic panelis simplify operatoriT ganxorcielebuli maTematikuri 

gamosaxulebebis gamartiveba moyvanilia nax.6.3_ze (3,4,6,7 magaliTebi), amasTan me_6 

da me_7 magaliTebSi gamartivebis Semdeg gamoyenebulia float operatori. 

maTematikuri gamosaxulebebis gamartiveba SesaZlebelia agreTve Symbolics → 

Simplify brZanebiT. gamovyoT gamosaxuleba da gamoviyenoT Symbolics → Simplify 

brZaneba. Nnax.6.3_ze (1,2,5 magaliTebi) moyvanilia sxvadasxva gamosaxulebebi, xolo 

gamosaxulebebis marjvniv Symbolics → Simplify brZanebiT miRebuli maTi gamartivebis 

Sedegi. gamartivebis es meTodi sasargebloa, rodesac Cven gvsurs SevasruloT 

gamosaxulebis nawilis gamartiveba. saqme imaSia, rom zogjer Mathcad_s ar ZaluZs 

moaxdinos mTliani gamosaxulebis gamartiveba, xolo gamosaxulebis calkeuli 

nawilebis gamartiveba SesaZlebelia. amisTvis unda gamovyoT gamosaxulebis 

nawili da mivceT brZaneba Symbolics → Simplify. 

Tu Mathcad_ma ver SeZlo gamosaxulebis gamartiveba, ekranze sawyisi 

gamosaxuleba gameordeba (nax.6.3_5), rac niSnavs, rom amocana dasmulia 

koreqtulad, magram misi gamartiveba ver moxerxda. 

gamartivebis operacia xSirad ixmareba modifikatorebTan erTad. 

nax.6.3. maTematikuri gamosaxulebebis gamartivebis 

(simplify) magaliTebi 

77

6.4 maTematikuri gamosaxulebis gaSla 

(expand) 

maTematikuri gamosaxulebis gaSla xdeba Symbolics → Expand brZanebiT. es 

brZaneba, SeiZleba iTqvas, warmoadgens gamartivebis sapirispiro brZanebas. misi 

meSveobiT rTuli funqciebi ufro martivi funqciebiT gamoisaxebian da xdeba 

algebruli gamosaxulebis warmodgena gaSlili formiT. 

maTematikuri gamosaxulebis gaSla SesaZlebelia agreTve Symbolic panelis 

expand operatoriT. 

nax.6.4_ze moyvanilia maTematikuri gamosaxulebebis gaSlis magaliTebi, 

Symbolics → Expand brZanebiT (magaliTebi 1,2) da Symbolic panelis expand operatoriT 

(3,4,5,6) ganxorcielebuli. Mme_4 magaliTSi gaSla ver moxerxda. 

nax.6.4. maTematikuri gamosaxulebebis gaSlis 

(expand) magaliTebi 

aRvniSnoT, rom Symbolic panelis punqtebiT simboluri operaciebis 

Sesrulebisas Mathcad_i jer amowmebs hqonda Tu ara masSi Sesul cvladebs da 

funqciebs ufro adre miniWebuli raime mniSvnelobebi, Tu ki, Mathcad_i iyenebs am 

mniSvnelobebs. es debuleba ilustrirebulia nax.6.5_ze (magaliTebi 1,2). rac 

78

Seexeba Symbolics menius brZanebebs, isini ar amowmeben masSi Sesuli cvladebis da 

funqciebis wina mniSvnelobebs da amitomac ar iyeneben maT. am cvladebis wina 

mniSvnelobebis Secvla ar gamoiwvevs Sesabamisi simboluri gamoTvlebis 

Sedegebis Secvlas (nax.6.5, mag.3). 

nax.6.5. gansxvaveba Symbolic panelis operatorebsa da 

Symbolics menius brZanebebs Soris 

6.5 maTematikuri gamosaxulebebis da ricxvebis 

martiv mamravlebad daSla (factor) 

maTematikuri gamosaxulebebis da ricxvebis daSla martiv mamravlebad 

xdeba Symbolics → Factor brZanebiT da Symbolic panelis factor operatoris meSveobiT. 

nax.6.6_ze (1,2,3,4,5 magaliTebi) moyvanilia Symbolics → Factor brZanebiT 

ganxorcielebuli gamosaxulebebis daSlis magaliTebi, xolo me_6 da me_7 

79

magaliTebSi daSla ganxorcielebulia Symbolic panelis factor operatoriT. Mme_2@ 

magaliTSi daSla ver ganxorcielda. 

nax.6.6. maTematikuri gamosaxulebebis da ricxvebis 

martiv mamravlebad daSlis (factor) magaliTebi 

6.6 maTematikuri gamosaxulebis mwkrivad gaSla 

msgavsi wevrebis SeerTebiT (collect) 

imisaTvis rom movaxdinoT maTematikuri gamosaxulebis mwkrivad gaSla 

(miTiTebuli cvladis mimarT), saWiroa Seyvanil maTematikur gamosaxulebaSi 

gamovyoT saWiro cvladi an funqcia (kuTxis formis lurji kursoriT), Semdeg ki 

avirCioT brZaneba Symbolics → Collect. moxdeba gamosaxulebis gaSla da msgavsi 

wevrebis SeerTeba. igives miviRebT Symbolic panelis collect operatoriT. orive 

meTodiT Sesrulebuli mwkrivad gaSla da msgavsi wevrebis SeerTeba naCvenebia 

nax.6.7_ze. 1 magaliTSi mwkrivad gaSla ganxorcielebulia Symbolics → Collect 

brZanebiT, xolo 2,3,4,5 magaliTebSi _ Symbolic panelis collect operatoriT. 

80

Nnax.6.7. maTematikuri gamosaxulebis mwkrivad gaSla 

da msgavsi wevrebis SeerTeba (collect) 

6.7 polinomis koeficientebis gansazRvra miTiTebuli 

cvladis mimarT (coeffs) 

Tu sawyisi maTematikuri gamosaxuleba polinomia, misi koeficientebis 

gansazRvra SesaZlebelia Symbolics → Polynomial Coefficients brZanebiT (nax.6.8, 

magaliTebi 1,2) an Symbolic panelis coeffs (koeficientebi) operatoriT (nax.6.8, 

magaliTebi 3,4). 

koeficientebis gansazRvra xdeba gamoyofili (miTiTebuli) cvladis 

mimarT. Sedegad miiReba veqtor_sveti, romlis nulovani elementi warmoadgens 

Tavisufali wevris koeficients, xolo bolo – gamoyofili (miTiTebuli) cvladis 

maqsimaluri xarisxis mqone wevris koeficients. 

rogorc Cans me_4 magaliTidan, polinomis koeficientebis gansazRvra 

SeiZleba ganxorcieldes agreTve gamosaxulebis mimarT. 

81

nax.6.8. polinomis koeficientebis gansazRvris 

(coeffs) magaliTebi 

6.8 gantolebebis da utolobebis amoxsna 

miTiTebuli cvladis mimarT (solve) 

gantolebebis da utolobebis amoxsna miTiTebuli cvladis mimarT xdeba 

Symbolics → Variable → Solve brZanebiT an Symbolic panelis solve operatoriT. 

Tu maTematikur gamosaxulebaSi ar Sedis tolobis an utolobis niSani, 

Mathcad_i awarmoebs cvladis iseTi mniSvnelobis moZebnas, romlisTvis sawyisi 

gamosaxuleba utoldeba nuls, winaaRmdeg SemTxvevaSi Cveulebriv amoxsnis 

moyvanil gantolebas. 

nax.6.9_ze (magaliTebi 1,2) moyvanilia Symbolics → Variable → Solve brZanebiT 

gantolebebis amoxsnis magaliTebi, xolo 3,4,5 magaliTebSi gantolebebi da 

utolobebi amoxsnilia ^ Symbolic panelis solve operatoriT, amasTan 2,3 da 5 

magaliTebSi gantolebebi da utolobebi Cawerilia sruli saxiT, xolo 1 da 4 

magaliTebSi nagulisxmevia, rom moyvanili gamosaxuleba udris nuls. 

82

nax.6.9. gantolebebis da utolobebis amoxsnis magaliTebi 

(solve) 

Mathcad_Si SesaZlebelia agreTve gantolebaTa sistemis amoxsna. imisaTvis 

rom amovxsnaT gantolebaTa sistema solve operatoris meSveobiT, unda SevqmnaT 

veqtor_sveti, romlis striqonebSi Caiwereba sawyisi monacemebi gantolebebis an 

utolobebis saxiT. cvladebi, romlis mimarT xdeba amoxsna, aseve Caiwereba 

veqtor_svetis saxiT. pasuxic miiReba veqtor_svetis saxiT. nax.6.10_ze (magaliTebi 

1,2) moyvanilia gantolebaTa sistemis amoxsna solve operatoris meSveobiT, xolo 

magaliTSi 3 _ wrfiv gantolebaTa sistemis amoxsna Given _ Find funqciebiT. 

6.9 gamosaxulebis Casma miTiTebuli cvladis 

Mmagivrad (substitute) 

imisaTvis rom ganvaxorcieloT maTematikuri gamosaxulebis Casma Symbolics 

menius meSveobiT, saWiroa: 

1) avkriboT maTematikuri gamosaxuleba, romliTac unda Seicvalos 

cvladi; 

83

nax.6.10. gantolebaTa sistemis amoxsna 

2) gamovyoT es gamosaxuleba da SevasruloT Edit → Cut an Edit → Copy 

brZaneba. Sedegad gamosaxuleba iqneba Senaxuli buferul mexsierebaSi 

misi amoWriT an amoWris gareSe; 

3) SevitanoT is maTematikuri gamosaxuleba, sadac saWiroa ganvaxorcieloT 

Casma; 

4) gamovyoT (lurji kuTxiT) cvladi, romlis magivrad Caismeba 

gamosaxuleba buferidan; 

5) SevasruloT Symbolics → Variable → Substitute brZaneba. 

Symbolic panelis substitute operatori axorcielebs maTematikuri 

gamosaxulebis Casmas buferidan miTiTebuli cvladis magivrad an, rac gacilebiT 

ufro moxerxebulia, rogorc cvladi, ise Casasmeli gamosaxuleba Caiwereba 

uSualod substitute operatorSi. 

nax.6.11_ze naCvenebia maTematikuri gamosaxulebebis Casmis magaliTebi, 

ganxorcielebuli Symbolics → Variable → Substitute brZanebiT (magaliTebi 1,2) da 

Symbolic panelis substitute punqtis SerCeviT (magaliTebi 3,4,5,6). rogorc Cans me_5 

magaliTidan, simboluri operacia SeiZleba ganxorcieldes miRebuli Sedegis 

mimarT. am dros Cven vxedavT Sualedur Sedegebsac. Tu ramdenime simboluri 

84

operacia miTiTebulia erTdroelad (nax.6.11, magaliTi 4), ekranze davinaxavT 

mxolod saboloo Sedegs. 

nax.6.11. gamosaxulebis Casma miTiTebuli cvladis 

Mmagivrad (substitute) 

6.10 maTematikuri gamosaxulebebis diferencireba 

da integreba 

maTematikuri gamosaxulebebis diferencireba gamoyofili cvladis mimarT 

xdeba Symbolics → Variable → Differentiate brZanebiT. Sedegi iqneba miRebuli simboluri 

saxiT. 

imisaTvis, rom miviRoT meore rigis warmoebuli, saWiroa gavimeoroT 

brZaneba, mesame rigis – gamoviyenoT is kidev erTxel da a.S. 

maTematikuri gamosaxulebebis integreba gamoyofili cvladis mimarT xdeba 

Symbolics → Variable → Integrate brZanebiT. Setanili maTematikuri gamosaxuleba 

integralqveSa funqcias warmoadgens. Sedegad miiReba ganusazRvreli integralis 

mniSvneloba simboluri saxiT. 

85

a Tqma unda, diferencirebis da integrebis operaciebis Sesruleba 

SesaZlebelia agreTve Calculus panelis meSveobiT gamosaxulebis CaweriT da Semdeg 

→ operatoriT. nax.6.12_ze da nax.6.13_ze naCvenebia diferencirebisa da integrebis 

magaliTebi. 

nax.6.12. maTematikuri gamosaxulebebis diferencirebis 

magaliTebi 

6.11 maTematikuri gamosaxulebebis teiloris 

mwkrivad gaSla (series) 

imisaTvis, rom movaxdinoT maTematikuri gamosaxulebebis teiloris 

mwkrivad gaSla Symbolics menius meSveobiT, saWiroa: 

1) SevitanoT maTematikuri gamosaxuleba; 

2) gamovyoT lurji kuTxiT cvladi, romlis mimarT moxdeba mwkrivad 

gaSla; 

3) avirCioT Symbolics → Variable → Expand to Series... brZaneba. 

86

nax.6.13. maTematikuri gamosaxulebebis integrebis 

magaliTebi 

gamoCndeba dialoguri fanjara, romelSic unda mivuTiToT 

aproqsimaciis rigi; 

4) davaWiroT OK Rilaks. 

Tu aproqsimaciis rigi ar iqneba miTiTebuli, Mathcad_i winaswari 

SeTanxmebis Tanaxmad CaTvlis mas 6_is tolad. es niSnavs, rom mwkrivis bolo 

wevris xarisxis maCvenebeli 6_ze naklebia. 

aRvniSnoT, rom Symbolics → Variable → Expand to Series... brZanebiT teiloris 

mwkrivad gaSla xorcieldeba erTi cvladis mimarT, xolo Symbolic panelis series 

operatorSi SeiZleba mivuTiToT ramdenime cvladi. am dros aproqsimaciis rigi 

Tu udris, mag., 8_s, es niSnavs, rom mwkrivis bolo wevris xarisxis maCveneblebis 

jami unda iyos 8_ze naklebi. Tu aproqsimaciis rigi miTiTebuli ar iqneba, 

Mathcad_i CaTvlis mas 6_is tolad. aRsaniSnavia agreTve, rom series operatorSi 

SeiZleba mivuTiToT cvladis ra wertilis midamoSi xdeba teiloris mwkrivad 

gaSla, xolo Tu es informacia ar aris moyvanili, igulisxmeba, rom gaSla xdeba 

cvladis 0 wertilis midamoSi. 

nax.6.14_ze naCvenebia teiloris mwkrivad gaSla Symbolics → Variable → Expand 

to Series... brZanebiT (magaliTebi 1,3) da Symbolic panelis series operatoriT 

87

(magaliTebi 2,4,5). me_5 magaliTSi gaSla ganxorcielebulia X=1 wertilis 

midamoSi, xolo danarCen magaliTebSi _ cvladis 0 wertilis midamoSi. 

nax.6.14. maTematikuri gamosaxulebebis teiloris 

mwkrivad gaSla (series) 

6.12 maTematikuri gamosaxulebebis warmodgena elementaruli 


Symbolics → Variable → Convert to Partial Fraction brZanebiT xdeba maTematikuri 

gamosaxulebis gaSla elementarul nawilebad gamoyofili cvladis mimarT. 

Sedegad miiReba maTematikuri gamosaxuleba, romelic warmoadgens elementaruli 

wiladebis jams. 

igives mivaRwevT Symbolic panelis parfrac operatoriT. Nnax.6.15_ze naCvenebia 

maTematikuri gamosaxulebebis elementarul nawilebad gaSla ganxorcielebuli 

Symbolics → Variable → Convert to Partial Fraction brZanebiT (magaliTi 1) da Symbolic 

panelis parfrac operatoriT (magaliTebi 2,3). 

88

nax.6.15. maTematikuri gamosaxulebebis warmodgena elementaruli 


6.13 matricebis transponireba, Sebruneba da 

determinantis gansazRvra 

Symbolics → Matrix menius aqvs sami punqti: Transpose, Invert, Determinant, 

romlebic xdebian aqtiurni (Sesrulebadi) romelime matricis gamoyofisas. 

matricis transponireba anu striqonebisa da svetebis urTierTSecvla 

xdeba Symbolics → Matrix → Transpose brZanebiT. transponireba xorcieldeba agreTve 

Symbolic panelis M T → operatoriT, Matrix panelis M T operatoriT an klaviaturis 

Ctrl + 1 klaviSebiT. 

Sebrunebuli matrica es aris iseTi matrica, romlis gamravlebiT sawyis 

matricaze miiReba erTeulovani matrica (erTeulovani matrica aris matrica, 

romlis diagonaluri elementebi erTis tolia, xolo danarCeni elementebi 

nulis). Sebrunebuli matrica miiReba Symbolics → Matrix → Invert brZanebiT. igive 

xorcieldeba Symbolic an Matrix panelebis Sesabamisad M _1 → da X _1 operatorebiT 

89

an ^ _ 1 klaviSebis rigrigobiT akrebiT. cxadia, sawyisi matrica unda iyos 

kvadratuli. 

matricis determinantis gansazRvra xdeba Symbolics → Matrix → Determinant 

brZanebiT an Symbolic an Matrix panelebis Sesabamisad |M|→ da |X| operatorebiT. 

SeiZleba agreTve gamoviyenoT | klaviSi. 

aRvniSnoT, rom Tu matrica Seicavs simbolur elementebs, mizanSewonilia 

visargebloT Symbolic panelis M T → , M _1 → da |M|→ operatorebiT, xolo Matrix 

panelis punqtebiT sargeblobisas Sesabamisi punqtis Semdeg saWiroa simboluri 

tolobis niSnis SerCeva. 

nax.6.16_ze naCvenebia matricebis transponirebis, Sebrunebis da 

determinantis povnis magaliTebi. 

nax.6.16. matricebis transponireba, Sebruneba da 

determinantis gansazRvra 

90

6.14 maTematikuri gamosaxulebebis gardaqmnebi 

Mathcad_Si SeiZleba Sesruldes furies pirdapiri da Sebrunebuli 

gardaqmna, laplasis pirdapiri da Sebrunebuli gardaqmna, Z_gardaqmna da 

Sebrunebuli Z_gardaqmna. 

rogorc cnobilia, furies pirdapiri da Sebrunebuli gardaqmna moicema 

formulebiT: 

da 

 

F ( w) 

 

iwt 

f ( t) 

e dt 

 

 

1 

f ( t) 

F w e 

iwt 

( ) dw 

2 

 

mag., rodesac procesi aRwerilia droSi cvladi funqciiT, furies 

pirdapiri gardaqmniT miiReba misi aRwera sixSireze damokidebuli funqciiT da 

piriqiT. 

Mathcad_i asrulebs furies gardaqmnebs gamoyofili cvladis mimarT 

Symbolics → Transform → Fourier da Symbolics → Transform → Inverse Fourier brZanebebiT an 

Symbolic panelis fourier da invfourier operatorebis meSveobiT. 

laplasis pirdapiri da Sebrunebuli gardaqmna moicema formulebiT: 

da 

F( 

S) 

 

f 

 

0 

f ( t) 

e 

91 

St 

dt 

i 

1 

St 

( t) 

F( 

S) 

e dt . 

2 

i 

laplasis pirdapiri da Sebrunebuli gardaqmna gamoiyeneba, mag., 

eleqtronul wredebSi gardamavali procesebis daTvlisas. 

Mathcad_i asrulebs laplasis gardaqmnebs gamoyofili cvladis mimarT 

Symbolics → Transform → Laplace da Symbolics → Transform → Inverse Laplace brZanebebiT 

an Symbolic panelis laplace da invlaplace operatorebis meSveobiT. 

X x , x , x ...) mimdevrobis pirdapiri Z_gardaqmna moicema formuliT: 

( 0 1 2 

x1 

x2 

F ( z) 

x0 

... . 

2 

z z 

.

is asrulebs iseTive rols diskretuli mimdevrobebisaTvis (vTqvaT, 

diskretuli signalebisaTvis), rogorc furies da laplasis gardaqmnebi uwyveti 

funqciebisaTvis. 

Z_gardaqmna SeiZleba Sesruldes uwyveti funqciisaTvisac, romelic 

warmodgenilia Tavisi mniSvnelobebiT sxvadasxva wertilebSi _ damoukidebeli 

cvladis diskretuli bijiT cvlilebisas: 

 

n 

F ( z) 

f ( n) 

z . 

n0 

Sebrunebuli Z_gardaqmna moicema formuliT: 

f 

n 

 

2i 

1 n1 

 

z 

92 

F ( z) 

dz 

Mathcad_i asrulebs pirdapir da Sebrunebul Z_gardaqmnebs gamoyofili 

cvladis mimarT Symbolics → Transform → Z da Symbolics → Transform → Inverse Z 

brZanebebiT an Symbolic panelis ztrans da invztrans operatorebis meSveobiT. 

nax.6.17_ze moyvanilia furies, laplasis da Z pirdapiri da Sebrunebuli 

gardaqmnebis magaliTebi. 

nax.6.17. furies, laplasis da Z_gardaqmnebi 

.

6.15 simboluri gamoTvlebis Sedegebis gamotanis 

stilis dayeneba 

Symbolics → Evaluation Style... brZanebiT gamoiZaxeba Sedegebis gamotanis stilis 

dialoguri fanjara (nax.6.18). 

Nnax.6.18. dialoguri fanjara Evaluation Style 

Evaluation Style dialoguri fanjris Show evaluation steps (gamoTvlebis 

safexurebis Cveneba) ganyofilebaSi gvaqvs gadamrTvelis dayenebis sami varianti: 

Vertically, inserting lines – Sedegebis ganlageba ZiriTadi gamosaxulebis qveS, 

carieli striqonebis CasmiT marjvniv; 

Vertically, without inserting lines – Sedegebis ganlageba carieli striqonebis 

Casmis gareSe; 

Horizontally – Sedegebis ganlageba ZiriTadi gamosaxulebis marjvniv. 

am dialogur fanjaraSi gvaqvs ori alami: 

Show Comments – komentarebis Cveneba; 

Evaluate In Place – adgilze gamoTvla anu sawyisi gamosaxulebis Secvla 

simboluri operaciis SedegiT. 

Nnax. 6.19_ze naCvenebia simboluri gamosaxulebis Sedegebis sxvadasxva stiliT 

gamotanis magaliTebi. 

6.16 cvladebis mniSvnelobebis SezRudva da instrumentTa 

paneli Modifier (modificikacia) 

Symbolic panelis assume punqtiT xdeba cvladis wina mniSvnelobis ignorireba 

da masze SezRudvis daweseba. tipiuri SezRudvebia, mag., 10 , b 5 da sxv. 

qvemoT moyvanil magaliTSi 

93

nax.6.19. simboluri gamoTvlebis Sedegebis gamotanis stili 

simboluri gamoTvla Sesrulebulia im pirobiT, rom namdvili dadebiTi 

ricxvia. 

Symbolic panelis Simplify operatorSi SesaZlebelia cvladebis 

mniSvnelobebze damatebiTi SezRudvebis daweseba, rac xorcieldeba Modifier 

instrumentTa panelis assume, real, RealRange, trig punqtebiT: 

assume punqtiT viziris adgilas Caismeba sityva_gasaRebi cvladis 

mniSvnelobebze SezRudvebis dasawesad; 

real SezRudva niSnavs, rom cvladi namdvili tipisaa; 

RealRange SezRudva gansazRvravs namdvili tipis cvladis 

mniSvnelobaTa ares. mag., c = RealRange(a,b) Canaweri niSnavs, rom c_s 

mniSvnelobebi unda iyos a_s da b_s Soris, sadac a da b namdvili 

ricxvebia an usasruloba; 

trig modifikatori zRudavs gamartivebis process trigonometriuli 

formulebiT (sin 2 (x)+cos 2 (x)=1; cosh(x) 2 _sinh(x) 2 =1). am dros Mathcad_i ar 

xmarobs logariTmebTan, xarisxebTan an radikalebTan dakavSirebul 

formulebs. 

94

aRvniSnoT, rom rodesac gvaqvs SezRudva assume=real, simboluri gamoTvlebi 

Sesruldeba im pirobiT, rom maTematikur gamosaxulebaSi Sesuli yvela 

cvladi namdvili tipisaa, xolo Tu dawesebulia assume=RealRange(a,b) 

SezRudva, simboluri gamoTvlebi Sesruldeba im pirobiT, rom maTematikur 

gamosaxulebaSi Sesuli yvela cvladi namdvili tipisaa da am cvladebis 

mniSvnelobaTa intervalia (a,b). 

nax.6.20_ze moyvanilia Modifier panelis operatorebis magaliTebi. 

nax.6.20. Modifier panelis operatorebi 

6.17 simboluri gamoTvlebis Sedegebis warmodgena 

kompleqsuri ricxvis saxiT da mcocavi wertiliT 

(complex, float) 

Symbolic panelis complex operatoriT simboluri gamoTvlebi Sesruldeba 

kompleqsur areSi da misi Sedegebi Caiwereba kompleqsuri ricxvis saxiT. am 

miznisaTvis SesaZlebelia gamoviyenoT agreTve Symbolics → Evaluate → Complex 

brZaneba. 

95

Symbolic panelis float operatoriT Sedegi Caiwereba mcocavi wertilis saxiT. 

igives miviRebT Symbolics → Evaluate → Floating Point... brZanebiT. 

nax. 6.21_ze moyvanil magaliTebSi Sedegebi warmodgenilia kompleqsuri 

ricxvis saxiT da mcocavi wertiliT Symbolic panelis operatorebis da Symbolics 

menius Sesabamisi brZanebebis gamoyenebiT. 

nax.6.21. simboluri gamoTvlebis Sedegebis warmodgena 

kompleqsuri ricxvis saxiT da mcocavi wertiliT 

96

Tavi VII daformateba Mathcad_Si 

7.1 Format menius da Formatting panelis Semadgenloba 

mTavari menius Format punqtiT an Alt + O klaviSebis kombinaciiT gamoiZaxeba 

Semdegi qvemeniu: 

Equation... (gantoleba) _ maTematikuri gamosaxulebebis daformateba; 

Result... (Sedegi) _ ricxviTi Sedegebis daformateba; 

Text... (teqsti) _ teqstis daformateba; 

Paragraph... (abzaci) _ abzacis daformateba; 

Tabs... (tabulacia) _ tabulaciis poziciebis dayeneba; 

Style... (stili) _ stilis daformateba; 

Properties... (Tvisebebi) _ Tvisebebis dayeneba; 

Graph (grafiki) _ grafikebis daformateba; 

Color (feri) _ ferebis dayeneba; 

Area (ubani) _ ubnebis daformateba; 

Separate Regions _ areebis gancalkeveba; 

Align Regions _ areebis sworeba; 

Repaginate Now _ dokumentis gverdebad xelmeore dayofa. 

(nax.7.1). 

Formatting instrumentTa paneli Sedgeba 3 velisagan da 10 Rilakisagan 

nax.7.1. Formatting instrumentTa paneli 

pirvel siisebur velSi (Style) Cawerilia mimdinare stilis saxeli. Tu 

saWiroa, am velis marjvniv mdebare Rilakis isarze dawkapunebiT SegviZlia 

gavxsnaT stilebis CamonaTvali da avirCioT sasurveli. 

Semdegi veli – Sriftebis siiseburi velia (Font). aq Cawerilia mimdinare 

Sriftis saxeli. am velis marjvniv mdebare Rilakis isarze dawkapunebiT 

gaixsneba Sriftebis CamonaTvali, saidanac survilisamebr airCeva saWiro. 

mesame velSi (Font Size) Cawerilia Sriftis mimdinare zoma. Font Size velis 

marjvniv mdebare Rilakis isarze dawkapunebiT gaixsneba Sriftis zomebis 

CamonaTvali, saidanac SeirCeva sasurveli zoma. 

Bold Rilakze (B) daWeriT CairTveba sqeli moyvanilobis simboloebis 

akrebis reJimi, Italic (I) _ aikribeba daxrili teqsti (kursivi), Underline (U) _ 

aikribeba xazgasmuli teqsti. 

97

Align Left Rilakze daWeriT xdeba abzacis sworeba teqstis aris marcxena 

sazRvarze, Center _ abzacis centrireba anu misi moTavseba sazRvrebs Soris SuaSi, 

Align Right _ abzacis sworeba teqstis aris marjvena sazRvarze. 

Bullets Rilakze daWeriT CairTveba markerebis Casmis reJimi, xolo 

Numbering _ punqtebis numeraciis. Ees ori punqti emsaxureba siebis Seqmnis 

process. siis erTi punqtis akrebis Semdeg Enter klaviSis daWerisas avtomaturad 

gadavalT siis momdevno punqtze. imisaTvis rom davamTavroT siis Seqmnis procesi, 

axal punqtze gadasvlis Semdeg isev davaWiroT Bullets Rilaks an siis bolo 

punqtis akrebis Semdeg orjer davawkapunoT Enter klaviSze. siis Sesaqmnelad 

SesaZlebelia agreTve jer misi punqtebis akreba da moniSvnis Semdeg Bullets an 

Numbering Rilakebze dawkapuneba. 

Superscript (zeda indeqsi) RilakiT simboloebi ganlagdebian striqonis 

zedoneze, xolo Subscript (qveda indeqsi) RilakiT _ qvedoneze. 

7.2 maTematikuri gamosaxulebebis daformateba 

Format → Equation… brZanebiT gamoiZaxeba Equation Format dialoguri fanjara 

(nax.7.2), romelic emsaxureba maTematikuri gamosaxulebebis daformatebas. 

nax.7.2. Equation Format dialoguri fanjara 

maTematikur gamosaxulebaSi Sedian cvladebi, mudmivebi, specialuri 

simboloebi da operatorebi. Mathcad_i iyenebs or maTematikur stils, romelTa 

parametrebi dayenebulia winaswari SeTaxmebiT. es stilebia Variables 

(cvladebisaTvis, simboloebisaTvis da operatorebisaTvis) da Constants 

(ricxvebisaTvis). survilisamebr SeiZleba stilebis parametrebis Secvla. 

Equation Format dialoguri fanjris Style Name (stilis saxeli) velSi iseve 

rogorc Formatting panelis Sesabamis velSi avtomaturad Caiwereba aqtiuri 

obieqtis stilis saxeli: Variables (cvladebi), Constants (mudmivebi) an momxmareblis 

98

mier Seqmnili stilis saxeli. mag., ricxvze dawkapunebis Semdeg am velSi iqneba 

Cawerili Constants. 

obieqtis stilis parametrebis Sesacvlelad: 

1. gamovyoT obieqti da mivceT Format → Equation… brZaneba an gamoviZaxoT 

Equation Format dialoguri fanjara obieqtis gaaqtiurebis gareSe da Style 

Name velis CamonaTvalidan avirCioT sasurveli stili; 

2. gamoviyenoT Modify… Rilaki. gamoCndeba obiqtis dialoguri fanjara, 

romelSic airCeva Srifti, misi moyvaniloba, zoma, feri, simboloebis 

nakrebi da dayendeba survilisamebr alami Underline; 

3. davaWiroT OK Rilaks. 

Sedegad Mathcad_i Secvlis dokumentSi yvela am tipis obieqtis gaformebas. 

nax.7.3_ze moyvanilia dialoguri fanjara Variables. 

nax.7.3. dialoguri fanjara Variables 

maTematikuri gamosaxulebis obieqtebis formatis Secvla SesaZlebelia 

agreTve Formatting panelis daxmarebiT. Mmag., Tu gvsurs mudmivebis formatis 

Secvla, jer gamovyoT ricxvi (an Formatting panelis stilebis CamonaTvalidan 

avirCioT stili Constants), Semdeg davawkapunoT Formatting panelis sasurvel 

Rilakebze. ase SeiZleba SevcvaloT Srifti, misi zoma da moyvaniloba. 

Equation Format dialogis Default Equation Color velis CamonaTvalidan SeirCeva 

garkveuli stilis obieqtebis gaformebis feri. mag., Tu gvsurs maTematikur 

gamosaxulebebs da komentarebs (teqsts) hqondeT gansxvavebuli feri, Default 

Equation Color velis CamonaTvalidan avirCioT sasurveli feri, romliTac iqneba 

gaformebuli, vTqvaT, yvela maTematikuri gamosaxuleba da davaWiroT OK Rilaks. 

99

momxmarebels SeuZlia Seqmnas damatebiTi maTematikuri stilebi. Sedegad 

rogorc Formatting panelis, aseve Equation Format dialoguri fanjris stilebis 

CamonaTvalSi iqneba Sesuli axali stilebis saxelebi. 

ganvixiloT axali stilis Seqmnis procesi. vTqvaT, gvsurs matricebis 

identifikatorebis gaformeba sqeli moyvanilobis xazgasmuli SriftiT. amisaTvis: 

1. gamovyoT elementi, romlisTvisac vqmniT axal stils (Cven magaliTSi 

matricis saxeli) da mivceT Format → Equation… brZaneba an gamoviZaxoT 

Equation Format dialoguri fanjara obieqtis gaaqtiurebis gareSe; 

2. davawkapunoT Style Name velis marjvniv mdebare isarze da gavxsnaT 

stilebis CamonaTvali; 

3. avirCioT maTematikuri stilebis CamonaTvalidan romelime gamouyenebeli 

saxeli (mag., User 1), romelic Caiwereba New Style Name (axali stilis 

saxeli) teqstur velSi; 

4. davayenoT kursori am teqstur velSi da SevcvaloT User 1, vTqvaT, 

Matrix_iT; 

5. davaWiroT Modify… Rilaks da gaxsnil dialogur fanjaraSi davayenoT 

sasurveli maxasiaTeblebi: Bold da Underline; 

6. davaWiroT OK Rilaks Variables dialogur fanjaraSi; 

7. davaWiroT OK Rilaks Equation Format dialogur fanjaraSi. 

Seiqmneba axali maTematikuri stili saxelad Matrix. SemdgomSi SeiZleba 

SevusabamoT axali stili saWiro obieqtebs. 

aRvniSnoT, rom zemoaRwerili moqmedebebiT SeiZleba gamosaxulebis 

calkeul cvladebs an mudmivebs SevusabamoT garkveuli maTematikuri stili, 

magram es ar exeba gamoTvlebis ricxviT Sedegebs, romlis stilia yovelTvis 

Constants. 

dayenebuli stilebis sxva dokumentSi gamosayeneblad saWiroa jer 

SevinaxoT dokumenti rogorc Sabloni anu .mct gafarToebiT, Semdeg ki gavxsnaT 

axali dokumenti Sablonis saxiT da SevavsoT is arCeul SablonSi. 

7.3 ricxviTi Sedegebis daformateba 

gamoTvlebis ricxviTi Sedegis miRebisas Mathcad_i aCvenebs mas winaswari 

SeTanxmebiT gaTvaliswinebul formatSi. am formatis Sesacvlelad davawkapunoT 

gamosaxulebis nebismier adgilas da mivceT Format → Result… brZaneba an 

movaxdinoT ormagi wkapuni gamoTvlebis Sedegze. gamova Result Format dialoguri 

fanjara (nax.7.4), romelic Sedgeba ramdenime CanarTisagan: 

Number Format (ricxvebis formati) CanarTis Format areSi SeirCeva sasurveli 

formati. Number of decimal places (aTobiTi Tanrigebis raodenoba) da 

Exponential threshold (eqsponentis zRurbli) mTvlelebis velebSi winaswari 

100

SeTanxmebiT miTiTebulia 3. saWiroebisamebr SegviZlia es ricxvi 

SevcvaloT. Tu saWiroa, davayenoT almebi: Show trailing zeros (bolo aTobiTi 

Tanrigebis nulebis Cveneba), Show exponents in engineering format (eqsponentebis 

Cveneba inJinrul formatSi). 

nax.7.4. dialoguri fanjara Result Format 

Mathcad_Si arsebobs ricxvis warmodgenis 5 formati: 

o General (zogadi). am formatSi SeiZleba dayendes Tanrigebis raodenoba 

aTobiTi wertilis marjvniv, eqsponentis zRurbli da bolo aTobiTi 

Tanrigebis nulebis Cvenebis reJimi. Tu eqsponentis zRurblis 

mniSvneloba gadametebulia, pasuxi iqneba warmodgenili 

eqsponencialur an inJinrul formatSi. bolo aTobiTi Tanrigebis 

nulebi iqneba naCvenebi mxolod 15 Tanrigis CaTvliT aTobiTi 

wertilis Semdeg; 

o Decimal (aTobiTi). am formatis arCevisas pasuxis warmodgena 

eqsponencialuri formiT ar xdeba. aqac SeiZleba dayendes aTobiTi 

Tanrigebis raodenoba da bolo aTobiTi Tanrigebis nulebis Cvenebis 

reJimi, xolo ricxvis warmodgenis sizustea 15 aTobiTi Tanrigi; 

o Scientific (samecniero anu eqsponencialuri formati) da Engineering 

(inJinruli). am formatebSi pasuxis warmodgena xdeba yovelTvis 

eqsponencialuri formiT. Scientific da Engineering formatebSi Show 

exponents as E 000 almis dayenebiT xarisxis maCveneblis Tanrigebis 

raodenoba gaxdeba 3_is jeradi ricxvi. orive formatSi SeiZleba 

dayendes aTobiTi Tanrigebis raodenoba da bolo aTobiTi Tanrigebis 

nulebis Cvenebis reJimi. 

o Fraction (wiladuri). am formatSi xdeba Sedegis Cveneba wiladis saxiT. 

nax.7.5_ze warmodgenilia cxrili, romelSic moyvanilia ricxvebis 

sxvadasxva formatSi warmodgenis magaliTebi. 

vTqvaT, x=8.25891, y=π*10 5 , z=150 000 000, a=1.25. 

101

x=8.26 

x=8.2589 

x=8.2589100 

General formati, Exponential threshold=15, 

Number of decimal places=2 

Decimal formati, Number of decimal places=4 

Decimal formati, Number of decimal places=7, 

dayenebulia alami Show trailing zeros 

z=1.50x10 8 General formati, Exponential threshold=6, 

Number of decimal places=2, dayenebulia alami Show 

trailing zeros 

y=3.142x10 5 Scientific formati 

y=31.416x10 4 Engineering formati 

x=8.259E+000 

y=31.416E+004 

1 

a= 1 

4 

5 

a= 

4 

Engineering formati, dayenebulia alami 

Show exponents as E 000 

Fraction formati 

Fraction formati, dayenebulia alami 

Use mixed numbers 

nax.7.5. ricxvebis warmodgena sxvadasxva formatSi 

Display Options (Cvenebis ofciebi) CanarTSi SeiZleba mivuTiToT kompleqsuri 

ricxvis warmosaxviTi nawilis warmodgenisaTvis gamosayenebeli aso (i an j), 

aTvlis sistema, Matrix display style siidan SeiZleba avirCioT masivebis Cvenebis 

stili: matricis saxiT (Matrix) an cxrilis saxiT (Table), Expand nested array 

almis gaaqtiurebiT SesaZlebelia rTuli masivebis gafarToebiT Cveneba. im 

SemTxvevaSi, rodesac rTul masivs anu masivs, romlis elementebi Tavis 

mxriv masivebia, matricis forma aqvs da ar aris gaTvaliswinebuli 

gafarToebis SesaZlebloba, ekranze davinaxavT ara TviT masivs Tavis 

elementebiTurT, aramed frCxilebSi Casmul Canawers, romelSic aRniSnulia 

rTuli masivis calkeuli elementebis striqonebisa da svetebis raodenoba. 

nax.7.6_ze naCvenebia rTuli masivis warmodgenis magaliTebi. 

aRvniSnoT, rom imisaTvis, rom davinaxoT cxrilis elementi srulad, 

elementis moniSvnis Semdeg avirCioT konteqsturi meniudan Down One Level 

(erTi doniT dabla) punqti, xolo aragafarToebuli formis aRsadgenad _ 

Up One Level (erTi doniT maRla). 

Tu gvsurs dokumentis yvela masivi iyos naCvenebi matricis an 

cxrilis saxiT anu maTi Cvenebis forma ar iyos damokidebuli masivis 

zomaze (zogadad, Tu matricis an veqtoris striqonebis (svetebis) 

raodenoba 9_s aRemateba, is avtomaturad cxrilis saxiT aris 

warmodgenili), Display Options CanarTSi Sesabamisi miTiTebebis Semdeg saWiroa 

davayenoT Set as Default alami. 

102

Tolerance (daSveba) CanarTSi dayendeba kompleqsuri ricxvis zRurbli 

(Complex threshold) da xdeba imis miTiTeba Tu ra sididis mcire ricxvi unda 

iyos aRqmuli rogorc nuli (Zero threshold). 

Unit Display (sazomi erTeulebis Cveneba) CanarTSi SesaZlebelia sazomi 

erTeulebis wiladis saxiT warmodgenis (Format units) da maTi gamartivebis 

reJimebis (Simplify units when possible) dayeneba. 

nax.7.6. rTuli masivis warmodgenis magaliTebi 

yvela Sedegis parametrebis Sesacvlelad: 

1. davawkapunoT dokumentis cariel adgilas; 

2. mivceT Format Result… brZaneba; 

3. SevcvaloT parametrebi; 

4. OK 

mTel dokumentSi dayendeba Sedegebis Cvenebis axali parametrebi da 

Seicvleba im Sedegebis warmodgenis forma, romelTa formati ar iyo 

individualurad specificirebuli. 

igives mivaRwevT calkeuli Sedegis parametrebis SecvliT da Set as Default 

almis dayenebiT. 

103

7.4 teqstisa da abzacis daformateba 

teqstis daformateba gulisxmobs Sriftis tipis, zomis, moyvanilobis 

stilisa da simboloTa feris SerCevas. 

teqstis daformatebisaTvis gamoiyeneba Formatting panelis Sesabamisi velebi 

da Rilakebi da menius Format → Text… brZaneba (an konteqsturi menius teqstis 

daformatebis punqtebi), romliTac gamoiZaxeba Text Format dialoguri fanjara 

(nax.7.7). 

Text Format dialoguri fanjris Font: velSi SeirCeva teqstis akrebis 

sasurveli Srifti, Font Style: velSi – moyvanilobis stili: Regular (Cveulebrivi), 

Italic (daxrili), Bold (sqeli), Bold Italic (sqeli daxrili), xolo Size: velSi _ 

Sriftis zoma. simboloTa feris arCeva xdeba Color: siiseburi velis 

CamonaTvalidan. Effects areSi gvaqvs almebis jgufi, romelTa dayenebiT SeirCeva 

daformatebis Semdegi reJimebi: Strikeout _ xazgadasmuli teqstis akreba, Underline _ 

xazgasma, Subscript _ qveda indeqsis akreba anu teqstis ganlageba striqonis 

qvedoneze, Superscript _ zeda indeqsis akreba anu teqstis ganlageba striqonis 

zedoneze. Sample areSi aisaxeba SerCeuli Sriftis nimuSi Tavisi maxasiaTeblebiT. 

nax.7.7. teqstis daformatebis dialoguri fanjara 

daformatebis maxasiaTeblebis dayeneba SesaZlebelia rogorc teqstis 

akrebamde, aseve akrebis Semdeg _ moniSnuli fragmentisaTvis. 

Tu Tagvis kursori imyofeba teqstur areSi, SesaZlebeli xdeba ara mxolod 

teqstis, aramed abzacis daformatebac. amas emsaxureba Formatting panelis 

Sesabamisi Rilakebi da Format → Paragraph Format… brZaneba. am brZanebiT da 

104

agreTve konteqsturi menius Paragraph... punqtiT gamoiZaxeba abzacis daformatebis 

dialoguri fanjara (nax.7.8). 

nax.7.8. abzacis daformatebis dialoguri fanjara 

Paragraph Format dialoguri fanjris Indent (wanacvleba, dacileba) 

ganyofilebis Left: (marcxena) da Right: (marjvena) velebSi SeirCeva abzacis yvela 

striqonis dacileba teqstis aris marcxena da marjvena sazRvrebidan. Special: 

velis CamonaTvalSi SeirCeva, xolo By: velSi dayendeba abzacis pirveli 

striqonis (First Line) an danarCeni striqonebis (Hanging) dacileba teqstis aris 

marcxena sazRvridan. standartulad aq gvaqvs reJimi none. wanacvlebis dayeneba 

SesaZlebelia agreTve saxazavis meSveobiT. amisaTvis davawkapunoT abzacis 

nebismier adgilas (an movniSnoT abzaci) da mivceT View → Ruler brZaneba. saxazavis 

zeda isris gadaadgilebiT dayendeba abzacis pirveli striqonis, xolo qveda 

isriT – danarCeni striqonebis dacileba. 

Bullets: velSi airCeva markerebis an cifrebis stili mimdinare da momdevno 

abzacebis siebis saxiT gasaformeblad, xolo Alignment ganyofilebaSi 

gadamrTveli unda iyos CarTuli erT_erT poziciaSi: Left – abzacis sworeba 

teqstis marcxena sazRvarze, Right _ abzacis sworeba teqstis marjvena sazRvarze, 

Center – abzacis centrireba anu misi moTavseba marcxena da marjvena sazRvrebidan 

Tanabari daSorebiT. 

Tabs… (tabulacia) Rilakze dawkapunebiT gamoiZaxeba Tabs dialoguri 

fanjara, sadac SesaZlebelia tabulaciis poziciebis dayeneba (ix. 7.5). 

abzacebis daformateba SesaZlebelia rogorc teqstis akrebamde, aseve 

akrebis Semdeg _ moniSnuli abzacebisaTvis, amasTan erTi abzacis maxasiaTeblebis 

misaTiTeblad sakmarisia movaTavsoT teqsturi kursori abzacis nebismier 

adgilas. 

105

7.5 tabulaciis poziciebis dayeneba 

klaviaturis Tabs klaviSze daWeriT xdeba garkveuli manZiliT kursoris 

poziciis gadaadgileba. tabulaciis poziciis dayeneba xdeba Tabs dialogur 

fanjaraSi, romlis gamoZaxeba SesaZlebelia Format → Tabs… brZanebiT an Paragraph 

Format dialoguri fanjris Tabs… Rilakze dawkapunebiT (nax.7.9). 

Tabs dialogis Tab stop position velSi sasurveli ricxvis Setanis Semdeg unda 

davaWiroT Set (dayeneba) Rilaks, tabulaciis meore poziciisaTvis isev SevitanoT 

ricxvi da davaWiroT Set_s da a.S. 

tabulaciis poziciebis dayeneba SesaZlebelia aseve saxazavis meSveobiT. 

amisaTvis davawkapunoT abzacis nebismier adgilas (an movniSnoT erTi an 

ramdenime abzaci) da mivceT View → Ruler brZaneba. saxazavze dawkapuneba daayenebs 

am adgilas tabulaciis pozicias da saxazavze gamoCndeba Sesabamisi simbolo. Tu 

gvsurs tabulaciis poziciis gadaadgileba, davaWiroT saxazavze tabulaciis 

simbolos da Tagvis marcxena RilakiT Drag and Drop teqnikiT gadavasrialoT 

sasurvel adgilas. 

nax.7.9. Tabs dialoguri fanjara 

aRvniSnoT, rom saxazavze Tagvis marjvena RilakiT dawkapuneba gamoitans 

mis konteqstur menius, romelSic SeirCeva is sazomi erTeuli, romelic iqneba 

gamoyenebuli Mathcad_is dialogebSi: Inches (diumebi), Centimeters (santimetrebi), 

Points (wertilebi) an Picas (piqselebi). 

7.6 stilis daformateba 

teqstur areSi teqstis Setana winaswari SeTanxmebiT xorcieldeba Normal 

(Cveulebrivi) stiliT. survilisamebr SesaZlebelia sxva stilis SerCeva Formatting 

106

panelis stilebis siidan an Text Styles dialogidan, romelSic SevdivarT Format → 

Style… brZanebiT (nax.7.10). 

nax.7.10. Text Styles dialoguri fanjara 

arCeuli stilis modifikaciisaTvis: 

1. mivceT brZaneba Format → Style…; 

2. Styles: velis CamonaTvalidan avirCioT sasurveli stili da davaWiroT 

Modify… Rilaks; 

3. gamoCndeba stilis parametrebis gansazRvris Define Style dialoguri fanjara 

(nax.7.11), romelSic xdeba stilis parametrebis Secvla. 

nax.7.11. Define Style dialoguri fanjara 

Define Style dialoguri fanjris Font... RilakiT SevalT dialogSi, sadac 

SesaZlebelia sxva Sriftis, misi parametrebis da specefeqtebis dayeneba, xolo 

Paragraph... RilakiT SevalT dialogSi, sadac SesaZlebelia wanacvlebis, sworebis 

da abzacis sxva parametrebis Secvla. modifikaciis Semdeg Seicvleba im teqsturi 

areebis gaformeba, sadac es stili iyo gamoyenebuli. 

axali stilis formirebisaTvis: 


2. Text Styles dialogur fanjaraSi davaWiroT New… Rilaks. gamoCndeba Define 

Style dialoguri fanjara (nax.7.11); 

107

3. Name: velSi SevitanoT axali stilis saxeli. Tu axali stilis Seqmnas 

romelime arsebuli stilis safuZvelze vapirebT, Based On: velis 

CamonaTvalidan avirCioT saWiro stili; 

4. Font... da Paragraph... RilakebiT SevideT Sesabamis dialogebSi da davayenoT 

axali stilis sasurveli parametrebi. 

Define Style dialoguri fanjris daxurvisas axali stilis saxels vnaxavT 

stilebis siaSi, amasTan im stilis saxeli, romlis safuZvelze axali stili iyo 

Seqmnili, aseve darCeba siaSi. 

stilis wasaSlelad: 


2. Styles: velis CamonaTvalSi davawkapunoT wasaSlel stilze; 

3. davaWiroT klaviaturis Delete Rilaks. 

7.7 obieqtis Tvisebebis dayeneba 

Mathcad_is obieqtebs: maTematikur gamosaxulebas Tu teqsts, komponents Tu 

ubans _ iseve rogorc Windows 95/XP operaciuli sistemis nebismieri gamoyenebiTi 

programis obieqtebs, gaaCnia Tavisi Tvisebebi, romlebic damokidebulia moniSnuli 

obieqtis tipze. 

avirCioT obieqtad maTematikuri are da Format → Properties… brZanebiT an 

konteqsturi menius Properties… punqtiT gamoviZaxoT Properties dialoguri fanjara 

(nax.7.12), romelic Sedgeba ramdenime CanarTisagan: 

nax.7.12. maTematikuri gamosaxulebis Tvisebebis 

dialoguri fanjara 

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Display CanarTis Highlight Region almis dayenebiT xdeba gamoyofili areebis 

feriT gaformeba. Highlight Region almis dayenebisas gaaqtiurdeba Choose 

Color… (feris SerCeva) Rilaki. masze daWeriT gamoiZaxeba ferTa palitra, 

sadac SeirCeva sasurveli feri. 

Show Border almiT xdeba CarCos dayeneba gamoyofili gamosaxulebis an 

rastris irgvliv. 

Display at Original Size almis dayenebiT xdeba gamosaxulebis an rastris 

Cveneba pirvandel zomebSi. 

Tag (etiketi) velSi SesaZlebelia gamoyofili aris markireba etiketiT, 

romelic warmoadgens asoebis, cifrebis da harebis krebuls, sadac 

dauSvebelia zogi specialuri simboloebi. 

Calculation CanarTis Calculation Options areSi gvaqvs ori alami: Disable Evaluation 

(gamoTvlebis gamorTva) da Enable Optimization (optimizaciis SesaZlebloba). 

Disable Evaluation almis CarTviT gamoyofili maTematikuri are kargavs 

Tavis Tvisebebs da ar monawileobs gamoTvlebSi. programa aRiqvams mas 

rogorc komentars. am dros aris marjvena zeda kideSi Cndeba Savi markeri. 

imisaTvis, rom maTematikuri are gaxdes xelmisawvdomi gamoTvlebisaTvis, 

davawkapunoT masze, Format → Properties… brZanebiT SevideT Properties 

dialogSi, romlis Calculation CanarTSi movxsnaT alami Disable Evaluation an 

gavxsnaT amave aris konteqsturi meniu da avirCioT Enable Evaluation brZaneba. 

Enable Optimization almis CarTva moaxdens gamoyofili maTematikuri aris 

optimizacias. 

Protect CanarTSi SeiZleba davayenoT alami Protect region from editing (aris dacva 

redaqtirebisagan). dacva SeiZleba ganxorcieldes im SemTxvevaSi, Tu 

redaqtirebisagan daculia TviT dokumentic. 

Tu obieqtad arCeulia teqsturi are, Properties dialogi Sesabamisad 

nax.7.13. teqsturi aris Tvisebebis dialogis Text CanarTi 

optimizaciis ganxilva moxdeba 8.7_Si 

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Seicvleba, kerZod, Calculation CanarTis magivrad gveqneba Text CanarTi (nax. 7.13) 

almebiT: Occupy Page Width da Push Regions Down As You Type. 

Occupy Page Width almiT teqsturi are daikavebs gverdis mTel siganes, 

xolo Push Regions Down As You Type almis dayenebiT xdeba beWdvisas areebis qveviT 

Caweva raTa ar moxdes areebis zeddeba. 

Tu obieqtad arCeulia ubani, Format → Properties… brZanebiT gamoviZaxebT 

ubnis Tvisebebis dialogs CanarTebiT: Display, Area da Protect. Area CanarTSi 

SesaZlebelia ubnisaTvis saxelis miniWeba (Area name), ubnis sazRvris (Line), 

miniWebuli saxelis (Name), piqtogramis (Icon) da Caketvis TariRisa da drois 

(Timestamp) Cvenebis reJimebis dayeneba. 

7.8 grafikebis daformateba 

Format → Graph brZanebas aqvs Semdegi qvebrZanebebi: X_Y Plot… (dekartis 

grafiki), Polar Plot… (polaruli grafiki), 3D Plot… (3_ganzomilebiani grafiki), 

Trace… (kvali, traeqtoria) da Zoom… (masStabi). 

dekartis, polaruli da 3_ganzomilebiani grafikebis daformateba iyo 

ganxiluli 5.3 _ 5.8 _Si. 

amisaTvis: 

Trace qvebrZanebiT xdeba traeqtoriis wertilebis koordinatebis amokiTxva. 

1. davawkapunoT grafikis nebismier adgilas; 

2. mivceT Format → Graph → Trace… brZaneba. gamoCndeba Sesabamisi tipis 

grafikis (dekartis an polarulis) traeqtoriis dialoguri fanjara. 

nax.7.14_ze naCvenebia X_Y Trace dialogi; 

nax.7.14. X_Y Trace dialogi 

3. davayenoT Track Data Points alami, romliTac xdeba mxolod uSualod 

traeqtoriaze mdebare (da ara nebismieri) wertilebis koordinatebis 

amokiTxva; 

4. gadavataroT Tagvi im traeqtoriis gaswvriv, romlis wertilebis 

koordinatebis amokiTxva gvsurs. punqtiruli gadajvaredinebuli 

wrfewirebic gadainacvlebian erTi wertilidan meoreze. mimdinare 

110

wertilis X da Y koordinatebi (an radiusis da kuTxis mniSvnelobebi) 

iqneba dafiqsirebuli Sesabamis velebSi (nax.7.15); 

nax.7.15. grafikis wertilebis koordinatebis amokiTxva 

5. Tu davaWerT klaviaturis marjvena an marcxena mimarTulebis klaviSs, 

gadavaadgildebiT traeqtoriis momdevno an wina wertilze, xolo zeda da 

qveda mimarTulebis klaviSebis gamoyenebiT gadavalT sxva traeqtoriebze. 

dafiqsirebuli koordinatebis mniSvnelobebi SeiZleba traeqtoriis 

dialoguri fanjris Copy X, Copy Y (an Copy Radius, Copy Angle) RilakebiT 

gadavitanoT buferul mexsierebaSi. 

ori punqtiruli gadajvaredinebuli wrfewiri darCeba grafikze dialoguri 

fanjris daxurvamde. 

ganvixiloT Format → Graph → Zoom… brZaneba; 

1. movniSnoT grafiki masze TagviT dawkapunebiT; 

2. mivceT Format → Graph → Zoom… brZaneba. gamova nax.7.16_ze moyvanili X_Y 

Zoom dialoguri fanjara (an Polar Zoom _ Tu moniSnuli iyo polaruli 

grafiki); 

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nax.7.16. X_Y Zoom dialoguri fanjara 

3. gamovyoT Tagvis gadaTrevis teqnikiT grafikis is regioni, romlis 

masStabirebas vapirebT. Min: da Max: teqstur velebSi davinaxavT 

gamoyofili regionis X da Y RerZebis koordinatebs (polaruli grafikis 

SemTxvevaSi am tipis grafikis Sesabamis koordinatebs); 

4. davaWiroT Zoom Rilaks. davinaxavT grafiks axali masStabiT. RerZebis 

koordinatebis minimaluri da maqsimaluri mniSvnelobebi iqnebian iseTebi, 

romlebic dafiqsirebulia Min: da Max: velebSi; 

5. Tu gvsurs am masStabis gauqmeba, davaWiroT Unzoom Rilaks; 

6. OK Rilakze daWeriT moxdeba axali masStabis dafiqsireba. 

Tu gvaqvs grafiki, romlis masStabis Secvla ukve moxda, SesaZlebelia 

sawyisi masStabis aRdgena. amisaTvis X_Y Zoom dialogSi davaWiroT Full View 

Rilaks. 

7.9 ferebis dayeneba 

Format → Color brZanebas aqvs Semdegi qvebrZanebebi: 

Background… _ samuSao furclis fonis feris Secvla; 

Highlight… _ gamoyofili areebis feris dayeneba; 

Annotation… _ anotaciis feris dayeneba; 

Use Default Palette _ winaswari SeTanxmebis palitris gamoyeneba; 

Optimize Palette _ palitris optimizacia. 

pirveli sami qvebrZanebiT gamoiZaxeba Sesabamisi dialoguri fanjrebi, 

sadac warmodgenil ferTa palitraSi SevirCevT CvenTvis sasurvel fers da OK 

Rilakis meSveobiT cvlilebas davadasturebT. 

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7.10 ubnebis daformateba 

arsebobs SemTxvevebi, rodesac saWiroa movaxdinoT samuSao furclis ubnis 

Caketva raTa davicvaT Cveni dokumenti (Tundac sxva momxmareblisagan) an SekumSva. 

Format → Area brZanebas aqvs Semdegi punqtebi: Lock… (Caketva), Unlock… (Caketvis 

moxsna), Collaps (SekumSva), Expand (gafarToeba). 

ubnis Casaketad: 

1. davawkapunoT ubnis SigniT; 

2. mivceT Format → Area → Lock… brZaneba. gamoCndeba Lock Area dialoguri 


nax.7.17. ubnis Caketvis dialoguriFfanjara 

3. Tu gvsurs ubnis Caketva paroliT, avkriboT paroli (asoebis, cifrebis da 

sxva simboloebis kombinacia) dialogis pirvel velSi; 

4. parolis Setanis SemTxvevaSi gavimeoroT is Reenter password: velSi; 

5. Collapse when locked almis dayenebiT xdeba Caketili ubnis SekumSva, xolo 

Show lock timestamp almis dayenebiT _ ubnis bolo Caketvis TariRis da 

drois Cveneba; 

6. SekumSuli ubnis dasamalad masze marjvena wkapuniT gamoviZaxoT 

konteqsturi meniu, avirCioT Properties... punqti, SevideT Properties dialogis 

Area CanarTSi, sadac Sesabamisi almebis moxsniT moxdeba ubnis sruli 

damalva; 


Caketili ubnis sazRvrebze davinaxavT boqlomis gamosaxulebas da Caketvis 

TariRsa da dros (Tu Show lock timestamp alami iyo dayenebuli), xolo SekumSul 

ubans winaswari SeTanxmebiT vnaxavT erTi wrfewiris saxiT. 

damalul areze Tagvis gadatarebiT gamoCndeba ori punqtiruli wrfewiri – 

ubnis zeda da qveda sazRvrebi. 

ubnis SesakumSad Caketvis gareSe: 

1. davawkapunoT masze; 

2. mivceT Format → Area → Collapse brZaneba. 

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ubnis Caketvis moxsna Semdegnairad xdeba: 

1. davawkapunoT Caketil ubanze; 

2. avirCioT Format → Area → Unlock… brZaneba (Tu ubani iyo Caketili paroliT, 

saWiroa misi Setana); 


ubnis blokireba moixsneba da SesaZlebeli gaxdeba misi redaqtireba. Tu 

ubani iyo Caketili parolis gareSe, nebismier momxmarebels SeuZlia blokirebis 

moxsna Format → Area → Unlock… brZanebiT. 

amisaTvis: 

SekumSuli ubnis misi pirvandeli saxiT dasanaxad saWiroa misi gafarToeba. 

1. davawkapunoT sazRvris wrfewirze; 

2. avirCioT Format → Area → Expand brZaneba. 

7.11 areebis gancalkeveba da sworeba. 

gverdebis xelmeore numeracia 

areebis urTierTgadafarvis SemTxvevaSi saWiro xdeba maTi gancalkeveba, 

rac Format → Separate Regions brZanebiTExorcieldeba. igives mivaRwevT calkeuli 

areebis individualuri gadaadgilebiTac da, Tu saWiroa, Sesabamis adgilebSi 

damatebiTi striqonebis CasmiT. amasTan ar unda daviviwyoT, rom zogjer Format → 

Separate Regions brZaneba ise gadaadgilebs areebs, rom gamoTvlebis mimdevroba 

Seicvleba, amitom ufro xelsayrelia areebis gancalkeveba movaxdinoT xeliT. 

areebis sworebisaTvis: 

1. gamovyoT areebi; 

2. avirCioT Format → Align Regions → Across brZaneba (sworeba horizontalis 

amisaTvis: 

gaswvriv) an Format → Align Regions → Down (sworeba vertikalis gaswvriv). 

igives mivaRwevT Standard panelis da RilakebiT. 

areebis vertikaluri sworeba SesaZlebelia agreTve saxazavis meSveobiT. 

1. mivceT View → Ruler brZaneba; 

2. davawkapunoT saxazavis im adgilas, romelic areebis marcxena kideebis 

sasurvel daSorebas Seesabameba. saxazavze gamoCndeba tabulaciis simbolo; 

3. tabulaciis simboloze marjvena wkapuni gamoitans konteqstur menius. 

avirCioT Show Guideline punqti. gamoCndeba mwvane vertikaluri xazi, romlis 

adgilmdebareobis Secvla SesaZlebelia tabulaciis simbolos gadaTreviT; 

4. gamovyoT da gadavaadgiloT areebi mwvane xazTan. 

Format → Repaginate Now brZanebiT xdeba dokumentis gverdebad xelmeore 

dayofa. Mathcad_i avtomaturad dayofs dokuments gverdebad ise, rom arc erTi 

are ar gadakveTs gverdis sazRvrebs. 

114

Tavi VIII mTavari menius Tools (instrumentebi) 

punqti 

8.1 mTavari menius Tools punqtis Semadgenloba 

mTavari menius Tools punqtiT an Alt + T klaviSebis kombinaciiT gamoiZaxeba 

Semdegi qvemeniu: 

Spelling... – marTlweris Semowmeba; 

Animation – animaciuri klipebis Seqmna da aRwarmoeba; 

Protect Worksheet... – samuSao furclis dacva; 

Calculate _ gamoTvlebis reJimis dayeneba; 

Optimize _ gamoTvlebis optimizacia; 

Disable Evaluation _ calkeuli maTematikuri aris gaangariSebis procesidan 

gamoricxva; 

Trace Error (Secdomis kvali) – Secdomis wyaros gamovlineba; 

Worksheet Options... _ samuSao furclis ofciebi; 

Preferences… (upiratesobani) _ parametrebis momarTva. 

8.2 marTlweris Semowmeba da koreqtireba 

marTlweris Semowmeba da koreqtireba xdeba Tools → Spelling… brZanebiT an 

Standard panelis Rilakze daWeriT. amisaTvis: 

1. davawkapunoT im adgilas, saidanac gvsurs daviwyoT marTlweris 

Semowmeba. Mathcad_i daiwyebs Semowmebas am adgilidan da gaagrZelebs 

dokumentis bolomde, ris Semdeg SesaZlebelia procesis Sewyveta an 

gagrZeleba dokumentis dasawyisidan; 

2. mivceT Tools → Spelling brZaneba an davaWiroT Standard panelis 

Rilaks. 

Mathcad_i daiwyebs marTlweris Semowmebas, risTvisac iyenebs 

inglisuri enis leqsikons, gamdidrebul maTematikuri terminologiiT da 

momxmareblis personaluri leqsikoniT. Tu dokumentSi aRmoCndeba 

Mathcad_isaTvis ucnobi sityva, gaixsneba Check Spelling (marTlweris 

Semowmeba) dialoguri fanjara (nax.8.1), sadac Not Found: velSi davinaxavT 

am sityvas da Change To: velSi savaraudo cvlilebebis CamonaTvals. Tu 

programa ver gvTavazobs Secvlis rekomendacias, naCvenebi iqneba 

mxolod misTvis ucnobi sityva; 

115

nax.8.1. marTlweris Semowmebis dialoguri fanjara 

3. Tu Secvlis rekomendaciebis CamonaTvali Seicavs sityvis swor variants, 

movniSnoT is, Tu ara _ avkriboT is Change To: velSi. davaWiroT Change 

Rilaks. Suggest Rilaks viyenebT, Tu gvsurs Secvlis damatebiTi, magram 

naklebi albaTobis variantebis daTvaliereba. Tu Mathcad_s ara aqvs 

damatebiTi SeTavazebebi, Suggest Rilaki ar iqneba aqtiuri. 

Tu sityvis Secvla ar gvsurs, viyenebT Ignore (ignorireba) Rilaks. am 

SemTxvevaSi Tu Mathcad_s momavalSi es sityva kidev Sexvdeba, is ar 

iqneba aRqmuli rogorc arasworad dawerili. 

Add RilakiT sityva iqneba Setanili momxmareblis personalur 

leqsikonSi. 

SeiZleba agreTve movaxdinoT marTlweris Semowmeba teqstis gamoyofili 

fragmentisaTvis. 

aRvniSnoT, rom marTlweris Sesamowmeblad SesaZlebelia inglisuris 

sasurveli dialeqtis miTiTeba. amisaTvis Tools → Preferences… brZanebiT SevdivarT 

dialogSi, romlis Language CanarTSi moyvanilia xelmisawvdomi dialeqtebis 

CamonaTvali. 

8.3 animaciuri klipebis Seqmna da aRwarmoeba 

Tools → Animation punqts gaaCnia ori qvebrZaneba: Record… (Cawera) da 

Playback… (aRwarmoeba). 

animaciuri klipebis Sesaqmnelad Mathcad_i iyenebs Frame (kadri) CaSenebul 

cvlads, romelic Rebulobs mTel mniSvnelobebs (winaswari SeTanxmebiT 0_dan 

9_mde bijiT 1). SesaZlebelia ara mxolod grafikebis animacia, aramed yvelafris, 

rac Frame cvladzea damokidebuli. Frame cvladi arsebiTad mimdinare kadris 

nomers warmoadgens. kadrebis mimdevrobiTi aRwarmoeba gansazRvruli siCqariT 

(winaswari SeTanxmebiT – 10 kadri 1 wuTSi) qmnis moZrav gamosaxulebas. 

116

animaciuri klipis Sesaqmnelad: 

1. SevqmnaT gamosaxuleba an gamosaxulebaTa jgufi, romelTa mniSvnelobebi 

saboloo jamSi arian Frame cvladze damokidebuli; 

2. mivceT Tools → Animation → Record… brZaneba. gamoCndeba Record Animation 

dialoguri fanjara (nax.8.2); 

3. punqtiruli marTkuTxediT gamovyoT dokumentis is nawili (nawilebi), 

romelTa animaciur klips vqmniT. Tu klipi iqmneba grafikisaTvis, gamovyoT 

uSualod grafiki (wina gansazRvrebebis gareSe); 

nax.8.2. grafikisaTvis klipis Seqmna 

4. Record Animation dialoguri fanjris For FRAME ganyofilebis From: da To: 

cifrul velebSi ganvsazRvroT FRAME cvladis mniSvnelobebis qveda da 

zeda sazRvrebi, xolo At: velSi – kadrebis aRwarmoebis siCqare; 

5. davaWiroT Animate Rilaks. daiwyeba klipis Seqmnis procesi. dialoguri 

fanjris SuaSi – daTvalierebis zonaSi – gamoCndeba dokumentis 

gamoyofili nawilebis miniaturuli gamosaxuleba. daTvalierebis zonaSi 

davinaxavT yovel axal Seqmnil kadrs warweriT zonis qveviT (mag., FRAME 

=5), romelic aCvenebs mimdinare kadris nomers. 

117

aRvniSnoT, rom axali kadrebis gamoCenis siCqare ar aris damokidebuli 

dialogis At: velSi miTiTebul cifrze, radgan Animation RilakiT xdeba 

kadrebis Seqmna da ara aRwarmoeba; 

6. Seqmnili animaciuri klipis Sesanaxad davaWiroT Save As… Rilaks. 

gamoCndeba dialoguri fanjara, romelSic Sesatania klipis saxeli da 

asarCevia saqaRalde, sadac is iqneba ganlagebuli. 

klipi Seinaxeba gafarToebiT .avi (Audio_Video Interleaved) da misawvdomi iqneba 

Windows operaciuli sistemis garemos yvela programisaTvis. 

animaciuri klipebi xSirad moiTxoven did mexsierebas, amitom maTi Senaxva 

xdeba SekumSuli formiT. Record Animation dialoguri fanjris Options… Rilakze 

daWeriT gamoiZaxeba dialogi, romelSic SesaZlebelia SekumSvis meTodis SerCeva. 

aRvniSnoT, rom grafikebis animaciis Seqmnis dros umjobesia gamovrToT 

grafikebis avtomaturi masStabirebis parametrebi da davayenoT Sesabamisi 

parametrebi xeliT, radgan avtomaturi masStabirebisas grafikis zomebi xSirad 

icvleba naxtomisebr FRAME cvladis diskretuli mniSvnelobebis Sesabamisad. 

rogorc ki animaciuri klipis Seqmna damTavrdeba, gamoCndeba Play Animation 

(animaciis aRwarmoeba) fanjara, romelSic Cans klipis pirveli kadri (nax.8.3). 

nax.8.3. animaciis aRwarmoebis fanjara 

Seqmnili animaciuri klipis aRwarmoebisaTvis davawkapunoT fanjris 

marcxena qveda kuTxis isarze. 

dialogis meore Rilaki (isris marjvniv) warmoadgens aRwarmoebis marTvis 

Rilaks. masze daWeriT gamoCndeba Semdegi meniu: 

View (xedi) _ klipis fanjris zomis marTva. menius am punqts aqvs 

qvepunqtebi: Half Size (fanjris zomis ganaxevreba), Normal Size (Cveulebrivi 

zoma), Double Size (ormagi zoma); 

Speed (siCqare) – sasurveli siCqare dayendeba mcocis meSveobiT; 

Open… – avi–failebis gaxsnis dialogis gamotana; 

Close – mimdinare fanjris daxurva; 

Copy – buferul mexsierebaSi kopireba; 

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Configure... (konfiguraciis dayeneba) – dialoguri fanjris gamoZaxeba, 

romelSic xdeba daTvalierebis reJimis dayeneba – mTel ekranze an 

garkveuli zomis fanjaraSi; 

Command… (brZaneba) – marTva brZanebaTa striqonidan. 

nebismieri arsebuli animaciuri klipis aRwarmoebisaTvis: 

1. mivceT Tools → Animation → Playback… brZaneba. gamoCndeba Play Animation 

dialogi, romelic jer SekumSulia, radgan ar aris gaxsnili avi_faili; 

2. aRwarmoebis marTvis dialogSi meore Rilakis menius Open… punqtze 

dawkapunebiT gavxsnaT Open File dialoguri fanjara, sadac avirCioT saWiro 

avi_faili; 

3. davaWiroT Play Animation dialogis pirvel Rilaks. 

aRvniSnoT, rom Tu dokumentSi iyo damyarebuli hiperlinki avi_failTan an 

Casmuli avi_failis iarliyi, iarliyze an hipermimarTvaze orjeradi dawkapunebiT 

moxdeba animaciuri klipis aRwarmoeba. 

8.4 samuSao furclis dacva 

dokumentis dacvisaTvis avirCioT Tools → Protect Worksheet... brZaneba. gamova 

Protect Worksheet dialoguri fanjara (nax.8.4). 

nax.8.4. Protect Worksheet dialogi 

Protect Worksheet dialoguri fanjris Protection Level ganyofilebaSi arsebuli 

gadamrTvelebidan avirCevT sasurvels: 

File – failis sruli dacva. am dros SeuZlebelia failis sxva gafarToebiT 

Senaxva; 

Content _ arsebuli areebis, ubnebis, teqsturi velebis dacva. SesaZlebelia 

axali monacemebis Seyvana da daculi areebis kopireba; 

Editing – samuSao furclis dacva redaqtirebisagan. am dros SeuZlebelia 

redaqtireba, kopireba da axali areebis Seqmna. 

119

Password (optional): velSi avkriboT sasurveli paroli. Reenter password: velSi 

gavimeoroT paroli da OK RilakiT davafiqsiroT Sesrulebuli moqmedebebi. 

Tu gvsurs dokumentis dacvis moxsna, avirCioT Tools → Unprotect Worksheet... 

brZaneba. Tu dacva gvqonda paroliT, unda avkriboT Sesabamisi sityva, ris Semdeg 

dokumentis dacva moixsneba. 

8.5 gamoTvlebis reJimebi 

winaswari SeTanxmebiT Mathcad_i muSaobs gamoTvlebis avtomatur reJimSi, 

rac niSnavs, rom yvelanairi angariSi da gardaqmna sruldeba myisierad, xolo 

nebismieri Secvla gamoiwvevs xelaxal gadaangariSebas. xelaxali gadaangariSeba 

xdeba mxolod dokumentis xiluli nawilisaTvis, xolo momdevno maTematikuri 

gamosaxulebebi dokumentis qveviT gadaadgilebisamebr gamoiTvleba manam mTeli 

samuSao furceli ar ganaxldeba. rodesac angariSebis dasamTavreblad programas 

dro sWirdeba, Tagvis maCvenebeli Seicvlis formas da furclis qveviT 

Setyobinebis striqonSi gamoCndeba sityva “Wait” (daicade). 

avtomaturi reJimis CarTva_gaTiSva xdeba Tools → Calculate → Automatic 

Calculation brZanebiT, romelic arsebiTad alams warmoadgens. 

roca avtomaturi reJimi gamorTulia, Mathcad_i muSaobs xeliT gamoTvlebis 

reJimSi (Manual Mode) . am dros gamoTvlebi ar sruldeba specialuri brZanebis 

miRebamde da momxmarebels ar sWirdeba angariSebis damTavrebis lodini. Tu 

xeliT gamoTvlebis reJimSi movaxdineT cvlilebebi, romelnic gamoiwveven 

ganaxlebis aucileblobas, Setyobinebis striqonSi wavikiTxavT “Calc”. amiT 

Mathcad_i gvaxsenebs, rom saWiroa ekranze gamosaxuli Sedegebis ganaxleba. 

Tools → Calculate → Calculate Now brZanebiT (an F9 klaviSiT an Standard panelis 

= RilakiT) xdeba gamoTvlebis ganaxleba, magram gadaangariSdeba mxolod 

dokumentis xiluli nawili. dokumentis qveviT gadaadgilebiT Setyobinebis 

striqonSi isev gamoCndeba “Calc” anu axali gamosaxulebebis gamosaTvlelad isev 

saWiro gaxdeba Tools → Calculate → Calculate Now brZaneba. 

xeliT gamoTvlebis reJimSi sifrTxiliT unda visargebloT beWdvis 

brZanebiT, radgan dokumentis nawili SeiZleba iyos ganaxlebuli, nawili ki – ara. 

Tu gvsurs movaxdinoT mTeli dokumentis gadaangariSeba, unda visargebloT 

Tools → Calculate → Calculate Worksheet (Ctrl + F9) brZanebiT. 

gamoTvlebis Sesawyvetad viyenebT Esc klaviSs. gamoCndeba dialoguri 

fanjara, sadac OK–ze daWeriT vadasturebT Sewyvetas. maTematikur 

gamosaxulebaze davinaxavT saTanado Setyobinebas. gamoTvlebis gasagrZeleblad 

davawkapunoT am gamosaxulebaze da davaWiroT F9 klaviSs an Standard panelis = 

Rilaks. 

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8.6 calkeuli maTematikuri aris gaangariSebis 

procesidan gamoricxva 

gamoTvlebis dros SesaZlebelia calkeuli maTematikuri aris 

gaangariSebis procesidan gamoricxva. amis gansaxorcieleblad arsebobs ramdenime 

saSualeba: 

davawkapunoT maTematikur areSi, Format → Properties… brZanebiT SevideT 

Properties dialogSi, romlis Calculation CanarTSi davayenoT Disable Evaluation 

alami (ix. 7.7); 

davawkapunoT maTematikur areSi da mivceT Tools → Disable Evaluation brZaneba, 

romelic arsebiTad alams warmoadgens; 

maTematikuri aris konteqsturi meniudan avirCioT Disable Evaluation punqti. 

8.7 gamoTvlebis optimizacia 

simboluri da ariTmetikuli gamoTvlebi Mathcad_Si erTmaneTisagan 

damoukideblad sruldeba sxvadasxva procesorebis mier. imisaTvis, rom am orma 

procesorma erTianad miiRon monawileoba gamoTvlebis procesSi, saWiroa 

movaxdinoT gamoTvlebis optimizacia. optimizacia mdgomareobs imaSi, rom jer 

simboluri procesori axdens maTematikuri gamosaxulebis gamartivebas, xolo 

Semdeg iwyeba miRebuli gamartivebuli gamosaxulebis ricxviTi gamoTvla. 

Tools → Optimize brZanebas aqvs sami qvebrZaneba: 

Equation _ maTematikuri gamosaxulebis optimizacia; 

Worksheet _ samuSao furclis optimizacia; 

Show optimization _ optimizaciis Sedegad miRebuli gamartivebuli 

gamosaxulebis Cveneba. 

nax.8.5_ze moyvanilia gamoTvlebis optimizaciis magaliTi. 

SeviyvanoT monacemebi. davawkapunoT gamosaxulebaze da mivceT Tools → 

Optimize → Equation brZaneba an am gamosaxulebis konteqsturi meniudan avirCioT 

Optimize punqti. Tu Mathcad_i “moZebnis” gamosaxulebis gamartivebul formas, mis 

marjvniv gamoCndeba wiTeli varskvlavi (rogorc naCvenebia nax.8.5_ze moyvanil 

magaliTSi), sawyisi gamosaxuleba Seicvleba gamartivebuliT (ara vizualurad, 

aramed programis “SigniT”) da gamoiTvleba gamartivebuli gamosaxuleba. 

Tu gvsurs gamartivebuli gamosaxulebis daTvaliereba, davawkapunoT masze 

Tagvis marjvena RilakiT da avirCioT Show Optimization punqti an davawkapunoT 

gamosaxulebaze da mivceT Tools → Optimize → Show Optimization brZaneba. gamoCndeba 

Optimized Result fanjara, sadac iqneba Cawerili gamartivebuli gamosaxuleba. 

swored am gamartivebuli gamosaxulebis gamoTvliT miiReba ricxviTi Sedegi. ra 

Tqma unda, igive Sedegs miviRebT optimizaciis gareSec, magram rTuli 

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gamosaxulebebis SemTxvevaSi optimizacia sagrZnoblad amcirebs gamoTvlebis 

xangrZlivobas. 

nax.8.5. gamoTvlebis optimizaciis magaliTi 

Tu Mathcad_ma ver SeZlo sawyisi gamosaxulebis gamartiveba, mis marjvniv 

gamoCndeba lurji varskvlavi. 

Tools → Optimize → Worksheet brZanebiT, romelic arsebiTad alams 

warmoadgens, xdeba optimizaciis reJimis dayeneba_moxsna mTeli dokumentisaTvis. 

Tu samuSao furclis optimizaciis reJimi dayenebulia, calkeuli gamosaxuleba 

SeiZleba gamovricxoT optimizaciis procesidan konteqsturi meniudan Optimize 

punqtis SerCeviT. 

8.8 Secdomis wyaros gamovlineba 

Tu Mathcad_i ver agrZelebs gamoTvlebs raRaca Secdomis gamo, is wiTlad 

gaaferadebs Sesabamis adgils, xolo gamosaxulebaze dawkapunebiT gamoitaneba 

Setyobineba Secdomis tipis mokle aRweriT (nax.8.6). 

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nax.8.6. Secdomis wyaros gamovlineba 

rogorc vxedavT magaliTidan, Secdoma gamoaSkaravda meoTxe 

gamosaxulebaSi, magram is warmoiSva g(x) funqciaSi, sadac moxda 0_ze gayofa. 

momxmarebels SeuZlia TviTon gamoavlinos Secdomis warmoSobis wyaro an 

miandos es procedura Mathcad_s. amisaTvis: 

1. davawkapunoT gamosaxulebaze, romelSic gamovlinda Secdoma, da mivceT 

Tools → Trace Error brZaneba. gamoCndeba Trace Error fanjara (nax.8.7); 

nax.8.7. Trace Error fanjara 

2. Trace Error fanjaraSi aris 4 Rilaki, romelTa meSveobiT xdeba SecdomasTan 

dakavSirebuli erTi gamosaxulebidan meoreze gadaadgileba. es Rilakebia: 

|| (bolo). |

Rilakis gamoyenebiT xdeba im gamosaxulebaSi gadasvla, romelSic 

warmoiSva Secdoma. 

8.9 samuSao furclis ofciebi 

Tools → Worksheet Options… brZanebiT gaixsneba Worksheet Options dialoguri 

fanjara (nax.8.8) Semdegi CanarTebiT: 

Built-In Variables _ CaSenebuli cvladebi; 

Calculation _ gamoTvla; 

Display _ displei; 

Unit System _ erTeulTa sistema; 

Dimensions _ ganzomilebebi. 

nax.8.8. Worksheet Options dialoguri fanjara 

Built-In Variables CanarTSi xdeba sistemuri cvladebis: ORIGIN (veqtorebis da 

matricebis sawyisi indeqsi, winaswari SeTanxmebiT udris 0); Convergence Tolerance 

(TOL) (ricxobrivi gamoTvlebis cdomileba, winaswari SeTanxmebiT udris 0.001); 

Constraint Tolerance (CTOL) (SezRudvebze daSveba, winaswari SeTanxmebiT udris 0.001) 

da sxv. _ mniSvnelobebis Secvla, ris Semdeg rekomendirebulia mivceT Tools → 

Calculate → Worksheet brZaneba raTa davrwmundeT, rom dokumentis yvela 

maTematikuri gamosaxuleba gamoTvlilia CaSenebuli cvladebis axali 

mniSvnelobebisaTvis. 

Calculation CanarTSi SeiZleba davayenoT ori alami: 

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Recalculate automatically – avtomaturi gadaangariSeba; 

Optimize expression before calculating – optimizaciis reJimis dayeneba. 

Tools → Worksheet Options → Display CanarTSi SesaZlebelia zogi 

operatorisaTvis sxva misi aRmniSvneli simbolos daweseba. es operatorebia: 

lokaluri da globaluri miniWeba, muqi toloba, gamravleba da gayofa. am 

operatorebis simboloebis Secvla calkeuli maTematikuri gamosaxulebisaTvis 

SesaZlebelia Sesabamisi simbolos konteqsturi meniudan. 

Unit System CanarTSi xdeba erTeulTa sistemis SerCeva ganzomilebis mqone 

sidideebisaTvis: SI, MKS, CGS, US customary (aSS_s sistema), None. winaswari 

SeTanxmebiT Mathcad_i iyenebs SI sistemas. 

Dimensions CanarTSi Display Dimensions almiT xdeba masis (Mass), sigrZis 

(Length), drois (Time), temperaturis (Temperature), ganaTebulobis (Luminosity), denis 

(Current) da nivTierebis raodenobis (Substance) ganzomilebebis Cvenebis reJimis 

dayeneba_moxsna. 

8.10 parametrebis momarTva 

Tools → Preferences… brZanebiT xdeba Preferences dialoguri fanjris 

gamoZaxeba, romelsac aqvs oTxi CanarTi: General, HTML Options, Script Security da 

Language (nax.8.9). 

nax.8.9. Preferences dialoguri fanjara 

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General CanarTis ganyofilebebia: 

o Startup Options (sastarto ofciebi), sadac SeiZleba davayenoT alami 

Show Mathcad tips at startup _ programis gaSvebisas sasargeblo rCevebis 

Cveneba; 

o Keyboard Options (klaviaturis ofciebi) 2 almiT: Standard Windows 

shortcut keys _ standartuli swrafmoqmedebis klaviSebis gamoyeneba da 

Context_sensitive equal signs _ konteqstis mimarT mgrZnobiare 

Semoklebebis gamoyeneba; 

o Default Worksheet Location (winaswari SeTanxmebiT dokumentis Senaxvis 

adgili), sadac Browse… RilakiT SesaZlebelia arsebuli Senaxvis 

adgilis Secvla; 

o Recently Used Files (bolos gamoyenebuli failebi), sadac misaTiTebelia 

bolos gamoyenebuli failebis raodenoba, romlebsac vnaxavT File 

menius CamonaTvalSi; 

o Undo History (istoriis gauqmeba), sadac Maximum number of undoable actions 

per document: velSi xdeba dokumentSi gauqmebul moqmedebaTa 

maqsimaluri ricxvis miTiTeba; 

HTML Options CanarTSi xdeba Mathcad_is dokumentis .html gafarToebis mqone 

failebis ofciebis SerCeva; 

Script Security CanarTSi SesaZlebelia Script_obieqtebis anu momxmareblis mier 

Casmuli komponentebis dacvis ofciis SerCeva; 

Language CanarTSi xdeba marTlweris leqsikonis dialeqtis SerCeva. 

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Tavi IX mTavari menius Window (fanjara) 

punqti 

9.1 mTavari menius Window punqtis Semadgenloba 

rogorc yvela programas, romelic muSaobs Windows operaciuli sistemis 

garemoSi, Mathcad_sac gaaCnia momxmareblisTvis moxerxebuli mravalfanjriani 

interfeisi. 

Mathcad_Si SesaZlebelia vimuSaoT erTdroulad ramdenime dokumentTan, 

romlebic programis CatvirTvis Semdeg iyvnen gamoyenebulni. maT Soris erT_erTi 

aqtiuria. danarCenebis gaaqtiureba nebismier momentSi SesaZlebelia. 

fanjrebTan muSaoba xdeba mTavari menius Window punqtis meSveobiT, 

romelic Sedgeba Semdegi qvepunqtebisagan: 

Cascade – dokumentis fanjrebis kaskaduri ganlageba; 

Tile Horizontal _ dokumentis fanjrebis horizontaluri ganlageba; 

Tile Vertical _ dokumentis fanjrebis vertikaluri ganlageba. 

am qvepunqtebis garda, Window menius qveda nawilSi moyvanilia programis 

CatvirTvis Semdeg gamoyenebuli dokumentebis sia. SesaZlebelia siis nebismieri 

dokumentis gaaqtiureba. 

Window punqtis qvepunqtebis gamoZaxeba xdeba agreTve klaviaturis Alt + W 

klaviSebis kombinaciiT. 

9.2 fanjrebis kaskaduri ganlageba 

(Cascade) 

Window → Cascade brZaneba dokumentebis fanjrebs kaskadurad ganalagebs. 

kaskaduri ganlagebisas fanjrebi ganTavsdebian Tanmimdevrulad, erTimeoris 

nawilobrivi gadafarviT. sxva fanjrebze zemoT ganlagebuli fanjara Cans 

mTlianad da aqtiuria. yvela dokumentis saTauris striqoni xilulia (nax.9.1). 

aseT mdgomareobaSi SesaZlebelia fanjrebis minimizacia, zomebis Secvla da 

daxurva saTauris striqonis marjvena kideSi arsebuli Sesabamisi Rilakebis 

gamoyenebiT. 

kaskaduri ganlageba moxerxebulia bevr fanjarasTan erTdrouli muSaobis 

dros maTi gadarTvisaTvis. GgadarTva da sxva fanjris gaaqtiureba xdeba 

saTauris striqonze dawkapunebiT. 

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nax.9.1. fanjrebis kaskaduri ganlageba 

9.3 fanjrebis horizontaluri da vertikaluri ganlageba 

(Tile Horizontal, Tile Vertical) 

Window → Tile Horizontal brZaneba dokumentebis fanjrebs horizontalurad 

ganalagebs (nax.9.2), xolo Window → Tile Vertical brZaneba dokumentebis fanjrebs 

ganalagebs vertikalurad (nax.9.3), amasTan rogorc horizontaluri, ise 

vertikaluri ganlagebis dros yvela fanjris zoma erTi da igive iqneba. 

rac ufro metia fanjrebis raodenoba ekranze, miT ufro mcirea maTi zoma 

da Sesabamisad miT ufro mcirea fanjrebSi moTavsebuli dokumentebis xiluli 

nawili. amitom am brZanebebis gamoyeneba mizanSewonilia ori_sami fanjris 

SemTxvevaSi. 

fanjrebis horizontaluri da vertikaluri ganlagebisas moxerxebulia 

erTi Ffanjridan meoreSi obieqtebis kopireba_gadatana rogorc Edit → Copy, Edit 

→ Cut, Edit → Paste brZanebebiT (an konteqsturi menius igive punqtebiT an Standard 

128

instrumentTa panelis Sesabamisi RilakebiT), aseve Drag and Drop teqnikiT Tagvis 

meSveobiT. 

Tu gvaqvs fanjrebis didi raodenoba, Mathcad_i uars ityvis damatebiTi 

dokumentebis gaxsnaze da gamoitans sainformacio Setyobinebas amis Taobaze. 

muSaobis gasagrZeleblad saWiroa nawili fanjrebis daxurva Sesabamisi 

fanjrebis saTauris striqonze mdebare daxurvis RilakiT an saTauris striqonis 

konteqsturi menius Close brZanebiT. 

nax.9.2. fanjrebis horizontaluri ganlageba 

9.4 dokumentebis fanjrebis marTva 

garda 9.1_Si moyvanili mTavari menius Window punqtis qvebrZanebebisa, 

dokumentebis fanjrebTan muSaoba SesaZlebelia sxva gziTac. 

rogorc ukve iTqva, programis CatvirTvis Semdeg momxmareblis mier yvela 

gamoyenebuli dokumenti dafiqsirdeba Sesabamisi saTauris saxiT mTavari menius 

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nax.9.3. fanjrebis vertikaluri ganlageba 

Window punqtSi, saidanac advilad SesaZlebelia sasurvel momentSi romelime 

maTganis gaaqtiureba. aqtiuri dokumentis saxels CarTuli aqvs alami. aqtiuri 

dokumentis fanjaraze SesaZlebelia vimoqmedoT menius striqonis marjvena kideSi 

arsebuli RilakebiT (minimizaciis, fanjris zomis Secvlis da fanjris daxurvis). 

aqtiuri dokumentis daxurva SesaZlebelia agreTve File → Close brZanebiT. 

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Tavi X sainformacio resursebi. mTavari 

menius Help punqti 

10.1 mTavari menius Help (daxmareba) punqtis Semadgenloba 

mTavari menius Help punqti gvexmareba Mathcad_is yvela SesaZleblobis 

gamoyenebaSi. is Sedgeba Semdegi qvepunqtebisagan: 

Mathcad Help F1 _ sacnobaro sistemis gamoZaxeba; 

What’s This? (ra aris es?) Shift +F1 – daxmareba miTiTebuli Temis 

Sesaxeb; 

Developer’s Reference – ganmviTareblebTan mimarTva; 

Author’s Reference – avtorebTan mimarTva; 

Tutorials _ Mathcad_Tan muSaobis TviTmaswavlebeli; 

QuickSheets _ Mathcad_is gamoyenebis magaliTebi; 

Reference Tables _ maTematikuri formulebis da cxrilebis sruli 

cnobari; 

E_books _ eleqtronuli wignebi; 

User Forum – momxmarebelTa forumi; 

Mathcad.com – Web_misamarTze gadasvla; 

Mathcad Update – Mathcad_is ganaxleba; 

About Mathcad... – mokle informacia Mathcad_is Sesaxeb. 

aqve aRvniSnoT, rom menius am punqtebTan muSaoba moiTxovs inglisuri enis 

sabazo codnas. 

10.2 Mathcad_is sacnobaro sistema 

sacnobaro sistema warmoadgens did monacemTa bazas, romelic moculobiT 

aRemateba eleqtronul wigns. sacnobaro sistemis da eleqtronuli wignebis 

daniSnuleba erTmaneTisagan gansxvavebulia. eleqtronuli wigni Mathcad_Si 

warmoadgens Tematikurad gaerTianebuli dokumentebis erTobliobas, romlebic 

exeba sistemis gamoyenebis sxvadasxva sferos da dakavSirebuli arian erTmaneTTan 

hiperlinkebiT. 

sacnobaro sistema Seicavs sistemasTan muSaobis yvela mniSvnelovani 

sakiTxis srul da detalur informacias. 

sacnobaro sistemis gamoZaxeba SesaZlebelia: 

menius Help → Mathcad Help brZanebiT; 

klaviaturidan F1 funqcionaluri klaviSiT; 

131

Standard instrumentTa panelis RilakiT. 

samive SesaZleblobis gamoyenebiT gamodis daxmarebis dialoguri fanjara 

(nax.10.1), romelic Sedgeba sami CanarTisagan: Contents (Semadgenloba), Index 

(sagnobrivi saZiebeli) da Search (Zieba): 

nax.10.1. Mathcad Help dialoguri fanjara 

Contents CanarTi warmodgenilia wignebis katalogis saxiT. yovel wigns 

gaaCnia Tavisi dasaxeleba da is Tavis mxriv Sedgeba qvesaTaurebisagan. mag., 

Tu gvainteresebs Mathcad_Tan muSaobis dawyeba, avirCioT Sesabamisi wigni 

(Getting Started), davawkapunoT mis marcxniv arsebul Rilakze da SevarCioT 

sasurveli qvesaTauri (nax.10.2). fanjris marjvena areSi ganTavsdeba arCeuli 

qvesaTauris Temis aRwera; 

Index CanarTSi moyvanilia terminebis da funqciebis CamonaTvali. 

informaciis mopoveba xdeba sagnobrivi miTiTebiT. Type in the keyword to find: 

teqstur velSi Caiwereba mosaZebni Temis dasaxeleba an dasaxelebis nawili. 

sasurvel Temaze ormagi wkapuniT an misi moniSvniT da Display Rilakze 

daWeriT fanjris marjvena areSi gamoitaneba arCeuli Temis aRwera; 

Search CanarTSi Type in the keyword to find: teqstur velSi mosaZebn 

informaciasTan dakavSirebuli sityvis SetaniT gamoitaneba yvela Tavebi, 

sadac naxsenebia miTiTebuli sityva. aseTi tipis Zieba gvaZlevs ufro 

farTo saSualebebs mivagnoT sasurvel Temas. 

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nax.10.2. Mathcad Help dialogi arCeuli qvesaTauris Temis ganxilviT 

mTavari menius Help → What’s This? brZanebis gamoyenebisas kursors eZleva 

kiTxvis niSnis simbolos forma, ris Semdeg SeiZleba menius brZanebebidan an 

instrumentTa panelidan avirCioT sasurveli Tema da davawkapunoT masze. miviRebT 

daxmarebas am Temis Sesaxeb. Help → What’s This? brZaneba warmoadgens informaciis 

mopovebis martiv da moxerxebul formas. 

mTavari menius Help → Developer’s Reference da Help → Autor’s Reference 

brZanebebiT SesaZlebelia eleqtronul biblioTekasTan dinamiuri kavSiris 

damyareba, sxva maTematikur sistemebTan mimarTva, gamoqveynebuli eleqtronuli 

publikaciebis avtorebTan dakavSireba da a.S. 

10.3 sainformacio resursebis gamoyeneba (Resource Center) 

sainformacio resurs_centri warmoadgens mZlavr monacemTa bazas, romelic 

aerTianebs eleqtronul wignebs, sistemis Seswavlis sawyis sakiTxebs, swraf 

magaliTebs, sistemis SemqmnelTa Web_biblioTekasTan kavSirs da a.S. 

menius Help → Tutorials (Help → QuickSheets, Help → Reference Tables) brZanebiT 

gamoiZaxeba Mathcad_is resursebis fanjara. Home Rilakze daWeriT gamoitaneba 

resurs_centrSi Semavali Tematikis CamonaTvali (nax.10.3), romelTa gaaqtiureba 

SesaZlebelia maTze dawkapunebiT. 

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nax.10.3. resurs_centris fanjara 

resurs_centris gamoZaxebisTanave aqtiurdeba Resources instrumentTa 

paneli, sadac siis saxiT warmodgenilia yvela masSi Semavali Tematika (nax.10.4). 

nax.10.4. Resources instrumentTa paneli 

resurs_centris TematikebTan muSaobaSi gvexmareba Mathcad_is resursebis 

fanjris instrumentTa paneli, romelSic Sedis Semdegi Rilakebi: 

_ sawyis furcelze dabruneba; 

_ Web_misamarTze gadasvlis instrumentTa panelis gaaqtiureba; 

134

_ aqtiuri dokumentidan erTi nabijiT ukan dabruneba (Back); 

_ Back moqmedebis uaryofa (Forward); 

_ aqtiuri Tematikidan wina Tematikaze gadasvla; 

_ aqtiuri Tematikidan momdevno Tematikaze gadasvla; 

_ istoriis anu momxmareblis mier Sesrulebuli yvela moqmedebis 

Cveneba; 

_ Zebnis fanjris gamoZaxeba, sadac misaTiTebelia saZebni Temis 

dasaxeleba; 

_ moniSnuli obieqtis kopireba buferSi; 

_ moniSnuli obieqtis Senaxva; 

_ aqtiuri dokumentis dabeWdva. 

resurs_centris Tematikebia: 

Tutorials – aq damxmare eleqtronul saxelmZRvaneloSi aRwerilia Mathcad_i 

da ganxilulia sistemis axali versiis siaxleebi; 

Quicksheets – aq moyvanilia yvelaze gavrcelebuli sxvadasxva saxis 

sainJinro amocanebi, sadac Tavmoyrilia rogorc martivi, aseve rTuli 

magaliTebi, romlebsac praqtikulad iyeneben maTematikur da 

samecniero_teqnikur gamoTvlebSi, miTiTebani statistikuri gamoTvlebis 

Casatareblad, programebis magaliTebi, miTiTebebi statistikuri analizisa 

da monacemTa damuSavebis Casatareblad da a.S.; 

Reference Tables – aq Tavmoyrilia yvela fundamenturi teqnikuri mecnierebis 

cxrilebi, kanonebi, Teoremebi, mag., mendeleevis periodulobis sistema, 

geometriuli sxeulebis moculobis, farTobisa da perimetris 

gamosaTvleli formulebi, yvela metalis kuTri winaRoba da a.S.; 

Image Processing – videogamosaxulebis Seqmna da damuSaveba, raSic 

igulisxmeba Mathcad_Si matricebis saxiT warmodgenili ricxviTi masivebis 

grafikul gamosaxulebad warmodgena, videogamosaxulebis warmodena 

ricxviTi masivebis saxiT, am procesebTan dakavSirebul funqciaTa aRwera 

da a.S.; 

Signal Processing – aq moyvanilia yvelaze gavrcelebul signalTa 

damuSavebasTan dakavSirebuli informacia, aRwerilia Sesabamisi funqciebi, 

maTi gamoyenebis semantika da a.S.; 

Wavelets Extension Pack – aq Tavmoyrilia veivletis analizis (signalebis 

modelirebis sinusoidebis kombinaciebiT) funqciebis aRwera da magaliTebi. 

sainformacio resurs_centrSi arsebuli nebismieri magaliTis Casma 

momxmareblis samuSao furcelSi martivad SesaZlebelia. 

135

10.4 daxmarebis sxva saSualebebi 

mTavari menius Help → User Forum brZanebiT SesaZlebelia internetis 

gamoyenebiT daregistrireba rogorc Mathcad_is momxmarebeli da sxva 

momxmareblebTan forumSi CarTva, sadac xdeba azrebis mimocvla, gamocdilebis 

gaziareba da a.S. (nax.10.5). 

nax.10.5. momxmarebelTa forumSi Sesvla 

Help → Mathcad.com brZanebiT xdeba Mathcad_is produqtis Semqmneli firmis 

Web_misamarTze gadasvla da siaxleebis gacnoba, xolo Help → Mathcad Update 

brZanebiT _ Mathcad_is ganaxleba. 

menius Help → About Mathcad... brZanebiT SesaZlebelia momxmareblis 

kompiuterze dayenebuli Mathcad_is versiis Sesaxeb informaciis moZieba. 

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Tavi XI funqciebi Mathcad_Si 

11.1 momxmareblis mier funqciebis Seqmna 

Mathcad_s gaaCnia fundamentur da teqnikur mecnierebebSi arsebuli 

maTematikuri funqciebis farTo speqtri. maTi im saxiT gamoyeneba, rogoricaa 

Cadebuli sistemaSi Tavisi sintaqsiTa da semantikiT, amartivebs dasaxuli 

amocanis gadaWras. funqciis mniSvnelobis gamosaTvlelad Insert → Function… 

brZanebiT CavsvaT SerCeuli funqciis Sabloni, markerebis adgilas SevitanoT 

funqciis argumentebis mniSvnelobebi da gamoviyenoT tolobis niSani an avkriboT 

funqciis saxeli, mrgval frCxilebSi mivuTiToT mZimeebiT erTimeorisagan 

gamoyofili argumentebis konkretuli mniSvnelobebi da gamoviyenoT tolobis 

niSani. 

saWiroebis SemTxvevaSi momxmarebels SeuZlia Seqmnas sakuTari funqciebic. 

funqciis Seqmnisas momxmarebelma unda daicvas moqmedebaTa Semdegi 

Tanmimdevroba: 

1. akribos funqciis saxeli; 

2. mrgval frCxilebSi Casvas funqciis argumenti an argumentebi, romlebic 

erTimeorisagan mZimiT gamoiyofa; 

3. gamoiyenos klaviaturis : simbolo an Calculator instrumentTa panelis 

miniWebis niSani; 

4. Seiyvanos formula, romelic gansazRvravs funqcias. 

momxmareblis mier Seqmnili funqciisa da CaSenebuli funqciis 

SedarebisaTvis ganvixiloT puasonis ganawileba – SevqmnaT sakuTari funqcia da 

gamoviyenoT Mathcad_Si arsebuli puasonis ganawilebis funqcia (nax.11.1). 

11.2 CaSenebuli funqciebis mimoxilva 

Mathcad_Si CaSenebuli funqciebi dayofilia kategoriebad: beselis 

funqciebi, kompleqsuri ricxvebis funqciebi, logariTmuli da eqsponencialuri 

funqciebi, trigonometriuli funqciebi, SemTxveviTi ricxvebis Ffunqciebi, 

finansuri funqciebi, interpolaciis da eqstrapolaciis funqciebi da a.S. 

aRvweroT ramdenime funqcia Tematikis mixedviT. 

funqciebi: 

matriculi da veqtoruli funqciebi 

arsebobs matricebTan muSaobisaTvis gankuTvnili Semdegi CaSenebuli 

augment(M1,M2,...) _ erT matricaSi aerTianebs M1,M2,... matricebs, romelTac 

striqonTa erTnairi raodenoba gaaCniaT; 

137

nax.11.1. momxmareblis mier Seqmnili puasonis ganawilebis amsaxveli funqciisa da 

Mathcad_Si arsebuli puasonis ganawilebis funqciis Sedareba 

identity(n) _ qmnis kvadratul erTeulovan n X n zomis matricas; 

stack(M1,M2,...) _ erT matricaSi aerTianebs M1,M2,... matricebs, romelTac 

svetebis erTnairi raodenoba gaaCniaT, amasTan M2 matricis 

elementebi M1_is qveS iqnebian ganlagebuli, M3 matricis _ 

M2_is qveS da a.S.; 

submatrix(A,ir,jr,ic,jc) _ gamoyofs sawyisi matricidan qvematricas, romlis striqonebi 

Sedgeba sawyisi matricis ir_dan jr_mde striqonebis 

elementebisagan, xolo svetebi – ic_dan jc_mde svetebis 

elementebisagan; 

diag(V) _ qmnis matricas, romlis mTavari diagonalis elementebi V 

veqtoris elementebia; 

matrix(m,n,f) _ qmnis matricas, romlis (i, j)_uri elementi udris f(i,j)_s, 

sadac i = 0,1..m da j = 0,1..n; 

length(V) _ gamoTvlis veqtoris sigrZes. 

138

kompleqsuri ricxvebis funqciebi 

Re(z) _ gvaZlevs kompleqsuri ricxvis namdvil nawils. z SeiZleba 

iyos rogorc skalari, ise kompleqsuri ricxvebiT Sedgenili 

veqtori an matrica; 

lm(z) _ gvaZlevs kompleqsuri ricxvis warmosaxviT nawils. z SeiZleba 

iyos rogorc skalari, ise kompleqsuri ricxvebiT Sedgenili 

veqtori an matrica; 

arg(z) _ gvaZlevs kompleqsuri ricxvis X RerZTan daxris kuTxis 

mniSvnelobas (radianebSi). 

interpolaciis da eqstrapolaciis funqciebi 

samecniero_teqnikuri gamoTvlebis Catarebisas xSirad warmoiqmneba 

interpolaciis (Caketili intervalis nebismier wertilSi fenqciis mniSvnelobebis 

gansazRvra am funqciis mocemuli diskretuli mniSvnelobebis mixedviT, rac 

grafikulad niSnavs funqciis warmodgenas sakvanZo (sayrdeni) wertilebis 

SeerTebiT ama Tu im saxis wirebis gamoyenebiT) da eqstrapolaciis (funqciis 

mniSvnelobebis gansazRvra Caketili intervalis gareT) Catarebis aucilebloba. 

interpolaciis amocana amoixsneba mocemul monacemTa aproqsimaciiT martivi 

funqciiT Secvlis safuZvelze, amasTan miRebuli funqcia zustad unda gadiodes 

sakvanZo wertilebSi. Mathcad sistemaSi SesaZlebelia ori saxis interpolacia: 

wrfivi da splainuri. 

wrfivi interpolacia grafikulad niSnavs sakvanZo wertilebis SeerTebas 

wrfis monakveTebiT, funqciis mniSvnelobebis gamoTvla xdeba wrfivi 

damokidebulebis safuZvelze. 

linterp(VX, VY, x) _ wrfivi interpolacia mocemuli sakvanZo wertilebis VX da 

VY veqtorTa safuZvelze; gamoiTvleba funqciis mniSvneloba 

miTiTebul x wertilSi. 

splainuri interpolaciis dros wertilebis SeerTeba xdeba garkveuli 

xarisxis mravalwevrebis gamoyenebiT, amasTan polinomis koeficientebi, rogorc 

wesi, gamoiTvleba ise, rom miRebuli funqcia splainebis SeerTebis wertilebSic 

iyos uwyveti. splainuri interpolacia Mathcad_Si 2 etapad tardeba: jer 

cspline(VX,VY), pspline(VX,VY) an lspline(VX,VY) funqciebis meSveobiT gamoiTvleba 

kuburi splainis koeficientebis VS veqtori, xolo Semdeg interp (VS, VX, VY, x) 

meSveobiT gamoiTvleba funqciis mniSvneloba mocemul wertilSi. 

interp (VS,VX,VY,x) _ gamoTvlis funqciis interpolirebul mniSvnelobas x 

wertilSi, romelic miiReba kuburi splainebis meSveobiT VX, VY 

veqtorebis mniSvnelobebis safuZvelze. 

cspline(VX,VY) _ gamoTvlis VS kuburi splainis koeficientebis veqtors. 

gamoTvlebisas gaTvaliswinebulia mrudis sayrden wertilebTan 

miaxloebisas kuburi damokidebuleba. 

139

pspline(VX,VY) _ gamoTvlis VS kuburi splainis koeficientebis veqtors. 


miaxloebisas paraboluri damokidebuleba. 

lspline(VX,VY) _ gamoTvlis VS kuburi splainis koeficientebis veqtors. 


miaxloebisas wrfivi damokidebuleba. 

predict(V,k,n) _ axdens eqstrapolacias, V _ monacemTa veqtori, k _ regresiis 

polinomis xarisxi, n _ wertilTa raodenoba. 

statistikuri funqciebi 

Mathcad sistemis meSveobiT SesaZlebelia statistikuri gamoTvlebis 

warmoeba. statistikuri funqciebia: 

corr(VX,VY) _ gamoTvlis VX da VY erTnairganzomilebiani masivebis elementebis 

korelaciis koeficients; 

cvar(VX,VY) _ gamoTvlis VX da VY erTnairganzomilebiani masivebis elementebis 

kovariaciis koeficients; 

mean(A,B,C,...) _ gamoTvlis A,B,C,... elementebis saSualo ariTmetikul 

mniSvnelobas, sadac A,B,C,... masivebia an skalarebi; 

var(A,B,C,...) _ gamoTvlis A,B,C,... elementebis dispersias (variacias), sadac A,B,C,... 

masivebia an skalarebi; 

stdev(A,B,C,...) _ gamoTvlis A,B,C,… elementebis standartul gadaxras, sadac 

A,B,C,... masivebia an skalarebi; 

hist(int, V) _ gamoTvlis V monacemebis int intervalebSi moxvedris sixSiris 

veqtors. am funqcias iyeneben histogramebis asagebad; 

cnorm(x) _ komuliatiuri normaluri funqcia (Sedis Probability Distribution 

kategoriaSi); 

erf(x) _ cdomilebis funqcia anu albaTobis integrali (Sedis Special 

kategoriaSi); 

erfc(x) _ cdomilebaTa funqcia kompleqsuri argumentisaTvis (Sedis Special 

kategoriaSi); 

rnd(x) _ SemTxveviTi ricxvebis generaciis funqcia (Sedis Random Numbers 

kategoriaSi). 

nax.11.2_ze moyvanilia statistikuri funqciebis (rnd, mean, var, min, max, stdev, 

hist) gamoyenebis magaliTebi. 

SemTxveviTi (stoqastikuri) ricxvebis funqciebi 

SemTxveviT (stoqastikur) ricxvebTan muSaobisaTvis gamosayenebeli 

funqciebi iyofa oTx klasad: 

Tu funqciis saxeli “d“–Ti iwyeba, miiReba ganawilebis albaTobis 

simkvrivis mniSvneloba; 

140

nax.11.2. statistikuri funqciebis (rnd, mean, var, min, max, stdev, hist) 

gamoyenebis magaliTebi 

Tu funqciis saxeli “p“–Ti iwyeba, miiReba albaTobis ganawileba anu imis 

albaToba, rom SemTxveviTi ricxvis mniSvneloba iqneba konkretul 

miTiTebul mniSvnelobaze naklebi an toli; 

Tu funqciis saxeli “q“–Ti iwyeba, miiReba albaTobis ganawilebis Sebruneba 

anu mocemuli albaTobis mixedviT gamoiTvleba ricxvis iseTi mniSvneloba, 

romlis albaToba albaTobis miTiTebul konkretul mniSvnelobaze tolia 

an naklebi; 

Tu funqciis saxeli “r“–iT iwyeba, Seiqmneba veqtorebi garkveuli 

kanonzomierebiT ganawilebuli elementebiT. 

qvemoT moyvanilia ganawilebis albaTobis simkvrivis gamoTvlis funqciebi, 

romelTa saxelebi “d“ –Ti iwyeba (“p“, “q“ da “r“–iT dawyebuli Sesabamisi funqciebi 

moyvanili ar aris): 

dbeta(x, s1, s2) _ β ganawileba (formebis parametrebi s1>0, s2>0 da 0< x0 – masStabis parametri); 

141

dchisq(x, d) _ x_kvadrat ganawileba (x>0, Tavisuflebis xarisxi d>0); 

dexp(x,r) _ eqsponencialuri ganawileba (r>0, x>0); 

dF(x,d1,d2) _ fiSeris ganawileba (Tavisuflebis xarisxebi d1>0, d2>0 da x>0); 

dgamma(x,s) _ gama_ganawileba (formis parametri s>0, x≥0); 

dgeom(k,p) _ geometriuli ganawileba (calkeuli cdis Sedegebis warmatebis 

albaToba, 00 , sadac σ _ saSualo kvadratuli gadaxris 

naturaluri logariTmi, x>0); 

dlogis(x,l,s) _ logistikuri ganawileba (l – daSlis parametri, s>0 – masStabis 

parametri); 

dnbinom(k,n,p) _ uaryofiTi binomialuri ganawileba (n da k – mTeli dadebiTi 

ricxvebi, 0≤p≤1); 

dnorm(x,μ,σ) _ normaluri ganawileba (μ –saSualo mniSvneloba, σ>0 _ saSualo 

kvadratuli gadaxra); 

dpois(k,λ) _ puasonis ganawileba (λ>0, k – mTeli dadebiTi ricxvi); 

dt(x,d) _ stiudentis ganawileba (d>0 – Tavisuflebis xarisxis maCvenebeli, x _ 

namdvili ricxvi); 

dunif(x,a,b) _ Tanabari ganawileba (a da b – intervalis zRvruli wertilebi, 

amasTan a0 – formis parametri, x>0). 

monacemTa gagluvebis funqciebi 

eqsperimentTa monacemebi umetesad Seicaven SemTxveviT cdomilebebs. amitom 

xSirad wamoiWreba monacemTa statistikuri gagluvebis aucilebloba. Mathcad_s 

gaaCnia gagluvebis Semdegi funqciebi: 

medsmooth(VY, n) _ axdens mcocavi medianis meTodiT monacemTa gagluvebas. 

Sedegad miiReba gagluvebuli monacemebis m_ganzomilebiani 

VY veqtori. n parametriT moicema gagluvebis CarCos sigane, 

amasTan n unda iyos m_ze naklebi kenti ricxvi; 

ksmooth(VX, VY, b) _ axdens gagluvebas gausis ganawilebis safuZvelze. Sedegad 

miiReba gagluvebuli monacemebis n_ganzomilebiani VY veqtori. 

VX da VY – n_ganzomilebiani namdvil ricxvTa veqtorebi, b 

parametriT (gatarebis zoli) moicema gagluvebis CarCos sigane 

(b ramdenimejer unda aRematebodes X RerZis wertilebs Soris 

intervals); 

supsmooth(VX, VY) _ axdens gagluvebas wrfivi gagluvebis proceduris 

safuZvelze umcires kvadratTa meTodiT (k uaxloesi 

mezoblebis wesis Tanaxmad k_s adapturi SerCeviT). miiReba 

n_ganzomilebiani gagluvebuli VY veqtori. n_ganzomilebiani 

142

VX veqtoris elementebi zrdadobis mixedviT unda iyos 

dalagebuli. monacemTa gagluveba supsmooth funqciiT 

ilustrirebulia nax.11.3_ze. 

nax.11.3. monacemTa gagluveba supsmooth funqciiT 

Ggantolebebis da gantolebaTa sistemebis amoxsnis funqciebi 

bevr algebrul gantolebas da maT sistemebs ar gaaCniaT analizuri 

amonaxsni. maTi amoxsna SesaZlebelia ricxviTi meTodebiT dadgenili 

cdomilebebis farglebSi. 

root(f(x),x) _ gamoTvlis martivi arawrfivi erTcvladiani gantolebis (f(x)=0) fesvs. 

fesvis povna xdeba iteraciuli meTodiT, romlis dros saWiroa 

cvladisaTvis sawyisi mniSvnelobis miniWeba. 

Polyroots(V) _ gamoTvlis Cveulebrivi polinomis fesvebs. am funqciis gamoyeneba 

mizanSewonilia rodesac polinomis xarisxi 6_s ar aRematema. 

Lsolve(A,B) _ wrfiv gantolebaTa sistemis (A. X=B) amoxsna, A _ koeficientebis 

matrica, B _ Tavisufal wevrTa veqtori. 

arawrfivi gantolebis an gantolebaTa sistemis amosaxsnelad iyeneben 

find(v1,v2,...,vn) da minerr(v1,v2,...,vn) funqciebs. gamoTvliTi bloki iwyeba given 

direqtiviT, ris Semdeg Caiwereba gantoleba (gantolebebi) da SezRudvebi 

143

cvladebze. gamoTvliTi bloki mTavrdeba find(v1,v2,...,vn) an minerr(v1,v2,...,vn) 

funqciiT. 

nax.11.4. arawrfivi erTcvladiani gantolebis amoxsna root da given _ minerr 

funqciebis gamoyenebiT 

find(v1,v2,...) _ gamoTvlis cvladis an cvladebis zust mniSvnelobebs, 

romlebic akmayofileben mocemul gantolebas (gantolebebs) da 

SezRudvebs. 

minerr(v1, v2,...) _ gamoTvlis cvladis an cvladebis miaxloebiT mniSvnelobebs. 

nax.11.4_ze moyvanilia arawrfivi erTcvladiani gantolebis amoxsna root da 

given _minerr funqciebis gamoyenebiT, xolo nax.11.5_ze _ arawrfiv gantolebaTa 

sistemis amoxsna given _ find funqciebis gamoyenebiT. 

Mathcad_Si CaSenebulia agreTve Cveulebrivi diferencialuri gantolebebis 

amosaxsneli funqciebi: 

rkadapt(Y,x1,x2,acc,n,F,k,s) _ miiReba matrica, romelic Seicavs koSis amocanis 

amonaxsnebs. Ddiferencialuri gantolebebis sistemis amoxsna xdeba 

runge_kutas meTodiT cvladi bijiT, Y _ sawyisi pirobebis veqtori x1_dan 

x2_mde intervalSi. gantolebaTa sistemis marjvena nawilebi Cawerilia F 

simbolur veqtorSi, n – bijTa raodenoba, k – amoxsnis Sualeduri 

144

wertilebis maqsimaluri raodenoba, s – wertilebs Soris minimaluri 

dasaSvebi intervali, acc _ amoxsnis cdomileba; 

nax.11.5. arawrfiv gantolebaTa sistemis amoxsna given _ find 

funqciebis gamoyenebiT 

Rkadapt(Y,x1,x2,n,F) _ miiReba matrica, romelic Seicavs Cveulebriv 

diferencialur gantolebaTa sistemis amonaxsnebs. diferencialuri 

gantolebebis sistemis amoxsna xdeba runge_kutas meTodiT adaptiuri 

bijiT, Y _ sawyisi pirobebis veqtori x1_dan x2_mde intervalSi. 

sistemis marjvena nawilebi Cawerilia F simbolur veqtorSi, n _ bijTa 

raodenoba; 

rkfixed(Y,x1,x2,n,F) _ miiReba matrica, romelic Seicavs x1_dan x2_mde 

intervalSi Cveulebriv diferencialur gantolebaTa sistemis amonaxsnebs. 

diferencialuri gantolebebis sistemis amoxsna xdeba runge_kutas 

meTodiT fiqsirebuli bijiT da Y veqtoris sawyisi mniSvnelobebiT. 

sistemis marjvena nawilebi Cawerilia F simbolur veqtorSi, n _ bijTa 

raodenoba. Rkadapt funqcia gvaZlevs ufro zust Sedegebs rkfixed 

funqciasTan SedarebiT, magram misi gamoTvlis siCqare, rogorc wesi, ufro 

dabalia. 

145

puasonis diferencialuri gantolebis (meore rigis kerZo warmoebulebSi) 

da laplasis gantolebis amosaxsnelad Mathcad_s aqvs Semdegi funqciebi: 

bvalfit(V1,V2,x1,x2,xi,F,L1,L2,score) _ miiReba sasazRvro amocanis sawyisi pirobebi 

mocemuli F, V1 da V2 veqtorebisaTvis x1_dan x2_mde intervalSi, amoxsna 

cnobilia garkveul Sualedur wertilSi xi; 

relax(M1,M2,M3,M4,M5,A,U,r) _ miiReba puasonis gantolebis amoxsnis kvadratuli 

matrica r speqtraluri radiusisaTvis; 

multigrid(M,n) _ miiReba puasonis gantolebis amoxsnis matrica (rodesac 

sazRvrebze amonaxsni 0_is tolia); 

sbval(Y,x1,x2,F,L,score) _ miiReba F simbolur veqtorSi gansazRvruli sasazRvro 

amocanis sawyisi pirobebi. sawyisi pirobebi Caiwereba Y veqtorSi x1_dan 

x2_mde intervalSi. 

furies pirdapiri da Sebrunebuli gardaqmna 

maTematikis fundamentur debulebas miekuTvneba periodul funqciaTa 

warmodgenis SesaZlebloba furies mwkriviT _ harmoniuli mdgenelebis jamis 

saxiT. amiT SeiZleba visargebloT mraval SemTxvevaSi. sakmarisia aRiniSnos, rom 

is udevs safuZvlad kavSirgabmulobis arxebisa da gadacemuli signalebis 

analizs. furies pirdapiri da Sebrunebuli gardaqmna saSualebas gvaZlevs 

signalis droiTi warmodgenidan gadavideT mis sixSirul warmodgenaze da 

piriqiT. Ffuries pirdapiri da Sebrunebuli gardaqmnis funqciebia: 

fft(V) _ furies pirdapiri swrafi gardaqmna. sawyisi monacemebis V veqtori 

Sedgenilia namdvili ricxvebisagan. amasTan V veqtors unda hqondes 2 n 

mdgeneli, sadac n – mTeli ricxvia. am funqciis Semotana ganpirobebulia 

imiT, rom namdvili elementebisagan Sedgenili veqtorisaTvis furies 

gardaqmna xorcieldeba ufro swrafi algoriTmiT da angariSs sWirdeba 

naklebi dro; 

cfft(A) _ furies pirdapiri gardaqmna. sawyisi A veqtori kompleqsur ricxvebs 

Seicavs. Tu A matricaa, cfft funqcia axdens furies organzomilebian 

pirdapir gardaqmnas; 

ifft(V) _ furies Sebrunebuli gardaqmna, Seesabameba fft pirdapir gardaqmnas. 

sawyisi V veqtori kompleqsur ricxvebs Seicavs. ifft funqciiT miiReba 

namdvili ricxvebisagan Sedgenili veqtori; 

cifft(A) _ furies Sebrunebuli gardaqmna sruli algoriTmiT, Seesabameba cfft 

pirdapir gardaqmnas. rogorc sawyisi, aseve miRebuli veqtorebi an 

matricebi Seicaven kompleqsur ricxvebs. Tu A matricaa, cifft funqcia 

axdens furies organzomilebian Sebrunebul gardaqmnas. 

nax.11.6_ze moyvanilia furies pirdapiri da Sebrunebuli gardaqmna fft da ifft 

funqciebis gamoyenebiT. 

146

nax.11.6. furies pirdapiri da Sebrunebuli gardaqmna 

fft da ifft funqciebis gamoyenebiT 

11.3 momxmareblis mier operatoris Seqmna 

funqciebs da operatorebs bevri saerTo gaaCniaT. isini gansxvavdebian 

erTmaneTisagan ara Sinaarsobrivad, aramed gamosaxvis formiT. magaliTad, funqcia 

f(x,y) SegviZlia gamovsaxoT xfy operatoris saxiT, x+y Canaweri SevcvaloT +(x,y)_iT 

da a.S. funqciebis msgavsad, momxmarebels SeuZlia Seqmnas sakuTari operatorebic. 

ganvixiloT momxmareblis mier operatoris Seqmna magaliTze (SevqmnaT 

gaerTianebis 

operatori): 

1. CavsvaT samuSao furcelSi gaerTianebis simbolo 

Help → QuickSheets → Extra Math Symbols CamonaTvalidan; 

2. avkriboT klaviaturidan (x,y); 

3. gamoviyenoT miniWebis operatori; 

147

4. markerSi SevitanoT operatoris gansazRvra (Cven 

gamoyeneba. 

magaliTSi gamoyenebulia gaerTianebis funqcia stack). 

SemdgomSi dokumentSi stack funqciis nacvlad SesaZlebelia operatoris 

momxmareblis mier Seqmnili operatorebis gamosayeneblad vsargeblobT 

Evaluation instrumentTa panelis (nax. 11.2) bolo oTxi RilakiT: 

nax.11.7. Evaluation instrumentTa paneli 

Cvens mier Seqmnili 

operatoris gamosayeneblad: 

1. SeviyvanoT operandebi; 

2. gamoviyenoT Evaluation instrumentTa panelis 

Rilaki; 

3. Sua markerSi SevitanoT operatoris simbolo; 

4. marcxena da marjvena markerebSi SevitanoT operandebi; 

5. gamoviyenoT tolobis niSani. 

oroperandiani operatoris gamoyeneba SesaZlebelia agreTve Evaluation 

instrumentTa panelis RilakiT. 

erToperandiani operatoris gamoyeneba SesaZlebelia Evaluation instrumentTa 

panelis da RilakebiT. 

148

Tavi XII daprogrameba Mathcad_Si 

12.1 Programming instrumentTa panelis operatorebis aRwera 

cvladebi da funqciebi Mathcad_Si SeiZleba ganvsazRvroT rogorc 

Cveulebrivi gamosaxulebebis meSveobiT, aseve programis saxiT. 

Mathcad_is programa warmoadgens daprogramebis operatorebis meSveobiT 

Seqmnil brZanebaTa erTobliobas. arsebiTad programa warmoadgens gamosaxulebis 

specifikur nairsaxeobas da sxva gamosaxulebebis msgavsad, ricxviTi an 

simboluri gamoTvlebisas miRebuli iqneba misi mniSvneloba. programis 

mniSvneloba Mathcad_Si SeiZleba iyos ricxvi, ricxviTi masivi, masivi masivSi 

(Nested Arrays) an striqoni (String). brZanebebis raodenoba programaSi ar aris 

SezRuduli. 

programis Sesaqmnelad gamoviZaxoT Programming instrumentTa paneli 

mTavari menius View → Toolbars CamonaTvalidan an maTematikuri panelis 

RilakiT (nax.12.1). 

nax.12.1. Programming instrumentTa paneli 

daprogramebis operatorebia (frCxilebSi miTiTebulia klaviaturis 

klaviSebi an klaviSebis kombinacia, romelTa meSveobiT SesaZlebelia Sesabamisi 

operatoris Casma programaSi): 

(]) _ xazis Casmis operatori. am operatoris gamoyenebiT iwyeba 

programis Cawera. gamodis vertikaluri xazi ori markeriT. 

programaSi SesaZlebelia nebismieri markeris gamoyofa da Add Line 

operatoris xelmeore gamoyeneba, ris Sedegad vertikaluri xazis 

sigrZe izrdeba da Sesabamisad matulobs markerTa ricxvic; 

({) _ miniWebis operatori; 

(}) _ if (Tu) pirobiTi gadasvlis operatori. misi gamoyenebisas 

marjvena markerSi Caiwereba piroba (logikuri gamosaxuleba), xolo 

149

marcxenaSi _ brZaneba an gamosaxuleba, romelic gamoiTvleba pirobis 

Sesrulebis SemTxvevaSi; 

(Ctrl + Shift) _ otherwise (sxva SemTxvevaSi) operatoris Casma, romelic 

gamoiyeneba if logikur operatorTan erTad. markerSi Caiwereba 

brZaneba an gamosaxuleba, romelic gamoiTvleba pirobis 

Seusruleblobis SemTxvevaSi; 

(Ctrl + Shift + “) _ ciklis operatori. for cikli gamoiyeneba rodesac 

ciklSi Sesasrulebeli brZanebebis gameorebis ricxvi winaswar anu 

ciklSi Sesvlamde gansazRvrulia. for operatoris marcxena markerSi 

Sesatania ciklis parametris identifikatori, marjvena markerSi am 

parametris mniSvnelobaTa Secvlis diapazoni, xolo qvedaSi _ ciklSi 

Sesasrulebeli brZaneba; 

(Ctrl + ]) _ ciklis operatori. while (manam ... sanam) cikli gamoiyeneba 

rodesac ciklSi Sesasrulebeli brZanebebis gameorebis ricxvi 

winaswar ar aris gansazRvruli. while operatoris marjvena markerSi 

Sesatania piroba, xolo QqvedaSi _ ciklSi Sesasrulebeli brZaneba. 

pirobis Seusruleblobisas xdeba ciklidan gamosvla; 

(Ctrl + Shift + {) _ ciklis Sesrulebis Sewyvetis operatori; 

(Ctrl + [) _ continue operatori, gamoiyeneba ciklis morig iteraciaze 

gadasasvlelad; 

(Ctrl + Shift + |) _ return operatori, gamoiyeneba programis Sesrulebis 

Sesawyvetad. Mmis markerSi Sesatania programidan dokumentSi misawodi 

informacia; 

(Ctrl + ‘) _ on error (Secdomis SemTxvevaSi) operatori. am operatoriT 

jer gamoiTvleba marjvena argumenti, xolo Secdomis SemTxvevaSi _ 

marcxena. 

unda aRiniSnos, rom operatorebis dasaxelebebis klaviaturidan akreba 

dauSvebelia. 

12.2 miniWebisa da striqonis Casmis operatorebi 

rogorc ukve iyo aRniSnuli, miniWebis operatori gamoiyeneba 

cvladebisaTvis an funqciebisaTvis mniSvnelobis misaniWeblad, xolo Add Line 

operatori Casvams programaSi axal xazs. 

x y 

f( x y) 

log 

ganvixiloT programis Seqmnis procesi. vTqvaT, gvinda ganvsazRvroT 

 

funqcia programis meSveobiT. amisaTvis: 

2 y 

 

 

150

1. avkriboT klaviaturidan f( x y) 

da : miniWebis niSnis 

Sesatanad; 

2. gamoviyenoT Programming panelis Add Line operatori; 

3. davawkapunoT zeda markerze, avkriboT k da 

gamoviyenoT Programming panelis operatori; 

x y 

4. miniWebis marjvniv myof markerSi SevitanoT ; 

2 y 

5. qveda markerze gadasaadgileblad davaWiroT Tab 

klaviSs da avkriboT log(k). 

aRvniSnoT, rom programis SigniT akrZalulia miniWebis niSnis (:=) 

gamoyeneba. is cvladebi, romlebic gansazRvrulia programis SigniT 

operatoriT (rogorc wina magaliTSi k cvladi), warmoadgenen programis lokalur 

cvladebs da ar arian gansazRvrulebi samuSao furclis sxva adgilas. 

12.3 pirobiTi gadasvlis iperatori 

programis operatorebi sruldeba mimdevrobiT, zemodan qvemoT. xSirad 

saWiroeba moiTxovs am Tanmimdevrobis Secvlas, rac SesaZlebelia if pirobiTi 

gadasvlis operatoriT. if operatori gamoiyeneba algoriTmis ganStoebuli 

struqturis aRsawerad. 

vTqvaT, gvinda ganvsazRvroT Semdegi funqcia: 

 

0 

w ( x) 

 

25 x 

amisaTvis: 

2 

, 

Tu 

sxva 

x 5 

SemTxvevaSi 

1. avkriboT w(x): da gamoviyenoT Programming 

panelis Add Line operatori; 

2. gamovyoT zeda markeri da gamoviyenoT Programming 

panelis if operatori; 

3. if sityva_gasaRebis marjvniv mdgom markerSi 

SevitanoT x >5 logikuri gamosaxuleba 

Boolean panelis gamoyenebiT. marcxena markerSi 

151 

. 

f( x y ) 

f( x y) 

 

f( x y) 

k 

f( x y ) k 

f( x y) 

k 

 

 

log( k) 

w( x) 

 

w( x) 

if 

x y 

2 y 

x y 

2 y 

w( x) 

0 if x 5

magaliTi. 

SevitanoT 0, romlis mniSvneloba mieniWeba w (x) 

funqcias, roca 

marjvena markerSi Setanili logikuri gamosaxulebis mniSvnelobaa 

“WeSmariti” (true); 

4. gamovyoT qveda markeri da gamoviyenoT Programming panelis otherwise 

operatori da mis marcxniv mdgom markerSi SevitanoT 

romlis mniSvneloba mieniWeba 

w (x) 

funqcias, roca programis 

logikuri pirobis mniSvnelobaa 

“mcdari” (false). 

152 

w ( x) 

 

0 if x 5 

2 

25 x , 

nax.12.2–ze moyvanilia if pirobiTi gadasvlis operatoris gamoyenebis 

nax.12.2. if logikuri operatoris gamoyenebis magaliTi 

25 x 2 

otherwise 

if operatoris piroba logikur gamosaxulebas warmoadgens, romlis 

Sesatanad vsargeblobT Boolean instrumentTa panelis operatorebiT (nax.12.3). 

Boolean instrumentTa panelSi Tavmoyrilia Sedarebis operatorebi (Equal to (Ctrl+ 

=) _ tolia, Less Than () _ metia, Less Than or Equal to

(Ctrl+ ( ) _ naklebia an toli, Greater Than or Equal to (Ctrl+ ) ) _ metia an toli, 

Not Equal to (Ctrl+ 3) _ ar udris) da logikuri operatorebi (Not (Ctrl+Shift+5) _ 

logikuri uaryofa, And (Ctrl+Shift+7) _ koniunqcia anu logikuri “da”, Or 

(Ctrl+Shift+6) _ dizunqcia anu logikuri “an”, Exclusive or (xor) (Ctrl+Shift+1) _ 

dizunqciis uaryofa). 

nax.12.3. Boolean instrumentTa paneli 

Sedarebis operatorebis operandebia ricxviTi an striqonuli tipis 

monacemebi (orive operandi unda iyos erTi da igive tipisa), xolo logikuri 

operatorebis operandebi logikuri gamosaxulebebia. striqonebis Sedareba 

warmoebs simboloebis mixedviT marcxnidan marjvniv. Tu striqonebis raime wyvili 

ar emTxveva erTmaneTs, ufro metis mniSvnelobis mqoned iTvleba is simbolo, 

romlis Sesabamisi kodi (koduri cxrilidan) ufro metia. Sedarebisa da logikuri 

operaciebis Sedegad miiReba 1 (“WeSmariti”) an 0 (“mcdari”). 

12.4 ciklis operatorebi 

gameorebadi anu cikluri procesi gamoTvliTi procesebis metad 

gavrcelebul tips warmoadgens. ciklis operatorebi gankuTvnilia algoriTmis 

cikluri struqturis aRsawerad. 

Mathcad_s aqvs ori ciklis operatori: for da while. 

rogorc ukve iyo aRniSnuli, for cikli gamoiyeneba rodesac ciklSi 

Sesasrulebeli brZanebebis gameorebis ricxvi winaswar anu ciklSi Sesvlamde 

gansazRvrulia. for ciklis Sesaqmnelad: 

1. davawkapunoT Programming panelis for operatorze; 

2. “”_is marcxniv mdebare markerSi SevitanoT ciklis cvladis saxeli, 

marjvniv mdebare markerSi _ ciklis cvladis sawyisi da bolo 

mniSvnelobebi da agreTve misi mniSvnelobis Secvlis for i 1 n 

biji (Tu es biji 1_sagan gansxvavebulia); 

3. qveda markerSi SevitanoT ciklSi Sesasrulebeli brZaneba. Tu ciklSi 

sruldeba ramdenime brZaneba, gamovyoT qveda markeri 

da Add Line operatoriT jer CavsvaT axali striqonebi, 

xolo Semdeg markerebSi SevitanoT ciklis brZanebebi. 

153 

for 

for 

 

i 1 n 

s s i

while (manam ... sanam) tipis cikls viyenebT rodesac ciklis gameorebis 

raodenoba ar aris winaswar cnobili da is dasruldeba mxolod miTiTebuli 

pirobis Seusruleblobisas. 

while ciklis Sesaqmnelad: 

1. davawkapunoT Programming panelis while operatorze; 

2. zeda markerSi SevitanoT gameorebis pirobis 

Sesabamisi logikuri gamosaxuleba, xolo qveda 

markerSi SevitanoT ciklSi Sesasrulebeli 

brZaneba. Tu ciklSi sruldeba ramdenime brZaneba, 

gamovyoT qveda markeri da Add Line operatoriT jer 

CavsvaT axali striqonebi, Semdeg ki markerebSi 

SevitanoT ciklis brZanebebi. 

nax.12.4_ze moyvanilia for da while operatorebis gamoyenebis magaliTebi. 

nax.12.4. for da while operatorebis gamoyenebis magaliTebi 

154 

while 

while 

v j 

j j 1 

t

12.5 Break, Continue da Return operatorebi 

break operatori gamoiyeneba ciklis Sesawyvetad anu raime pirobis 

Sesrulebisas ciklidan gamosasvlelad. 

Tu saWiroa pirobis Sesrulebisas SevwyvitoT ciklis morigi iteracia da 

gavagrZeloT ciklis Sesruleba Semdegi iteraciebisaTvis, vsargeblobT continue 

operatoriT. 

break da continue operatorebis Sesatanad vsargeblobT Programming 

panelis Sesabamisad da punqtebiT. 

break da continue operatorebi, rogorc wesi, gvxdebian if operatorSi da 

ciklis operatorebSi. 

return operatoris meSveobiT SesaZlebelia programis Sesrulebis Sewyveta. 

am dros cvlads an funqcias mieniWeba ara bolo, aramed mimdinare brZanebiT 

gamoTvlili mniSvneloba (skalari, veqtori, masivi an striqoni). return operatori, 

break da continue operatorebis msgavsad, ZiriTadad gvxdeba if operatorSi. 

return operatoris Sesatanad: 

1. davawkapunoT Programming panelis operatorze; 

2. operatoris marcxena markerSi CavsvaT Programming panelis 

operatori; 

3. return sityva_gasaRebis marjvniv mdgom markerSi avkriboT gamosaxuleba. 

Tu gamosaxuleba striqonuli tipis konstantaa, klaviaturidan 

SevitanoT “ simbolo da Sesabamisi teqsti; 

4. if operatoris marjvniv mdebare markerSi davbeWdoT logikuri 

gamosaxuleba. 

12.6 operatori on error 

am operatoris programaSi CarTva saSualebas gvaZlevs gamoTvlebSi 

SesaZlo Secdomebis SemTxvevaSi movaxdinoT Secdomis damuSaveba raTa Mathcad_ma 

ar Sewyvitos programis Sesruleba da gaagrZelos gamoTvlebi. on error operatori 

arsebiTad SecdomebisaTvis “xafangs” warmoadgens. 

on error operatoris Sesaqmnelad gamoviyenoT Programming panelis 

punqti. marjvena markerSi Caiwereba ZiriTadi gamosaTvleli gamosaxuleba, xolo 

marcxenaSi _ is gamosaxuleba, romelic Sesruldeba Secdomis SemTxvevaSi. 

nax.12.5_Si moyvanilia on error operatoris da error funqciis, romelic 

gamoiyeneba Secdomis Sesaxeb teqsturi Setyobinebis gamosatanad, gamoyenebis 

magaliTebi. 

155

nax.12.5. on error operatorisa da error funqciis gamoyeneba 

156

gamoyenebuli literatura 

1. Brent Maxfield, “ENGINEERING with MATHCAD”. Using Mathcad to Create and Organize your 

Engineering Calculations. B/H, 2007. 

2. Е. Макаров, «Инженерные расчеты в Маthcad». Учебный курс. Издательство «Питер», 2007, 

486 стр. 

3. В.П. Дьяконов, «Энциклопедия Mathcad 2001 и Mathcad 11». Солон-Пресс, 2004, 832 стр. 

4. Mathcad 11. User’s Guide. Mathsoft Engineering &Education, Inc, 2001, p. 473. 

5. Е.М.Кудрявцев, «Mathcad 8». Издательство ДМК. Москва, 2000, 318 стр. 

6. В.П.Дьяконов, “MathCAD Plus 7.0 PRO”. Справочник по MathCAD Plus 7.0 PRO. 

Издательство « СК ПРЕСС», Москва, 1998, 345 стр. 

7. www. mathsoft.com . 

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ლ.ფერაძე, მ.სორდია maTematikuri sistema M athcad

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