Attention! Your ePaper is waiting for publication!
By publishing your document, the content will be optimally indexed by Google via AI and sorted into the right category for over 500 million ePaper readers on YUMPU.
This will ensure high visibility and many readers!
Your ePaper is now published and live on YUMPU!
You can find your publication here:
Share your interactive ePaper on all platforms and on your website with our embed function
Mathematical Methods for Physics and Engineering - Matematica.NET
Mathematical Methods for Physics and Engineering - Matematica.NET
Mathematical Methods for Physics and Engineering - Matematica.NET
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
PDES: SEPARATION OF VARIABLES AND OTHER METHODSComparing this expression <strong>for</strong> r = z, θ = 0 with the z
PDES: SEPARATION OF VARIABLES AND OTHER METHODSComparing this expression <strong>for</strong> r = z, θ = 0 with the z
- Page 2:
This page intentionally left blank
- Page 6:
Physicists. He is also a Director o
- Page 10:
cambridge university pressCambridge
- Page 14:
CONTENTS2.2 Integration 59Integrati
- Page 18:
CONTENTS7.7 Equations of lines, pla
- Page 22:
CONTENTS12.2 The Fourier coefficien
- Page 26:
CONTENTS18.6 Spherical Bessel funct
- Page 30:
CONTENTS24.9 Cauchy’s theorem 849
- Page 34:
CONTENTS29.6 Characters 1092Orthogo
- Page 40:
CONTENTSI am the very Model for a S
- Page 44:
PREFACE TO THE THIRD EDITIONthe phy
- Page 48:
Preface to the second editionSince
- Page 52:
Preface to the first editionA knowl
- Page 56:
PREFACE TO THE FIRST EDITIONsupport
- Page 62:
PRELIMINARY ALGEBRAforms an equatio
- Page 66:
PRELIMINARY ALGEBRAmany real roots
- Page 70:
PRELIMINARY ALGEBRAat a value of x
- Page 74:
PRELIMINARY ALGEBRAwhere f 1 (x) is
- Page 78:
PRELIMINARY ALGEBRAIn the case of a
- Page 82:
PRELIMINARY ALGEBRAdrawn through R,
- Page 86:
PRELIMINARY ALGEBRAand use made of
- Page 90:
PRELIMINARY ALGEBRAwith the coordin
- Page 94:
PRELIMINARY ALGEBRAthe well-known r
- Page 98:
PRELIMINARY ALGEBRAnumerators on bo
- Page 102:
PRELIMINARY ALGEBRAWe illustrate th
- Page 106:
PRELIMINARY ALGEBRAIn this form, al
- Page 110:
PRELIMINARY ALGEBRAIn fact, the gen
- Page 114:
PRELIMINARY ALGEBRAThe first is a f
- Page 118:
PRELIMINARY ALGEBRAbe obvious, but
- Page 122:
PRELIMINARY ALGEBRAThis is precisel
- Page 126:
PRELIMINARY ALGEBRA◮The prime int
- Page 130:
PRELIMINARY ALGEBRA1.8 ExercisesPol
- Page 134:
PRELIMINARY ALGEBRA1.16 Express the
- Page 138:
PRELIMINARY ALGEBRA1.11 Show that t
- Page 142:
PRELIMINARY CALCULUSf(x +∆x)AP∆
- Page 146:
PRELIMINARY CALCULUS◮Find from fi
- Page 150:
PRELIMINARY CALCULUSand using (2.6)
- Page 154:
PRELIMINARY CALCULUS◮Find dy/dx i
- Page 158:
PRELIMINARY CALCULUSf(x)QABCSFigure
- Page 162:
PRELIMINARY CALCULUSf(x)GxFigure 2.
- Page 166:
PRELIMINARY CALCULUSrelative to the
- Page 170:
PRELIMINARY CALCULUSf(x)a b cxFigur
- Page 174:
PRELIMINARY CALCULUSIn each case, a
- Page 178:
PRELIMINARY CALCULUSf(x)ax 1 x 2 x
- Page 182:
PRELIMINARY CALCULUSFrom the last t
- Page 186:
PRELIMINARY CALCULUS◮Evaluate the
- Page 190:
PRELIMINARY CALCULUSSincethe requir
- Page 194:
PRELIMINARY CALCULUSThe separation
- Page 198:
PRELIMINARY CALCULUS2.2.10 Infinite
- Page 202:
PRELIMINARY CALCULUS2.2.12 Integral
- Page 206:
PRELIMINARY CALCULUSf(x)y = f(x)∆
- Page 210:
PRELIMINARY CALCULUS◮Find the vol
- Page 214:
PRELIMINARY CALCULUSOcCρr +∆rrρ
- Page 218:
PRELIMINARY CALCULUS(c) [(x − a)/
- Page 222:
PRELIMINARY CALCULUSy2aπa2πaxFigu
- Page 226:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 230:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 234:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 238:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 242:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 246:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 250:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 254:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 258:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 262:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 266:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 270:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 274:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 278:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 282:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 286:
COMPLEX NUMBERS AND HYPERBOLIC FUNC
- Page 290:
SERIES AND LIMITSsome sort of relat
- Page 294:
SERIES AND LIMITSFor a series with
- Page 298:
SERIES AND LIMITSThe difference met
- Page 302:
SERIES AND LIMITS◮Sum the seriesN
- Page 306:
SERIES AND LIMITSAgain using the Ma
- Page 310:
SERIES AND LIMITSwhich is merely th
- Page 314:
SERIES AND LIMITS◮Given that the
- Page 318:
SERIES AND LIMITSThe divergence of
- Page 322:
SERIES AND LIMITSalthough in princi
- Page 326:
SERIES AND LIMITSr = − exp iθ. T
- Page 330:
SERIES AND LIMITS4.6 Taylor seriesT
- Page 334:
SERIES AND LIMITSx = a + h in the a
- Page 338:
SERIES AND LIMITSvalue of ξ that s
- Page 342:
SERIES AND LIMITS◮Evaluate the li
- Page 346:
SERIES AND LIMITSSummary of methods
- Page 350:
SERIES AND LIMITS4.15 Prove that∞
- Page 354:
SERIES AND LIMITSsin 3x(a) limx→0
- Page 358:
SERIES AND LIMITS4.15 Divide the se
- Page 362:
PARTIAL DIFFERENTIATIONto x and y r
- Page 366:
PARTIAL DIFFERENTIATIONcan be obtai
- Page 370:
PARTIAL DIFFERENTIATIONit exact. Co
- Page 374:
PARTIAL DIFFERENTIATIONFrom equatio
- Page 378:
PARTIAL DIFFERENTIATIONThus, from (
- Page 382:
PARTIAL DIFFERENTIATIONtheorem then
- Page 386:
PARTIAL DIFFERENTIATIONTo establish
- Page 390:
PARTIAL DIFFERENTIATIONmaximum0.40.
- Page 394:
PARTIAL DIFFERENTIATIONvaried. Howe
- Page 398:
PARTIAL DIFFERENTIATION◮Find the
- Page 402:
PARTIAL DIFFERENTIATION◮A system
- Page 406:
PARTIAL DIFFERENTIATIONP 1PP 2yf(x,
- Page 410:
PARTIAL DIFFERENTIATION5.11 Thermod
- Page 414:
PARTIAL DIFFERENTIATIONAlthough the
- Page 418:
PARTIAL DIFFERENTIATION(a) Find all
- Page 422:
PARTIAL DIFFERENTIATIONthe horizont
- Page 426:
PARTIAL DIFFERENTIATIONBy consideri
- Page 430:
PARTIAL DIFFERENTIATION5.19 The cos
- Page 434:
MULTIPLE INTEGRALSydSdxdA = dxdyRVd
- Page 438:
MULTIPLE INTEGRALSy1dyRx + y =100dx
- Page 442:
MULTIPLE INTEGRALSzcdV = dx dy dzdz
- Page 446:
MULTIPLE INTEGRALSzz =2yz = x 2 + y
- Page 450:
MULTIPLE INTEGRALSza√a2 − z 2dz
- Page 454:
MULTIPLE INTEGRALSaθdCFigure 6.8Su
- Page 458:
MULTIPLE INTEGRALSyu =constantv =co
- Page 462:
MULTIPLE INTEGRALS◮Evaluate the d
- Page 466:
MULTIPLE INTEGRALSzRTu = c 1v = c 2
- Page 470:
MULTIPLE INTEGRALSwhich agrees with
- Page 474:
MULTIPLE INTEGRALS6.6 The function(
- Page 478:
MULTIPLE INTEGRALSover the ellipsoi
- Page 482:
7Vector algebraThis chapter introdu
- Page 486:
VECTOR ALGEBRAabcb + cbcab + ca +(b
- Page 490:
VECTOR ALGEBRACEAGFDacBbOFigure 7.6
- Page 494:
VECTOR ALGEBRAkaja z ka y ja x iiFi
- Page 498:
VECTOR ALGEBRAFrom (7.15) we see th
- Page 502:
VECTOR ALGEBRAa × bθbaFigure 7.9s
- Page 506:
VECTOR ALGEBRAis the forward direct
- Page 510:
VECTOR ALGEBRA◮Find the volume V
- Page 514:
VECTOR ALGEBRAˆnARadrOFigure 7.13
- Page 518:
VECTOR ALGEBRAPp − apdAbθaOFigur
- Page 522:
VECTOR ALGEBRAQbqˆnPpaOFigure 7.16
- Page 526:
VECTOR ALGEBRAnot coplanar. Moreove
- Page 530:
VECTOR ALGEBRA7.12 The plane P 1 co
- Page 534:
VECTOR ALGEBRA7.22 In subsection 7.
- Page 538:
VECTOR ALGEBRAof vector plots for p
- Page 542:
MATRICES AND VECTOR SPACESa discuss
- Page 546:
MATRICES AND VECTOR SPACESWe reiter
- Page 550:
MATRICES AND VECTOR SPACES8.1.3 Som
- Page 554:
MATRICES AND VECTOR SPACESmay be th
- Page 558:
MATRICES AND VECTOR SPACESIn a simi
- Page 562:
MATRICES AND VECTOR SPACES◮The ma
- Page 566:
MATRICES AND VECTOR SPACESThese are
- Page 570:
MATRICES AND VECTOR SPACES◮Find t
- Page 574:
MATRICES AND VECTOR SPACESthe right
- Page 578:
MATRICES AND VECTOR SPACESdetermina
- Page 582:
MATRICES AND VECTOR SPACESIt follow
- Page 586:
MATRICES AND VECTOR SPACESequivalen
- Page 590:
MATRICES AND VECTOR SPACESand may b
- Page 594:
MATRICES AND VECTOR SPACESmay be sh
- Page 598:
MATRICES AND VECTOR SPACESClearly r
- Page 602:
MATRICES AND VECTOR SPACESHence 〈
- Page 606:
MATRICES AND VECTOR SPACESWe also s
- Page 610:
MATRICES AND VECTOR SPACESa result
- Page 614:
MATRICES AND VECTOR SPACESHence λ
- Page 618:
MATRICES AND VECTOR SPACES8.14 Dete
- Page 622:
MATRICES AND VECTOR SPACES◮Constr
- Page 626:
MATRICES AND VECTOR SPACESComparing
- Page 630:
MATRICES AND VECTOR SPACESthat is,
- Page 634:
MATRICES AND VECTOR SPACES| exp A|.
- Page 638:
MATRICES AND VECTOR SPACESalso. Ano
- Page 642:
MATRICES AND VECTOR SPACES8.17.2 Qu
- Page 646:
MATRICES AND VECTOR SPACESIf a vect
- Page 650:
MATRICES AND VECTOR SPACES◮Show t
- Page 654:
MATRICES AND VECTOR SPACESThis set
- Page 658:
MATRICES AND VECTOR SPACESthe uniqu
- Page 662:
MATRICES AND VECTOR SPACESthe numbe
- Page 666:
MATRICES AND VECTOR SPACESnon-zero
- Page 670:
MATRICES AND VECTOR SPACESUsing the
- Page 674:
MATRICES AND VECTOR SPACES8.3 Using
- Page 678:
MATRICES AND VECTOR SPACES(b) find
- Page 682:
MATRICES AND VECTOR SPACES8.26 Show
- Page 686:
MATRICES AND VECTOR SPACES8.40 Find
- Page 690:
9Normal modesAny student of the phy
- Page 694:
NORMAL MODESP P Pθ 1θ 2θ 2lθ 1
- Page 698:
NORMAL MODESfrequency corresponds t
- Page 702:
NORMAL MODESThe final and most comp
- Page 706:
NORMAL MODESThe potential matrix is
- Page 710:
NORMAL MODESneous equations for α
- Page 714:
NORMAL MODESbe shown that they do p
- Page 718:
NORMAL MODESunder gravity. At time
- Page 722:
NORMAL MODES9.8 (It is recommended
- Page 726:
10Vector calculusIn chapter 7 we di
- Page 730:
VECTOR CALCULUSyê φjê ρρiφxFi
- Page 734:
VECTOR CALCULUSThe order of the fac
- Page 738:
VECTOR CALCULUSzCˆnPˆtˆbr(u)OyxF
- Page 742:
VECTOR CALCULUSTherefore, rememberi
- Page 746:
VECTOR CALCULUSFinally, we note tha
- Page 750:
VECTOR CALCULUStotal derivative, th
- Page 754:
VECTOR CALCULUSmathematical point o
- Page 758:
VECTOR CALCULUS◮For the function
- Page 762:
VECTOR CALCULUSIn addition to these
- Page 766:
VECTOR CALCULUS∇(φ + ψ) =∇φ
- Page 770:
VECTOR CALCULUSa is a vector field,
- Page 774:
VECTOR CALCULUSρ, φ, z, wherex =
- Page 778:
VECTOR CALCULUS∇Φ = ∂Φ∂ρ
- Page 782:
VECTOR CALCULUSand r ≥ 0, 0 ≤
- Page 786:
VECTOR CALCULUS10.10 General curvil
- Page 790:
VECTOR CALCULUSFor orthogonal coord
- Page 794:
VECTOR CALCULUS◮Prove the express
- Page 798:
VECTOR CALCULUS10.3 The general equ
- Page 802:
VECTOR CALCULUSUse this formula to
- Page 806:
VECTOR CALCULUS10.21 Paraboloidal c
- Page 810:
VECTOR CALCULUS10.23 The tangent ve
- Page 814:
LINE, SURFACE AND VOLUME INTEGRALSE
- Page 818:
LINE, SURFACE AND VOLUME INTEGRALSy
- Page 822:
LINE, SURFACE AND VOLUME INTEGRALSi
- Page 826:
LINE, SURFACE AND VOLUME INTEGRALSy
- Page 830:
LINE, SURFACE AND VOLUME INTEGRALSy
- Page 834:
LINE, SURFACE AND VOLUME INTEGRALSw
- Page 838:
LINE, SURFACE AND VOLUME INTEGRALSS
- Page 842:
LINE, SURFACE AND VOLUME INTEGRALSw
- Page 846:
LINE, SURFACE AND VOLUME INTEGRALSd
- Page 850:
LINE, SURFACE AND VOLUME INTEGRALSI
- Page 854:
LINE, SURFACE AND VOLUME INTEGRALS1
- Page 858:
LINE, SURFACE AND VOLUME INTEGRALSz
- Page 862:
LINE, SURFACE AND VOLUME INTEGRALSy
- Page 866:
LINE, SURFACE AND VOLUME INTEGRALS1
- Page 870:
LINE, SURFACE AND VOLUME INTEGRALS1
- Page 874:
LINE, SURFACE AND VOLUME INTEGRALSS
- Page 878:
LINE, SURFACE AND VOLUME INTEGRALSi
- Page 882:
LINE, SURFACE AND VOLUME INTEGRALS1
- Page 886:
LINE, SURFACE AND VOLUME INTEGRALS1
- Page 890:
FOURIER SERIESf(x)xLLFigure 12.1 An
- Page 894:
FOURIER SERIESapply for r = 0 as we
- Page 898:
FOURIER SERIESare not used as often
- Page 902:
FOURIER SERIES(a)0L(b)0L2L(c)0L2L(d
- Page 906:
FOURIER SERIESconverge to the corre
- Page 910:
FOURIER SERIES12.8 Parseval’s the
- Page 914:
FOURIER SERIESbe better for numeric
- Page 918:
FOURIER SERIES12.21 Find the comple
- Page 922:
FOURIER SERIES12.21 c n =[(−1) n
- Page 926:
INTEGRAL TRANSFORMSc(ω)expiωt−
- Page 930:
INTEGRAL TRANSFORMS◮Find the Four
- Page 934:
INTEGRAL TRANSFORMSYyk ′k0θx−Y
- Page 938:
INTEGRAL TRANSFORMSequals zero. Thi
- Page 942:
INTEGRAL TRANSFORMS◮Prove relatio
- Page 946:
INTEGRAL TRANSFORMS(i) Differentiat
- Page 950:
INTEGRAL TRANSFORMSg(y)(a)(b)(c)(d)
- Page 954:
INTEGRAL TRANSFORMSgiven by∫1 ∞
- Page 958:
INTEGRAL TRANSFORMS◮Prove the Wie
- Page 962:
INTEGRAL TRANSFORMStwo- or three-di
- Page 966:
INTEGRAL TRANSFORMS(iii) Once again
- Page 970:
INTEGRAL TRANSFORMS◮Find the Lapl
- Page 974:
INTEGRAL TRANSFORMSFigure 13.7text)
- Page 978:
INTEGRAL TRANSFORMS13.4 Exercises13
- Page 982:
INTEGRAL TRANSFORMS13.10 In many ap
- Page 986:
INTEGRAL TRANSFORMS13.18 The equiva
- Page 990:
INTEGRAL TRANSFORMS13.27 The functi
- Page 994:
14First-order ordinary differential
- Page 998:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1002:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1006:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1010:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1014:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1018:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1022:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1026:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1030:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1034:
FIRST-ORDER ORDINARY DIFFERENTIAL E
- Page 1038:
15Higher-order ordinary differentia
- Page 1042:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1046:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1050:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1054:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1058:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1062:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1066:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1070:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1074:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1078:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1082:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1086:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1090:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1094:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1098:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1102:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1106:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1110:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1114:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1118:
HIGHER-ORDER ORDINARY DIFFERENTIAL
- Page 1122:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1126:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1130:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1134:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1138:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1142:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1146:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1150:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1154:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1158:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1162:
SERIES SOLUTIONS OF ORDINARY DIFFER
- Page 1166:
17Eigenfunction methods fordifferen
- Page 1170:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1174:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1178:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1182:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1186:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1190:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1194:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1198:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1202:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1206:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1210:
EIGENFUNCTION METHODS FOR DIFFERENT
- Page 1214:
SPECIAL FUNCTIONSwhich on collectin
- Page 1218:
SPECIAL FUNCTIONSwhere P l (x) is a
- Page 1222:
SPECIAL FUNCTIONSwhich reduces to(x
- Page 1226:
SPECIAL FUNCTIONS◮Prove the expre
- Page 1230:
SPECIAL FUNCTIONSr and r ′ must b
- Page 1234:
SPECIAL FUNCTIONSin (18.3) and (18.
- Page 1238:
SPECIAL FUNCTIONSto be zero, since
- Page 1242:
SPECIAL FUNCTIONSGenerating functio
- Page 1246:
SPECIAL FUNCTIONSorthonormal set, i
- Page 1250:
SPECIAL FUNCTIONSand has three regu
- Page 1254:
SPECIAL FUNCTIONS4U 2U 32U 0U 1−1
- Page 1258:
SPECIAL FUNCTIONSThe normalisation,
- Page 1262:
SPECIAL FUNCTIONSUsing (18.65) and
- Page 1266:
SPECIAL FUNCTIONSthe form of a Frob
- Page 1270:
SPECIAL FUNCTIONS1.51J 0J 1J 20.52
- Page 1274:
SPECIAL FUNCTIONS10.5Y 0Y 1 Y22 4 6
- Page 1278:
SPECIAL FUNCTIONSevaluated using l
- Page 1282:
SPECIAL FUNCTIONSFinally, subtracti
- Page 1286:
SPECIAL FUNCTIONSUsing de Moivre’
- Page 1290:
SPECIAL FUNCTIONS◮Show that the l
- Page 1294:
SPECIAL FUNCTIONS105L 2L 3L 0L 11 2
- Page 1298:
SPECIAL FUNCTIONSThe above orthogon
- Page 1302:
SPECIAL FUNCTIONSIn particular, we
- Page 1306:
SPECIAL FUNCTIONSwhere, in the seco
- Page 1310:
SPECIAL FUNCTIONS18.9.1 Properties
- Page 1314:
SPECIAL FUNCTIONSDifferentiating th
- Page 1318:
SPECIAL FUNCTIONSgamma function. §
- Page 1322:
SPECIAL FUNCTIONSwhere in the secon
- Page 1326:
SPECIAL FUNCTIONSsecond solution to
- Page 1330:
SPECIAL FUNCTIONSThe gamma function
- Page 1334:
SPECIAL FUNCTIONSIf we let x = n +
- Page 1338:
SPECIAL FUNCTIONSwhich is the requi
- Page 1342:
SPECIAL FUNCTIONSand hence that the
- Page 1346:
SPECIAL FUNCTIONSDeduce the value o
- Page 1350:
SPECIAL FUNCTIONS18.24 The solution
- Page 1354:
19Quantum operatorsAlthough the pre
- Page 1358:
QUANTUM OPERATORSis to produce a sc
- Page 1362:
QUANTUM OPERATORSIf A| a n 〉 = a|
- Page 1366:
QUANTUM OPERATORSSimple identities
- Page 1370:
QUANTUM OPERATORSlater algebraic co
- Page 1374:
QUANTUM OPERATORSRHS gives(−i) 2
- Page 1378:
QUANTUM OPERATORSwith[L 2 ,L z]=[L2
- Page 1382:
QUANTUM OPERATORSoperate repeatedly
- Page 1386:
QUANTUM OPERATORS19.2.2 Uncertainty
- Page 1390:
QUANTUM OPERATORShence formally an
- Page 1394:
QUANTUM OPERATORSan arbitrary compl
- Page 1398:
QUANTUM OPERATORSThe proof, which m
- Page 1402:
QUANTUM OPERATORSFor a particle of
- Page 1406:
QUANTUM OPERATORS19.4 Hints and ans
- Page 1410:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1414:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1418:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1422:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1426:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1430:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1434:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1438:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1442:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1446:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1450:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1454:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1458:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1462:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1466:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1470:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1474:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1478:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1482:
PDES: GENERAL AND PARTICULAR SOLUTI
- Page 1486:
PDES: SEPARATION OF VARIABLES AND O
- Page 1490:
PDES: SEPARATION OF VARIABLES AND O
- Page 1494: PDES: SEPARATION OF VARIABLES AND O
- Page 1498: PDES: SEPARATION OF VARIABLES AND O
- Page 1502: PDES: SEPARATION OF VARIABLES AND O
- Page 1506: PDES: SEPARATION OF VARIABLES AND O
- Page 1510: PDES: SEPARATION OF VARIABLES AND O
- Page 1514: PDES: SEPARATION OF VARIABLES AND O
- Page 1518: PDES: SEPARATION OF VARIABLES AND O
- Page 1522: PDES: SEPARATION OF VARIABLES AND O
- Page 1526: PDES: SEPARATION OF VARIABLES AND O
- Page 1530: PDES: SEPARATION OF VARIABLES AND O
- Page 1534: PDES: SEPARATION OF VARIABLES AND O
- Page 1538: PDES: SEPARATION OF VARIABLES AND O
- Page 1542: PDES: SEPARATION OF VARIABLES AND O
- Page 1548: 21.3 SEPARATION OF VARIABLES IN POL
- Page 1552: 21.4 INTEGRAL TRANSFORM METHODS21.4
- Page 1556: 21.4 INTEGRAL TRANSFORM METHODS◮A
- Page 1560: 21.5 INHOMOGENEOUS PROBLEMS - GREEN
- Page 1564: 21.5 INHOMOGENEOUS PROBLEMS - GREEN
- Page 1568: 21.5 INHOMOGENEOUS PROBLEMS - GREEN
- Page 1572: 21.5 INHOMOGENEOUS PROBLEMS - GREEN
- Page 1576: 21.5 INHOMOGENEOUS PROBLEMS - GREEN
- Page 1580: 21.5 INHOMOGENEOUS PROBLEMS - GREEN
- Page 1584: 21.5 INHOMOGENEOUS PROBLEMS - GREEN
- Page 1588: 21.5 INHOMOGENEOUS PROBLEMS - GREEN
- Page 1592: 21.6 EXERCISESUsing plane polar coo
- Page 1596:
21.6 EXERCISES(a) Evaluate dPl m(µ
- Page 1600:
21.6 EXERCISES21.18 A sphere of rad
- Page 1604:
21.7 HINTS AND ANSWERSin V and take
- Page 1608:
22Calculus of variationsIn chapters
- Page 1612:
22.2 SPECIAL CASESto these variatio
- Page 1616:
22.2 SPECIAL CASESydsdydxxFigure 22
- Page 1620:
22.3 SOME EXTENSIONSbzρ−ba(a) (b
- Page 1624:
22.3 SOME EXTENSIONSy(x)+η(x)∆yy
- Page 1628:
22.4 CONSTRAINED VARIATIONwhere k i
- Page 1632:
22.5 PHYSICAL VARIATIONAL PRINCIPLE
- Page 1636:
22.5 PHYSICAL VARIATIONAL PRINCIPLE
- Page 1640:
22.6 GENERAL EIGENVALUE PROBLEMScon
- Page 1644:
22.7 ESTIMATION OF EIGENVALUES AND
- Page 1648:
22.8 ADJUSTMENT OF PARAMETERSIt is
- Page 1652:
22.9 EXERCISES22.9 Exercises22.1 A
- Page 1656:
22.9 EXERCISESpath of a small test
- Page 1660:
22.10 HINTS AND ANSWERStotal energy
- Page 1664:
23Integral equationsIt is not unusu
- Page 1668:
23.3 OPERATOR NOTATION AND THE EXIS
- Page 1672:
23.4 CLOSED-FORM SOLUTIONS23.4.1 Se
- Page 1676:
23.4 CLOSED-FORM SOLUTIONS23.4.2 In
- Page 1680:
23.4 CLOSED-FORM SOLUTIONSso we can
- Page 1684:
23.5 NEUMANN SERIES23.5 Neumann ser
- Page 1688:
23.6 FREDHOLM THEORYcommon ratio λ
- Page 1692:
23.7 SCHMIDT-HILBERT THEORYLet us b
- Page 1696:
23.8 EXERCISESthus Hermitian. In or
- Page 1700:
23.8 EXERCISES(b) Obtain the eigenv
- Page 1704:
23.9 HINTS AND ANSWERS23.9 Hints an
- Page 1708:
24.1 FUNCTIONS OF A COMPLEX VARIABL
- Page 1712:
24.2 THE CAUCHY-RIEMANN RELATIONS
- Page 1716:
24.2 THE CAUCHY-RIEMANN RELATIONSSi
- Page 1720:
24.3 POWER SERIES IN A COMPLEX VARI
- Page 1724:
24.4 SOME ELEMENTARY FUNCTIONSreal-
- Page 1728:
24.5 MULTIVALUED FUNCTIONS AND BRAN
- Page 1732:
24.6 SINGULARITIES AND ZEROS OF COM
- Page 1736:
24.7 CONFORMAL TRANSFORMATIONSThus
- Page 1740:
24.7 CONFORMAL TRANSFORMATIONSpoint
- Page 1744:
24.7 CONFORMAL TRANSFORMATIONSysw 5
- Page 1748:
24.8 COMPLEX INTEGRALSyw 3 s w 3w =
- Page 1752:
24.8 COMPLEX INTEGRALSyRtyyC 1 C 2R
- Page 1756:
24.9 CAUCHY’S THEOREMnamely Cauch
- Page 1760:
24.10 CAUCHY’S INTEGRAL FORMULAyC
- Page 1764:
24.11 TAYLOR AND LAURENT SERIESFurt
- Page 1768:
24.11 TAYLOR AND LAURENT SERIESof o
- Page 1772:
24.11 TAYLOR AND LAURENT SERIESdeno
- Page 1776:
24.12 RESIDUE THEOREMSuppose the fu
- Page 1780:
24.13 DEFINITE INTEGRALS USING CONT
- Page 1784:
24.13 DEFINITE INTEGRALS USING CONT
- Page 1788:
24.13 DEFINITE INTEGRALS USING CONT
- Page 1792:
24.14 EXERCISESWe have seen that
- Page 1796:
24.14 EXERCISES24.14 Prove that, fo
- Page 1800:
25Applications of complex variables
- Page 1804:
25.1 COMPLEX POTENTIALSthe field pr
- Page 1808:
25.1 COMPLEX POTENTIALSyQxPˆnFigur
- Page 1812:
25.2 APPLICATIONS OF CONFORMAL TRAN
- Page 1816:
25.3 LOCATION OF ZEROSφ =0yπ/αz
- Page 1820:
25.3 LOCATION OF ZEROSpolynomials,
- Page 1824:
25.4 SUMMATION OF SERIES◮By consi
- Page 1828:
25.5 INVERSE LAPLACE TRANSFORMΓRΓ
- Page 1832:
25.5 INVERSE LAPLACE TRANSFORMf(x)1
- Page 1836:
25.6 STOKES’ EQUATION AND AIRY IN
- Page 1840:
25.6 STOKES’ EQUATION AND AIRY IN
- Page 1844:
25.6 STOKES’ EQUATION AND AIRY IN
- Page 1848:
25.7 WKB METHODSthere exist many re
- Page 1852:
25.7 WKB METHODSThis still requires
- Page 1856:
25.7 WKB METHODSThe precise combina
- Page 1860:
25.7 WKB METHODSfor some constant A
- Page 1864:
25.7 WKB METHODSone function and th
- Page 1868:
25.8 APPROXIMATIONS TO INTEGRALSFin
- Page 1872:
25.8 APPROXIMATIONS TO INTEGRALSFro
- Page 1876:
25.8 APPROXIMATIONS TO INTEGRALSany
- Page 1880:
25.8 APPROXIMATIONS TO INTEGRALSto
- Page 1884:
25.8 APPROXIMATIONS TO INTEGRALSwhi
- Page 1888:
25.8 APPROXIMATIONS TO INTEGRALS(a)
- Page 1892:
25.8 APPROXIMATIONS TO INTEGRALSare
- Page 1896:
25.8 APPROXIMATIONS TO INTEGRALS◮
- Page 1900:
25.9 EXERCISESimaginary z-axes, fin
- Page 1904:
25.9 EXERCISES(b) Calculate F(s) on
- Page 1908:
25.10 HINTS AND ANSWERSt = −i and
- Page 1912:
26TensorsIt may seem obvious that t
- Page 1916:
26.2 CHANGE OF BASISIn the second o
- Page 1920:
26.3 CARTESIAN TENSORSx 2x ′ 1x
- Page 1924:
26.4 FIRST- AND ZERO-ORDER CARTESIA
- Page 1928:
26.5 SECOND- AND HIGHER-ORDER CARTE
- Page 1932:
26.5 SECOND- AND HIGHER-ORDER CARTE
- Page 1936:
26.7 THE QUOTIENT LAWAn operation t
- Page 1940:
26.8 THE TENSORS δ ij AND ɛ ijkN
- Page 1944:
26.8 THE TENSORS δ ij AND ɛ ijk
- Page 1948:
26.9 ISOTROPIC TENSORSare independe
- Page 1952:
26.10 IMPROPER ROTATIONS AND PSEUDO
- Page 1956:
26.11 DUAL TENSORSformations, for w
- Page 1960:
26.12 PHYSICAL APPLICATIONS OF TENS
- Page 1964:
26.12 PHYSICAL APPLICATIONS OF TENS
- Page 1968:
26.14 NON-CARTESIAN COORDINATESThe
- Page 1972:
26.15 THE METRIC TENSORsecond-order
- Page 1976:
26.15 THE METRIC TENSORwhere we hav
- Page 1980:
26.16 GENERAL COORDINATE TRANSFORMA
- Page 1984:
26.17 RELATIVE TENSORS◮Show that
- Page 1988:
26.18 DERIVATIVES OF BASIS VECTORS
- Page 1992:
26.18 DERIVATIVES OF BASIS VECTORS
- Page 1996:
26.19 COVARIANT DIFFERENTIATIONcons
- Page 2000:
26.20 VECTOR OPERATORS IN TENSOR FO
- Page 2004:
26.20 VECTOR OPERATORS IN TENSOR FO
- Page 2008:
26.21 ABSOLUTE DERIVATIVES ALONG CU
- Page 2012:
26.23 EXERCISESWriting out the cova
- Page 2016:
26.23 EXERCISES26.10 A symmetric se
- Page 2020:
26.23 EXERCISES26.23 A fourth-order
- Page 2024:
26.24 HINTS AND ANSWERSin the (mult
- Page 2028:
27.1 ALGEBRAIC AND TRANSCENDENTAL E
- Page 2032:
27.1 ALGEBRAIC AND TRANSCENDENTAL E
- Page 2036:
27.1 ALGEBRAIC AND TRANSCENDENTAL E
- Page 2040:
27.1 ALGEBRAIC AND TRANSCENDENTAL E
- Page 2044:
27.2 CONVERGENCE OF ITERATION SCHEM
- Page 2048:
27.3 SIMULTANEOUS LINEAR EQUATIONSv
- Page 2052:
27.3 SIMULTANEOUS LINEAR EQUATIONSt
- Page 2056:
. . .. . .27.3 SIMULTANEOUS LINEAR
- Page 2060:
27.4 NUMERICAL INTEGRATION(a) (b) (
- Page 2064:
27.4 NUMERICAL INTEGRATIONThis prov
- Page 2068:
27.4 NUMERICAL INTEGRATION27.4.3 Ga
- Page 2072:
27.4 NUMERICAL INTEGRATIONso, provi
- Page 2076:
27.4 NUMERICAL INTEGRATIONfactor is
- Page 2080:
27.4 NUMERICAL INTEGRATIONhas becom
- Page 2084:
27.4 NUMERICAL INTEGRATIONwill have
- Page 2088:
27.4 NUMERICAL INTEGRATIONy = f(x)y
- Page 2092:
27.4 NUMERICAL INTEGRATIONIt will b
- Page 2096:
27.5 FINITE DIFFERENCESmany values
- Page 2100:
27.6 DIFFERENTIAL EQUATIONSx h y(ex
- Page 2104:
27.6 DIFFERENTIAL EQUATIONSbut they
- Page 2108:
27.6 DIFFERENTIAL EQUATIONSThe forw
- Page 2112:
27.6 DIFFERENTIAL EQUATIONSWe assum
- Page 2116:
27.7 HIGHER-ORDER EQUATIONSy1.00.80
- Page 2120:
27.8 PARTIAL DIFFERENTIAL EQUATIONS
- Page 2124:
27.9 EXERCISES27.9 Exercises27.1 Us
- Page 2128:
27.9 EXERCISES(b) Try to repeat the
- Page 2132:
27.9 EXERCISES27.21 Write a compute
- Page 2136:
27.10 HINTS AND ANSWERS27.27 The Sc
- Page 2140:
28Group theoryFor systems that have
- Page 2144:
28.1 GROUPS28.1.1 Definition of a g
- Page 2148:
28.1 GROUPS◮Using only the first
- Page 2152:
28.1 GROUPSLMKFigure 28.2 Reflectio
- Page 2156:
28.2 FINITE GROUPS28.2 Finite group
- Page 2160:
28.2 FINITE GROUPS(a)1 5 7 111 1 5
- Page 2164:
28.3 NON-ABELIAN GROUPSAs a first e
- Page 2168:
28.3 NON-ABELIAN GROUPSI A B C D EI
- Page 2172:
28.4 PERMUTATION GROUPSSuppose that
- Page 2176:
28.5 MAPPINGS BETWEEN GROUPS28.5 Ma
- Page 2180:
28.6 SUBGROUPS(a)I A B C D EI I A B
- Page 2184:
28.7 SUBDIVIDING A GROUP(i) the set
- Page 2188:
28.7 SUBDIVIDING A GROUPthis implie
- Page 2192:
28.7 SUBDIVIDING A GROUP• Two cos
- Page 2196:
28.7 SUBDIVIDING A GROUP(iii) In an
- Page 2200:
28.8 EXERCISES28.4 Prove that the r
- Page 2204:
28.8 EXERCISESSimilarly compute C 2
- Page 2208:
28.9 HINTS AND ANSWERS≠For Φ 4 ,
- Page 2212:
29.1 DIPOLE MOMENTS OF MOLECULESABA
- Page 2216:
29.2 CHOOSING AN APPROPRIATE FORMAL
- Page 2220:
29.2 CHOOSING AN APPROPRIATE FORMAL
- Page 2224:
29.2 CHOOSING AN APPROPRIATE FORMAL
- Page 2228:
29.3 EQUIVALENT REPRESENTATIONSresp
- Page 2232:
29.4 REDUCIBILITY OF A REPRESENTATI
- Page 2236:
29.4 REDUCIBILITY OF A REPRESENTATI
- Page 2240:
29.5 THE ORTHOGONALITY THEOREM FOR
- Page 2244:
29.6 CHARACTERS3m I A, B C, D, EA 1
- Page 2248:
29.7 COUNTING IRREPS USING CHARACTE
- Page 2252:
29.7 COUNTING IRREPS USING CHARACTE
- Page 2256:
29.7 COUNTING IRREPS USING CHARACTE
- Page 2260:
29.8 CONSTRUCTION OF A CHARACTER TA
- Page 2264:
29.10 PRODUCT REPRESENTATIONSgive a
- Page 2268:
29.11 PHYSICAL APPLICATIONS OF GROU
- Page 2272:
29.11 PHYSICAL APPLICATIONS OF GROU
- Page 2276:
29.11 PHYSICAL APPLICATIONS OF GROU
- Page 2280:
29.11 PHYSICAL APPLICATIONS OF GROU
- Page 2284:
29.12 EXERCISESas the sum of two on
- Page 2288:
29.12 EXERCISESUse this to show tha
- Page 2292:
29.13 HINTS AND ANSWERS(a) Make an
- Page 2296:
30ProbabilityAll scientists will kn
- Page 2300:
30.1 VENN DIAGRAMSA42 6 3BS15Figure
- Page 2304:
30.1 VENN DIAGRAMSgets beyond three
- Page 2308:
30.2 PROBABILITYtimes then we expec
- Page 2312:
30.2 PROBABILITYHowever, we may wri
- Page 2316:
30.2 PROBABILITYace from a pack of
- Page 2320:
30.2 PROBABILITYA 4A 3OA 1A 2BFigur
- Page 2324:
30.3 PERMUTATIONS AND COMBINATIONSW
- Page 2328:
30.3 PERMUTATIONS AND COMBINATIONSt
- Page 2332:
30.3 PERMUTATIONS AND COMBINATIONSm
- Page 2336:
30.4 RANDOM VARIABLES AND DISTRIBUT
- Page 2340:
30.4 RANDOM VARIABLES AND DISTRIBUT
- Page 2344:
30.5 PROPERTIES OF DISTRIBUTIONSIn
- Page 2348:
30.5 PROPERTIES OF DISTRIBUTIONSInt
- Page 2352:
30.5 PROPERTIES OF DISTRIBUTIONS|x
- Page 2356:
30.5 PROPERTIES OF DISTRIBUTIONSWe
- Page 2360:
30.6 FUNCTIONS OF RANDOM VARIABLESf
- Page 2364:
30.6 FUNCTIONS OF RANDOM VARIABLESY
- Page 2368:
30.6 FUNCTIONS OF RANDOM VARIABLESw
- Page 2372:
30.7 GENERATING FUNCTIONSvariance o
- Page 2376:
30.7 GENERATING FUNCTIONSand differ
- Page 2380:
30.7 GENERATING FUNCTIONSi.e. the P
- Page 2384:
30.7 GENERATING FUNCTIONSThe MGF wi
- Page 2388:
30.7 GENERATING FUNCTIONSprobabilit
- Page 2392:
30.7 GENERATING FUNCTIONSComparing
- Page 2396:
30.8 IMPORTANT DISCRETE DISTRIBUTIO
- Page 2400:
30.8 IMPORTANT DISCRETE DISTRIBUTIO
- Page 2404:
30.8 IMPORTANT DISCRETE DISTRIBUTIO
- Page 2408:
30.8 IMPORTANT DISCRETE DISTRIBUTIO
- Page 2412:
30.8 IMPORTANT DISCRETE DISTRIBUTIO
- Page 2416:
30.9 IMPORTANT CONTINUOUS DISTRIBUT
- Page 2420:
30.9 IMPORTANT CONTINUOUS DISTRIBUT
- Page 2424:
30.9 IMPORTANT CONTINUOUS DISTRIBUT
- Page 2428:
30.9 IMPORTANT CONTINUOUS DISTRIBUT
- Page 2432:
30.9 IMPORTANT CONTINUOUS DISTRIBUT
- Page 2436:
30.9 IMPORTANT CONTINUOUS DISTRIBUT
- Page 2440:
30.9 IMPORTANT CONTINUOUS DISTRIBUT
- Page 2444:
30.9 IMPORTANT CONTINUOUS DISTRIBUT
- Page 2448:
30.10 THE CENTRAL LIMIT THEOREMand
- Page 2452:
30.11 JOINT DISTRIBUTIONSconsult on
- Page 2456:
30.12 PROPERTIES OF JOINT DISTRIBUT
- Page 2460:
30.12 PROPERTIES OF JOINT DISTRIBUT
- Page 2464:
30.12 PROPERTIES OF JOINT DISTRIBUT
- Page 2468:
30.13 GENERATING FUNCTIONS FOR JOIN
- Page 2472:
30.15 IMPORTANT JOINT DISTRIBUTIONS
- Page 2476:
30.15 IMPORTANT JOINT DISTRIBUTIONS
- Page 2480:
30.16 EXERCISEStivariate Gaussian.
- Page 2484:
30.16 EXERCISES30.11 A boy is selec
- Page 2488:
30.16 EXERCISES30.18 A particle is
- Page 2492:
30.16 EXERCISESaccording to one of
- Page 2496:
30.17 HINTS AND ANSWERSconstraint
- Page 2500:
31StatisticsIn this chapter, we tur
- Page 2504:
31.2 SAMPLE STATISTICS188.7 204.7 1
- Page 2508:
31.2 SAMPLE STATISTICSand the sampl
- Page 2512:
31.2 SAMPLE STATISTICSmoments of th
- Page 2516:
31.3 ESTIMATORS AND SAMPLING DISTRI
- Page 2520:
31.3 ESTIMATORS AND SAMPLING DISTRI
- Page 2524:
31.3 ESTIMATORS AND SAMPLING DISTRI
- Page 2528:
31.3 ESTIMATORS AND SAMPLING DISTRI
- Page 2532:
31.3 ESTIMATORS AND SAMPLING DISTRI
- Page 2536:
31.3 ESTIMATORS AND SAMPLING DISTRI
- Page 2540:
31.3 ESTIMATORS AND SAMPLING DISTRI
- Page 2544:
31.4 SOME BASIC ESTIMATORSâ 2a 2(a
- Page 2548:
31.4 SOME BASIC ESTIMATORSexact exp
- Page 2552:
31.4 SOME BASIC ESTIMATORSwhere s 4
- Page 2556:
31.4 SOME BASIC ESTIMATORSthe form(
- Page 2560:
31.4 SOME BASIC ESTIMATORS(known) c
- Page 2564:
31.4 SOME BASIC ESTIMATORSSince the
- Page 2568:
31.5 MAXIMUM-LIKELIHOOD METHODSubst
- Page 2572:
31.5 MAXIMUM-LIKELIHOOD METHODL(x;
- Page 2576:
31.5 MAXIMUM-LIKELIHOOD METHOD◮In
- Page 2580:
31.5 MAXIMUM-LIKELIHOOD METHOD31.5.
- Page 2584:
31.5 MAXIMUM-LIKELIHOOD METHOD31.5.
- Page 2588:
31.5 MAXIMUM-LIKELIHOOD METHODwhere
- Page 2592:
31.5 MAXIMUM-LIKELIHOOD METHODL(x;
- Page 2596:
31.5 MAXIMUM-LIKELIHOOD METHODBy su
- Page 2600:
31.6 THE METHOD OF LEAST SQUARESThe
- Page 2604:
31.6 THE METHOD OF LEAST SQUARESwhe
- Page 2608:
31.6 THE METHOD OF LEAST SQUARESy76
- Page 2612:
31.7 HYPOTHESIS TESTINGhowever, suc
- Page 2616:
31.7 HYPOTHESIS TESTINGP (t|H 0 )α
- Page 2620:
31.7 HYPOTHESIS TESTING◮Ten indep
- Page 2624:
31.7 HYPOTHESIS TESTING◮Ten indep
- Page 2628:
31.7 HYPOTHESIS TESTINGThe sum of s
- Page 2632:
31.7 HYPOTHESIS TESTINGP (t|H 0 )0.
- Page 2636:
31.7 HYPOTHESIS TESTINGdistribution
- Page 2640:
31.7 HYPOTHESIS TESTINGλ(u)0.100.0
- Page 2644:
31.7 HYPOTHESIS TESTINGWe now turn
- Page 2648:
31.7 HYPOTHESIS TESTINGC n1 ,n 2(F)
- Page 2652:
31.7 HYPOTHESIS TESTINGIn the last
- Page 2656:
31.8 EXERCISES31.6 Prove that the s
- Page 2660:
31.8 EXERCISES31.13 A similar techn
- Page 2664:
31.9 HINTS AND ANSWERS31.9 Hints an
- Page 2668:
IndexWhere the discussion of a topi
- Page 2672:
INDEXrecurrence relations, 611-612s
- Page 2676:
INDEXcomplement, 1121probability fo
- Page 2680:
INDEXin spherical polars, 362Stoke
- Page 2684:
INDEXin cylindrical polars, 360in s
- Page 2688:
INDEXdiscontinuous functions, 420-4
- Page 2692:
INDEXnomenclature, 1102non-Abelian,
- Page 2696:
INDEXtriple, see multiple integrals
- Page 2700:
INDEXlevel lines, 905, 906Levi-Civi
- Page 2704:
INDEXMonte Carlo methods, of integr
- Page 2708:
INDEXorthogonal transformations, 93
- Page 2712:
INDEXstandard deviation σ, 1146var
- Page 2716:
INDEXwave equation, 714-716, 737, 7
- Page 2720:
INDEXsymmetric tensors, 938symmetry
- Page 2724:
INDEXvolume integrals, 396and diver
Inappropriate
Loading...
Inappropriate
You have already flagged this document.
Thank you, for helping us keep this platform clean.
The editors will have a look at it as soon as possible.
Mail this publication
Loading...
Embed
Loading...
Delete template?
Are you sure you want to delete your template?
DOWNLOAD ePAPER
This ePaper is currently not available for download.
You can find similar magazines on this topic below under ‘Recommendations’.