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ToKate,TomandHarvey -- A.C.
ToKathy-- R.D.
Tomyfatherandmother --M.H.
ToSuzanne,AlexandraandDominic --J.F.
ToKate,TomandHarvey -- A.C.ToKathy-- R.D.Tomyfatherandmother --M.H.ToSuzanne,AlexandraandDominic --J.F.
ContentsPrefaceAcknowledgementsxviixixChapter1 Reviewofalgebraictechniques 11.1 Introduction 11.2 Laws of indices 21.3 Number bases 111.4 Polynomial equations 201.5 Algebraicfractions 261.6 Solution of inequalities 331.7 Partial fractions 391.8 Summation notation 46Review exercises 1 50Chapter2 Engineeringfunctions 542.1 Introduction 542.2 Numbers and intervals 552.3 Basic concepts of functions 562.4 Review of some common engineering functions and techniques 70Review exercises 2 113Chapter3 Thetrigonometricfunctions 1153.1 Introduction 1153.2 Degreesand radians 1163.3 The trigonometric ratios 1163.4 The sine, cosine and tangent functions 1203.5 The sincxfunction 1233.6 Trigonometric identities 1253.7 Modellingwavesusing sint and cost 1313.8 Trigonometric equations 144Review exercises 3 150
- Page 1 and 2: ENGINEERINGMATHEMATICSA Foundation
- Page 3 and 4: At Pearson, we have a simple missio
- Page 5: PEARSONEDUCATIONLIMITEDEdinburghGat
- Page 9 and 10: Contents ix8.3 Addition,subtraction
- Page 11 and 12: Contents xiChapter17 Numericalinteg
- Page 13 and 14: Contents xiiiChapter24 TheFouriertr
- Page 15 and 16: Contents xvAppendixI Representing a
- Page 17 and 18: PrefaceAudienceThis book has been w
- Page 19 and 20: AcknowledgementsWearegratefultothef
- Page 21 and 22: 1 ReviewofalgebraictechniquesConten
- Page 23 and 24: 1.2 Laws of indices 3So6 2 6 3 =6 5
- Page 25 and 26: 1.2 Laws of indices 5(c)(d)x 9x 5 =
- Page 27 and 28: 1.2 Laws of indices 71.2.4 Multiple
- Page 29 and 30: 1.2 Laws of indices 9Similarly(2 1/
- Page 31 and 32: 1.3 Number bases 11Solutions1 (a) 8
- Page 33 and 34: 1.3 Number bases 13giving83=64+16+3
- Page 35 and 36: 1.3 Number bases 15Example1.16 Conv
- Page 37 and 38: 1.3 Number bases 17Table1.4isusedto
- Page 39 and 40: 1.3 Number bases 19The display show
- Page 41 and 42: 1.4 Polynomial equations 21Example1
- Page 43 and 44: 1.4 Polynomial equations 23We now i
- Page 45 and 46: so thatβ=−13Bycomparing coeffici
- Page 47 and 48: 1.5.1 Properandimproperfractions1.5
- Page 49 and 50: 1.5 Algebraic fractions 29(b) Facto
- Page 51 and 52: 1.5 Algebraic fractions 31and4x +2
- Page 53 and 54: 1.6 Solution of inequalities 33(g)(
- Page 55 and 56: 1.6 Solution of inequalities 35Exam
- Page 57 and 58:
1.6 Solution of inequalities 37Case
- Page 59 and 60:
1.7 Partial fractions 391.7 PARTIAL
- Page 61 and 62:
1.7 Partial fractions 41Thus we hav
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1.7 Partial fractions 43Solution Th
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1.7 Partial fractions 45EXERCISES1.
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1.8 Summation notation 47Engineerin
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1.8 Summation notation 49thecircuit
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Review exercises 1 513 Removethe br
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Review exercises 1 53[ ((d) 3 z −
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2.2 Numbers and intervals 55in orde
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2.3 Basic concepts of functions 57f
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2.3 Basic concepts of functions 59s
- Page 81 and 82:
2.3 Basic concepts of functions 61b
- Page 83 and 84:
2.3 Basic concepts of functions 63E
- Page 85 and 86:
2.3 Basic concepts of functions 65f
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2.3 Basic concepts of functions 67T
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2.3 Basic concepts of functions 691
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2.4 Review of some common engineeri
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2.4 Review of some common engineeri
- Page 95 and 96:
2.4.2 Rationalfunctions2.4 Review o
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2.4 Review of some common engineeri
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2.4 Review of some common engineeri
- Page 101 and 102:
Table2.2Values ofa x fora = 0.5, 2
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2.4 Review of some common engineeri
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2.4.4 Logarithmfunctions2.4 Review
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2.4 Review of some common engineeri
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2.4 Review of some common engineeri
- Page 111 and 112:
2.4 Review of some common engineeri
- Page 113 and 114:
2.4 Review of some common engineeri
- Page 115 and 116:
2.4 Review of some common engineeri
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2.4 Review of some common engineeri
- Page 119 and 120:
2.4 Review of some common engineeri
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2.4 Review of some common engineeri
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2.4 Review of some common engineeri
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2.4 Review of some common engineeri
- Page 127 and 128:
2.4 Review of some common engineeri
- Page 129 and 130:
2.4 Review of some common engineeri
- Page 131 and 132:
2.4 Review of some common engineeri
- Page 133 and 134:
Review exercises 2 113REVIEWEXERCIS
- Page 135 and 136:
3 ThetrigonometricfunctionsContents
- Page 137 and 138:
Note thattanθ = BCAB = BCAC × ACA
- Page 139 and 140:
3.3 The trigonometric ratios 119yyB
- Page 141 and 142:
3.4 The sine, cosine and tangent fu
- Page 143 and 144:
3.5 The sincxfunction 123EXERCISES3
- Page 145 and 146:
3.6 Trigonometric identities 125ors
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3.6 Trigonometric identities 127Exa
- Page 149 and 150:
3.6 Trigonometric identities 129Exa
- Page 151 and 152:
3.7 Modelling waves using sint and
- Page 153 and 154:
3.7 Modelling waves using sint and
- Page 155 and 156:
3.7 Modelling waves using sint and
- Page 157 and 158:
3.7 Modelling waves using sint and
- Page 159 and 160:
3.7 Modelling waves using sint and
- Page 161 and 162:
3.7 Modelling waves using sint and
- Page 163 and 164:
3.7 Modelling waves using sint and
- Page 165 and 166:
3.8 Trigonometric equations 145sin
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3.8 Trigonometric equations 147tan
- Page 169 and 170:
Usingascientific calculator wehavez
- Page 171 and 172:
Review exercises 3 1516 Simplify th
- Page 173 and 174:
Review exercises 3 153(d) 1.581sin(
- Page 175 and 176:
4.2 Cartesian coordinate system --
- Page 177 and 178:
4.3 Cartesian coordinate system --
- Page 179 and 180:
4.4 Polar coordinates 1594.4 POLARC
- Page 181 and 182:
4.4 Polar coordinates 161yOurxFigur
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4.5 Some simple polar curves 163EXE
- Page 185 and 186:
4.5 Some simple polar curves 165uAn
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4.6 Cylindrical polar coordinates 1
- Page 189 and 190:
4.6 Cylindrical polar coordinates 1
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4.7 Spherical polar coordinates 171
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Review exercises 4 173zzFeeding lin
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5 DiscretemathematicsContents 5.1 I
- Page 197 and 198:
5.2 Set theory 177Example5.1 Useset
- Page 199 and 200:
5.2 Set theory 179EMNM fNfFigure5.2
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5.2 Set theory 181someelementsinA.W
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5.3 Logic 183CDCD(a)(b)CDCD(c)(d)(e
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5.4 Boolean algebra 185ABA . BFigur
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5.4 Boolean algebra 187Table5.12Tru
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5.4 Boolean algebra 189However, we
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5.4 Boolean algebra 191S0Stage0A0 B
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5.4 Boolean algebra 193V DDPMOSQ1DD
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5.4 Boolean algebra 195(d) A ·B·(
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Review exercises 5 19712 (a) A·B+A
- Page 219 and 220:
Review exercises 5 1997 (a) (A·B)
- Page 221 and 222:
6.2 Sequences 2016.2 SEQUENCESAsequ
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6.2 Sequences 203sin t1x[k]1- 3p-2p
- Page 225 and 226:
6.2 Sequences 205Ageneralgeometricp
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6.2 Sequences 207can sensibly letk
- Page 229 and 230:
6.3 Series 20913 ±12814 315 016 (a
- Page 231 and 232:
6.3.2 Sumofafinitegeometricseries6.
- Page 233 and 234:
6.3 Series 213whereS ∞is known as
- Page 235 and 236:
6.4 The binomial theorem 215Example
- Page 237 and 238:
6.4 The binomial theorem 217EXERCIS
- Page 239 and 240:
6.6 Sequences arising from the iter
- Page 241 and 242:
6.6 Sequences arising from the iter
- Page 243 and 244:
Review exercises 6 22315 (a) Write
- Page 245 and 246:
7.2 Vectors and scalars: basic conc
- Page 247 and 248:
7.2 Vectors and scalars: basic conc
- Page 249 and 250:
7.2 Vectors and scalars: basic conc
- Page 251 and 252:
7.2 Vectors and scalars: basic conc
- Page 253 and 254:
yjOirFigure7.19Thex--y plane withpo
- Page 255 and 256:
7.3 Cartesian components 235Solutio
- Page 257 and 258:
7.3 Cartesian components 237Enginee
- Page 259 and 260:
7.3 Cartesian components 2393 Ifa=4
- Page 261 and 262:
7.5 The scalar product 241OEFigure7
- Page 263 and 264:
7.5 The scalar product 243Example7.
- Page 265 and 266:
----------7.5 The scalar product 24
- Page 267 and 268:
7.6 The vector product 247a 3 bubPl
- Page 269 and 270:
7.6 The vector product 249The k com
- Page 271 and 272:
7.6 The vector product 251Engineeri
- Page 273 and 274:
7.7 Vectors ofndimensions 253andH =
- Page 275 and 276:
Review exercises 7 255EXERCISES7.71
- Page 277 and 278:
8 MatrixalgebraContents 8.1 Introdu
- Page 279 and 280:
8.3 Addition, subtraction and multi
- Page 281 and 282:
8.3 Addition, subtraction and multi
- Page 283 and 284:
Example8.8 IfB =( ) 123andC=456⎛
- Page 285 and 286:
8.3 Addition, subtraction and multi
- Page 287 and 288:
8.4 Using matrices in the translati
- Page 289 and 290:
8.4 Using matrices in the translati
- Page 291 and 292:
8.5 Some special matrices 271V new=
- Page 293 and 294:
Example8.18 IfA =Solution We haveA
- Page 295 and 296:
8.6.1 FindingtheinverseofamatrixFor
- Page 297 and 298:
8.6 The inverse of a 2 × 2 matrix
- Page 299 and 300:
8.7 Determinants 279In addition to
- Page 301 and 302:
8.8 The inverse of a 3 × 3 matrix
- Page 303 and 304:
8.9 Application to the solution of
- Page 305 and 306:
8.9 Application to the solution of
- Page 307 and 308:
Solution Firstconsider the equation
- Page 309 and 310:
8.10 Gaussian elimination 289anythi
- Page 311 and 312:
Eliminating the unwanted values int
- Page 313 and 314:
⎛R 1R 2→R 2−6R 1⎝R 3→R 3
- Page 315 and 316:
8.11 Eigenvalues and eigenvectors 2
- Page 317 and 318:
8.11 Eigenvalues and eigenvectors 2
- Page 319 and 320:
Itfollows thatso that(2−λ)(4−
- Page 321 and 322:
8.11 Eigenvalues and eigenvectors 3
- Page 323 and 324:
8.11 Eigenvalues and eigenvectors 3
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8.11 Eigenvalues and eigenvectors 3
- Page 327 and 328:
8.12 Analysis of electrical network
- Page 329 and 330:
8.12 Analysis of electrical network
- Page 331 and 332:
8.12 Analysis of electrical network
- Page 333 and 334:
8.13 Iterative techniques for the s
- Page 335 and 336:
8.13 Iterative techniques for the s
- Page 337 and 338:
8.13 Iterative techniques for the s
- Page 339 and 340:
8.14 Computer solutions of matrix p
- Page 341 and 342:
Review exercises 8 321V = [3;−6;4
- Page 343 and 344:
Review exercises 8 3234 (a) −8⎛
- Page 345 and 346:
9.2 Complex numbers 3259.2 COMPLEXN
- Page 347 and 348:
9.2 Complex numbers 3279.2.1 Thecom
- Page 349 and 350:
Similarly, wefind, by equating imag
- Page 351 and 352:
9.3 Operations with complex numbers
- Page 353 and 354:
9.5 Polar form of a complex number
- Page 355 and 356:
9.5.1 Multiplicationanddivisioninpo
- Page 357 and 358:
9.7 The exponential form of a compl
- Page 359 and 360:
9.7 The exponential form of a compl
- Page 361 and 362:
9.8 Phasors 341example, in the case
- Page 363 and 364:
9.8 Phasors 343Therefore,Ṽ S=ṼR
- Page 365 and 366:
which isclearly true,and the theore
- Page 367 and 368:
9.9 De Moivre’s theorem 347y25p
- Page 369 and 370:
9.9 De Moivre’s theorem 349Now, w
- Page 371 and 372:
9.10 Loci and regions of the comple
- Page 373 and 374:
9.10 Loci and regions of the comple
- Page 375 and 376:
Review exercises 9 3559 Sketch the
- Page 377 and 378:
10.2 Graphical approach to differen
- Page 379 and 380:
10.3 Limits and continuity 359f (t)
- Page 381 and 382:
10.3 Limits and continuity 361Theli
- Page 383 and 384:
10.4 Rate of change at a specific p
- Page 385 and 386:
10.5 Rate of change at a general po
- Page 387 and 388:
10.5 Rate of change at a general po
- Page 389 and 390:
10.5 Rate of change at a general po
- Page 391 and 392:
10.6 Existence of derivatives 371x
- Page 393 and 394:
10.7 Common derivatives 373Table10.
- Page 395 and 396:
10.8 Differentiation as a linear op
- Page 397 and 398:
10.8 Differentiation as a linear op
- Page 399 and 400:
10.8 Differentiation as a linear op
- Page 401 and 402:
10.8 Differentiation as a linear op
- Page 403 and 404:
10.8 Differentiation as a linear op
- Page 405 and 406:
Review exercises 10 385REVIEWEXERCI
- Page 407 and 408:
11.2 Rules of differentiation 387Th
- Page 409 and 410:
11.2 Rules of differentiation 389Th
- Page 411 and 412:
(b) Ify = ln(1 −t),theny ′ =
- Page 413 and 414:
11.3 Parametric, implicit and logar
- Page 415 and 416:
11.3 Parametric, implicit and logar
- Page 417 and 418:
11.3 Parametric, implicit and logar
- Page 419 and 420:
11.3 Parametric, implicit and logar
- Page 421 and 422:
11.4 Higher derivatives 401Example1
- Page 423 and 424:
11.4 Higher derivatives 403yCByCAyB
- Page 425 and 426:
Review exercises 11 405Solutions1 (
- Page 427 and 428:
12.2 Maximum points and minimum poi
- Page 429 and 430:
12.2 Maximum points and minimum poi
- Page 431 and 432:
12.2 Maximum points and minimum poi
- Page 433 and 434:
12.2 Maximum points and minimum poi
- Page 435 and 436:
12.3 Points of inflexion 415Solutio
- Page 437 and 438:
12.3 Points of inflexion 417y ′ =
- Page 439 and 440:
12.4 The Newton--Raphson method for
- Page 441 and 442:
12.4 The Newton--Raphson method for
- Page 443 and 444:
12.5 Differentiation of vectors 423
- Page 445 and 446:
Solution (a) Ifa = 3t 2 i +cos2tj,
- Page 447 and 448:
Review exercises 12 427REVIEWEXERCI
- Page 449 and 450:
13.2 Elementary integration 42913.2
- Page 451 and 452:
13.2 Elementary integration 431Tabl
- Page 453 and 454:
Solution (a)sinx+cosx(j)2(k) 2t −
- Page 455 and 456:
13.2 Elementary integration 435Engi
- Page 457 and 458:
13.2 Elementary integration 4374.00
- Page 459 and 460:
Therefore,∫∫ 1sinmtsinnt dt = {
- Page 461 and 462:
13.2 Elementary integration 4412 (a
- Page 463 and 464:
13.3 Definite and indefinite integr
- Page 465 and 466:
13.3 Definite and indefinite integr
- Page 467 and 468:
13.3 Definite and indefinite integr
- Page 469 and 470:
13.3 Definite and indefinite integr
- Page 471 and 472:
13.3 Definite and indefinite integr
- Page 473 and 474:
Review exercises 13 4536716438 (a)
- Page 475 and 476:
Review exercises 13 45522 Calculate
- Page 477 and 478:
14 TechniquesofintegrationContents
- Page 479 and 480:
14.2 Integration by parts 459Usingt
- Page 481 and 482:
Usingintegration by parts we have
- Page 483 and 484:
14.3 Integration by substitution 46
- Page 485 and 486:
14.3 Integration by substitution 46
- Page 487 and 488:
14.4 Integration using partial frac
- Page 489 and 490:
Review exercises 14 469∫ π/3(b)
- Page 491 and 492:
15 ApplicationsofintegrationContent
- Page 493 and 494:
15.2 Average value of a function 47
- Page 495 and 496:
15.3 Root mean square value of a fu
- Page 497 and 498:
15.3 Root mean square value of a fu
- Page 499 and 500:
Review exercises 15 479(d) 0.7071(e
- Page 501 and 502:
[Example16.1 Show that f (x) =xandg
- Page 503 and 504:
Solution (a) We use the trigonometr
- Page 505 and 506:
16.3 Improper integrals 485iC 1 C 2
- Page 507 and 508:
∫ 2either of the integrals failst
- Page 509 and 510:
16.4 Integral properties of the del
- Page 511 and 512:
16.5 Integration of piecewise conti
- Page 513 and 514:
16.6 Integration of vectors 49316.6
- Page 515 and 516:
Review exercises 16 49512 Given14 G
- Page 517 and 518:
17.2 Trapezium rule 497y{ {y 0 y ny
- Page 519 and 520:
17.2 Trapezium rule 499The differen
- Page 521 and 522:
yABCDE17.3 Simpson’s rule 501quad
- Page 523 and 524:
17.3 Simpson’s rule 503Table17.6T
- Page 525 and 526:
Review Exercises 17 505EXERCISES17.
- Page 527 and 528:
18 Taylorpolynomials,Taylorseriesan
- Page 529 and 530:
18.2 Linearization using first-orde
- Page 531 and 532:
18.2 Linearization using first-orde
- Page 533 and 534:
18.3 Second-order Taylor polynomial
- Page 535 and 536:
18.3 Second-order Taylor polynomial
- Page 537 and 538:
18.4 Taylor polynomials of the nth
- Page 539 and 540:
18.4. Taylor polynomials of the nth
- Page 541 and 542:
18.5 Taylor’s formula and the rem
- Page 543 and 544:
We know |x| < 1, and so 4x51518.5 T
- Page 545 and 546:
18.6 Taylor and Maclaurin series 52
- Page 547 and 548:
18.6 Taylor and Maclaurin series 52
- Page 549 and 550:
18.6 Taylor and Maclaurin series 52
- Page 551 and 552:
18.6 Taylor and Maclaurin series 53
- Page 553 and 554:
Review exercises 18 5337 (a) 0, 2,
- Page 555 and 556:
19.2 Basic definitions 535In engine
- Page 557 and 558:
19.2 Basic definitions 537Note also
- Page 559 and 560:
19.2 Basic definitions 539fromwhich
- Page 561 and 562:
19.3 First-order equations: simple
- Page 563 and 564:
19.3 First-order equations: simple
- Page 565 and 566:
19.3 First-order equations: simple
- Page 567 and 568:
19.4 First-order linear equations:
- Page 569 and 570:
and so, upon integrating,so that(co
- Page 571 and 572:
19.4 First-order linear equations:
- Page 573 and 574:
19.4 First-order linear equations:
- Page 575 and 576:
19.4 First-order linear equations:
- Page 577 and 578:
19.4 First-order linear equations:
- Page 579 and 580:
19.5 Second-order linear equations
- Page 581 and 582:
19.6 Constant coefficient equations
- Page 583 and 584:
19.6 Constant coefficient equations
- Page 585 and 586:
19.6 Constant coefficient equations
- Page 587 and 588:
19.6 Constant coefficient equations
- Page 589 and 590:
19.6 Constant coefficient equations
- Page 591 and 592:
thatis,β = 332The required particu
- Page 593 and 594:
19.6 Constant coefficient equations
- Page 595 and 596:
19.6 Constant coefficient equations
- Page 597 and 598:
19.6 Constant coefficient equations
- Page 599 and 600:
19.6 Constant coefficient equations
- Page 601 and 602:
19.6 Constant coefficient equations
- Page 603 and 604:
19.6 Constant coefficient equations
- Page 605 and 606:
19.7 Series solution of differentia
- Page 607 and 608:
19.8 Bessel’s equation and Bessel
- Page 609 and 610:
19.8 Bessel’s equation and Bessel
- Page 611 and 612:
fromwhicha 5=− 124 a 3 = 1192 a 1
- Page 613 and 614:
n 5 2n 5 3n5 419.8 Bessel’s equat
- Page 615 and 616:
19.8 Bessel’s equation and Bessel
- Page 617 and 618:
19.8 Bessel’s equation and Bessel
- Page 619 and 620:
19.8 Bessel’s equation and Bessel
- Page 621 and 622:
Review exercises 19 601quencies, kn
- Page 623 and 624:
20 OrdinarydifferentialequationsIIC
- Page 625 and 626:
20.2 Analogue simulation 605y iy i
- Page 627 and 628:
20.3 Higher order equations 607High
- Page 629 and 630:
20.4 State-space models 609Solution
- Page 631 and 632:
20.4 State-space models 611statevar
- Page 633 and 634:
20.4 State-space models 613R a L aT
- Page 635 and 636:
20.5 Numerical methods 615Combining
- Page 637 and 638:
20.6 Euler’s method 617and we can
- Page 639 and 640:
20.6 Euler’s method 619Whenx = 1,
- Page 641 and 642:
20.7 Improved Euler method 621Table
- Page 643 and 644:
20.8 Runge--Kutta method of order 4
- Page 645 and 646:
20.8.1 Higherorderequations20.8 Run
- Page 647 and 648:
21 TheLaplacetransformContents 21.1
- Page 649 and 650:
21.3 Laplace transforms of some com
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21.4 Properties of the Laplace tran
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(b) Usethe first shift theorem with
- Page 655 and 656:
21.5 Laplace transform of derivativ
- Page 657 and 658:
21.5 Laplace transform of derivativ
- Page 659 and 660:
21.6 Inverse Laplace transforms 639
- Page 661 and 662:
21.7 Using partial fractions to fin
- Page 663 and 664:
21.8 Finding the inverse Laplace tr
- Page 665 and 666:
21.8 Finding the inverse Laplace tr
- Page 667 and 668:
21.9 The convolution theorem 64721.
- Page 669 and 670:
21.9 Solving linear constant coeffi
- Page 671 and 672:
21.10 Solving linear constant coeff
- Page 673 and 674:
21.10 Solving linear constant coeff
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X(s)= s3 −3s 2 −4s+6s 2 (s 2
- Page 677 and 678:
21.10 Solving linear constant coeff
- Page 679 and 680:
21.11 Transfer functions 659(c) x
- Page 681 and 682:
21.11 Transfer functions 661R(s)G(s
- Page 683 and 684:
21.11 Transfer functions 663R(s) +-
- Page 685 and 686:
21.11 Transfer functions 665Fuel va
- Page 687 and 688:
21.11 Transfer functions 667u a (t)
- Page 689 and 690:
21.12 Poles, zeros and thesplane 66
- Page 691 and 692:
21.12 Poles, zeros and thesplane 67
- Page 693 and 694:
21.12 Poles, zeros and thesplane 67
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21.13 Laplace transforms of some sp
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21.13.2 Periodicfunctions21.13 Lapl
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Review exercises 21 6792 Find the L
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22 Differenceequationsandtheztransf
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22.2 Basic definitions 68322.2.2 Th
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22.2 Basic definitions 685an inhomo
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22.3 Rewriting difference equations
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22.4 Block diagram representation o
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22.4 Block diagram representation o
- Page 713 and 714:
22.5 Design of a discrete-time cont
- Page 715 and 716:
22.6 Numerical solution of differen
- Page 717 and 718:
22.6 Numerical solution of differen
- Page 719 and 720:
22.7 Definition of the z transform
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22.7 Definition of the z transform
- Page 723 and 724:
22.8 Sampling a continuous signal 7
- Page 725 and 726:
22.9 The relationship between the z
- Page 727 and 728:
22.9 The relationship between the z
- Page 729 and 730:
22.10 Properties of the z transform
- Page 731 and 732:
22.10 Properties of the z transform
- Page 733 and 734:
22.10 Properties of the z transform
- Page 735 and 736:
22.11 Inversion of z transforms 715
- Page 737 and 738:
22.11 Inversion of z transforms 717
- Page 739 and 740:
22.12 The z transform and differenc
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Review exercises 22 721(e) q[k +3]
- Page 743 and 744:
23.2 Periodic waveforms 72323.2 PER
- Page 745 and 746:
23.2 Periodic waveforms 725f(t)1f(t
- Page 747 and 748:
23.3 Odd and even functions 727f(t)
- Page 749 and 750:
23.3 Odd and even functions 729f(t)
- Page 751 and 752:
23.3 Odd and even functions 731the
- Page 753 and 754:
23.5 Fourier series 733Table23.1Som
- Page 755 and 756:
23.5 Fourier series 735point out th
- Page 757 and 758:
23.5 Fourier series 737but cos(−n
- Page 759 and 760:
23.5 Fourier series 739Example23.16
- Page 761 and 762:
23.5 Fourier series 741y4- 3π -- -
- Page 763 and 764:
23.5 Fourier series 743We conclude
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23.6 Half-range series 745EXERCISES
- Page 767 and 768:
23.6 Half-range series 747Half-rang
- Page 769 and 770:
23.8 Complex notation 749Engineerin
- Page 771 and 772:
23.9 Frequency response of a linear
- Page 773 and 774:
23.9 Frequency response of a linear
- Page 775 and 776:
̸̸̸Review exercises 23 755The va
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24 TheFouriertransformContents 24.1
- Page 779 and 780:
24.2 The Fourier transform -- defin
- Page 781 and 782:
24.3 Some properties of the Fourier
- Page 783 and 784:
∫ 2[ ] eSolution (a) F(ω)=3 e
- Page 785 and 786:
24.3 Some properties of the Fourier
- Page 787 and 788:
24.4 Spectra 767uF(v)u2-4p -3p -2p
- Page 789 and 790:
The t−ω duality principle 769f(t
- Page 791 and 792:
24.6 Fourier transforms of some spe
- Page 793 and 794:
24.7 The relationship between the F
- Page 795 and 796:
24.8 Convolution and correlation 77
- Page 797 and 798:
and theirproduct isF(ω)G(ω) =1(1+
- Page 799 and 800:
24.8 Convolution and correlation 77
- Page 801 and 802:
24.8 Convolution and correlation 78
- Page 803 and 804:
24.9 The discrete Fourier transform
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24.9 The discrete Fourier transform
- Page 807 and 808:
24.10 Derivation of the d.f.t. 787T
- Page 809 and 810:
(Solution ConsiderF˜ ω + 2π )for
- Page 811 and 812:
24.11 Using the d.f.t.to estimate a
- Page 813 and 814:
24.13 Some properties of the d.f.t.
- Page 815 and 816:
24.14 The discrete cosine transform
- Page 817 and 818:
24.14 The discrete cosine transform
- Page 819 and 820:
24.14 The discrete cosine transform
- Page 821 and 822:
24.15 Discrete convolution and corr
- Page 823 and 824:
24.15 Discrete convolution and corr
- Page 825 and 826:
24.15 Discrete convolution and corr
- Page 827 and 828:
24.15 Discrete convolution and corr
- Page 829 and 830:
24.15 Discrete convolution and corr
- Page 831 and 832:
24.15 Discrete convolution and corr
- Page 833 and 834:
24.15 Discrete convolution and corr
- Page 835 and 836:
24.15 Discrete convolution and corr
- Page 837 and 838:
24.15 Discrete convolution and corr
- Page 839 and 840:
24.15 Discrete convolution and corr
- Page 841 and 842:
Review exercises 24 821REVIEWEXERCI
- Page 843 and 844:
25 FunctionsofseveralvariablesConte
- Page 845 and 846:
25.3 Partial derivatives 825DCAz =
- Page 847 and 848:
25.3 Partial derivatives 827Enginee
- Page 849 and 850:
25.4 Higher order derivatives 829
- Page 851 and 852:
25.4 Higher order derivatives 831Ex
- Page 853 and 854:
25.5 Partial differential equations
- Page 855 and 856:
25.6 Taylor polynomials and Taylor
- Page 857 and 858:
25.6 Taylor polynomials and Taylor
- Page 859 and 860:
25.6 Taylor polynomials and Taylor
- Page 861 and 862:
25.7 Maximum and minimum points of
- Page 863 and 864:
25.7 Maximum and minimum points of
- Page 865 and 866:
25.7 Maximum and minimum points of
- Page 867 and 868:
Review exercises 25 8474 Find allfi
- Page 869 and 870:
26 VectorcalculusContents 26.1 Intr
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26.3 The gradient of a scalar field
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(b) At (0,0,0), ∇φ =0i+3j+0k =3j
- Page 875 and 876:
26.3 The gradient of a scalar field
- Page 877 and 878:
26.4.1 Physicalinterpretationof ∇
- Page 879 and 880:
26.5 The curl of a vector field 859
- Page 881 and 882:
26.6 Combining the operators grad,
- Page 883 and 884:
26.6 Combining the operators grad,
- Page 885 and 886:
Equation3Review exercises 26 865cur
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27 Lineintegralsandmultipleintegral
- Page 889 and 890:
27.2 Line integrals 869SolutionThe
- Page 891 and 892:
27.3 Evaluation of line integrals i
- Page 893 and 894:
27.4 Evaluation of line integrals i
- Page 895 and 896:
27.5 Conservative fields and potent
- Page 897 and 898:
27.5 Conservative fields and potent
- Page 899 and 900:
Substitutingy =x 2 and dy = 2xdx we
- Page 901 and 902:
27.6 Double and triple integrals 88
- Page 903 and 904:
27.6 Double and triple integrals 88
- Page 905 and 906:
27.6 Double and triple integrals 88
- Page 907 and 908:
y10GDR27.6 Double and triple integr
- Page 909 and 910:
27.7 Some simple volume and surface
- Page 911 and 912:
27.7 Some simple volume and surface
- Page 913 and 914:
27.7 Some simple volume and surface
- Page 915 and 916:
27.8 The divergence theorem and Sto
- Page 917 and 918:
27.8 The divergence theorem and Sto
- Page 919 and 920:
27.9 Maxwell’s equations in integ
- Page 921 and 922:
Review exercises 27 901REVIEWEXERCI
- Page 923 and 924:
28 ProbabilityContents 28.1 Introdu
- Page 925 and 926:
28.2 Introducing probability 905Ifm
- Page 927 and 928:
28.2 Introducing probability 907Eng
- Page 929 and 930:
28.3 Mutually exclusive events: the
- Page 931 and 932:
28.3 Mutually exclusive events: the
- Page 933 and 934:
28.4 Complementary events 913EXERCI
- Page 935 and 936:
28.5 Concepts from communication th
- Page 937 and 938:
28.5 Concepts from communication th
- Page 939 and 940:
28.6 Conditional probability: the m
- Page 941 and 942:
28.6 Conditional probability: the m
- Page 943 and 944:
P(A ∩C) =P(C ∩A) =P(C)P(A|C)P(A
- Page 945 and 946:
28.7 Independent events 9255 Compon
- Page 947 and 948:
28.7 Independent events 927Solution
- Page 949 and 950:
28.7 Independent events 929E 1,E 2a
- Page 951 and 952:
Review exercises 28 931(d) A compon
- Page 953 and 954:
29 Statisticsandprobabilitydistribu
- Page 955 and 956:
29.3 Probability distributions -- d
- Page 957 and 958:
29.4 Probability density functions
- Page 959 and 960:
29.5 Mean value 939Example29.3 Find
- Page 961 and 962:
29.6 Standard deviation 94129.6 STA
- Page 963 and 964:
29.7 Expected value of a random var
- Page 965 and 966:
29.7 Expected value of a random var
- Page 967 and 968:
29.8 Standard deviation of a random
- Page 969 and 970:
29.9 Permutations and combinations
- Page 971 and 972:
29.9 Permutations and combinations
- Page 973 and 974:
29.10 The binomial distribution 953
- Page 975 and 976:
29.10 The binomial distribution 955
- Page 977 and 978:
29.11 The Poisson distribution 957I
- Page 979 and 980:
Table29.6Theprobabilitiesforbinomia
- Page 981 and 982:
29.12 The uniform distribution 9615
- Page 983 and 984:
29.14 The normal distribution 963So
- Page 985 and 986:
29.14 The normal distribution 965N(
- Page 987 and 988:
29.14 The normal distribution 967Ta
- Page 989 and 990:
29.14 The normal distribution 969EX
- Page 991 and 992:
29.15 Reliability engineering 971in
- Page 993 and 994:
29.15 Reliability engineering 973En
- Page 995 and 996:
29.15 Reliability engineering 975k
- Page 997 and 998:
Review exercises 29 977Solutions1 0
- Page 999 and 1000:
AppendicesContents I Representingac
- Page 1001 and 1002:
II The Greek alphabet 981f(t)T0 t 0
- Page 1003 and 1004:
Indexabsolute quantity88absorption
- Page 1005 and 1006:
Index 985chord 357--8circuital law
- Page 1007 and 1008:
Index 987cycle ofsint 131cycles ofl
- Page 1009 and 1010:
Index 989eigenvalues andeigenvector
- Page 1011 and 1012:
Index 991spectra 766--8t-w duality
- Page 1013 and 1014:
Index 993characteristic impedance o
- Page 1015 and 1016:
Index 995exclusive OR gate 189NAND
- Page 1017 and 1018:
Index 997second-order 829--30, 833,
- Page 1019 and 1020:
Index 999remainder term,Taylor’s
- Page 1021 and 1022:
Index 1001solenoidal vectorfield 85
- Page 1023 and 1024:
Index 1003calculus 849--66curl859--
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