082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

Recommendations

Info

94 Chapter 2 Engineering functions19876543Second cycle2Logarithmic scale19876543First cycle2Linear1Figure2.36Two-cycle log--lineargraph paper.Useoflog–linearandlog–loggraphpaperThe requirement to take logarithms is a tedious process which can be avoided by usingspecialgraphpaperscalledlog--lineargraphpaperandlog--loggraphpaper.Anexampleof log--linear graph paper isshown inFigure 2.36.Note that on one axis the scale is uniform; this is the linear scale. On the other, thescaleisnotuniformandismarkedincyclesfrom1to9.Thisisthelogarithmicscale.Onthis scale values ofyare plotted directly, without first taking logarithms. On the graphpapershowninFigure2.36therearetwocyclesbutpapersarealsoavailablewiththree
2.4 Review of some common engineering functions and techniques 95or more cycles. To decide which sort of graph paper is appropriate it is necessary toexamine the variation in size of the variable to be plotted measured in powers of 10. If,for example,yvaries from 1 to 10, then paper with one cycle is appropriate. Ifyvariesfrom 1 to 10 2 , two-cycle paper is necessary. If y varies from 10 −1 to 10 4 , then paperwith4 − (−1) = 5cycleswouldbeappropriate.Toseehowlog--linearpaperisusedinpractice, consider the following example.Example2.18 During anexperiment the following pairs of data values wererecorded:A B C Dx 0 1 5 12y 4.00 5.20 14.85 93.19It is believed thatyandxare related by the equationy = ab x . By plotting a log--lineargraph verify the relationship isof thisform and determineaandb.Solution If the relationship isgiven byy =ab x , then taking logarithms yieldslogy=loga+xlogbSo, plotting logy againstxshould produce a straight line graph with gradient logbandvertical intercept loga. The need to find logy is eliminated by plotting theyvalues directlyon a logarithmic scale. Examining the table of data we see that y varies fromapproximately 10 0 to 10 2 so that two-cycle paper is appropriate. Values ofybetween 1and 10 are plotted on the first cycle, and those between 10 and 100 are plotted on thesecond.ThepointsareplottedinFigure2.37.Noteinparticularthatinthisexamplethe‘1’atthestartofthesecondcyclerepresentsthevalue10,the‘2’representsthevalue20and so on. From the graph, the straight line relationship between logy andxis evident.It is therefore reasonable to assume that the relationship betweenyandxis of the formy =ab x .Tofindthegradientofthegraphwecanchooseanytwopointsontheline,forexampleCand B. The gradient isthenlog14.85 −log5.205 −1= log(14.85/5.20)4Recall thatlogbisthe gradient ofthe lineand so= 0.1139logb = 0.1139, thatisb= 10 0.1139 = 1.2999The vertical intercept isloga. From the graph the vertical intercept islog4 so thatloga=log4,thatisa=4We conclude that the relationship betweenyandxisgiven byy = 4(1.3) x .
Page 1 and 2:
ENGINEERINGMATHEMATICSA Foundation
Page 3 and 4:
At Pearson, we have a simple missio
Page 5 and 6:
PEARSONEDUCATIONLIMITEDEdinburghGat
Page 7 and 8:
ContentsPrefaceAcknowledgementsxvii
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
Page 63 and 64: 1.7 Partial fractions 43Solution Th
Page 65 and 66: 1.7 Partial fractions 45EXERCISES1.
Page 67 and 68: 1.8 Summation notation 47Engineerin
Page 69 and 70: 1.8 Summation notation 49thecircuit
Page 71 and 72: Review exercises 1 513 Removethe br
Page 73 and 74: Review exercises 1 53[ ((d) 3 z −
Page 75 and 76: 2.2 Numbers and intervals 55in orde
Page 77 and 78: 2.3 Basic concepts of functions 57f
Page 79 and 80: 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
Page 87 and 88: 2.3 Basic concepts of functions 67T
Page 89 and 90: 2.3 Basic concepts of functions 691
Page 91 and 92: 2.4 Review of some common engineeri
Page 95 and 96: 2.4.2 Rationalfunctions2.4 Review o
Page 101 and 102: Table2.2Values ofa x fora = 0.5, 2
Page 105 and 106: 2.4.4 Logarithmfunctions2.4 Review
Page 113: 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
Page 147 and 148: 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 165 and 166:
3.8 Trigonometric equations 145sin
Page 167 and 168:
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
Page 183 and 184:
4.5 Some simple polar curves 163EXE
Page 185 and 186:
4.5 Some simple polar curves 165uAn
Page 187 and 188:
4.6 Cylindrical polar coordinates 1
Page 189 and 190:
4.6 Cylindrical polar coordinates 1
Page 191 and 192:
4.7 Spherical polar coordinates 171
Page 193 and 194:
Review exercises 4 173zzFeeding lin
Page 195 and 196:
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
Page 201 and 202:
5.2 Set theory 181someelementsinA.W
Page 203 and 204:
5.3 Logic 183CDCD(a)(b)CDCD(c)(d)(e
Page 205 and 206:
5.4 Boolean algebra 185ABA . BFigur
Page 207 and 208:
5.4 Boolean algebra 187Table5.12Tru
Page 209 and 210:
5.4 Boolean algebra 189However, we
Page 211 and 212:
5.4 Boolean algebra 191S0Stage0A0 B
Page 213 and 214:
5.4 Boolean algebra 193V DDPMOSQ1DD
Page 215 and 216:
5.4 Boolean algebra 195(d) A ·B·(
Page 217 and 218:
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
Page 223 and 224:
6.2 Sequences 203sin t1x[k]1- 3p-2p
Page 225 and 226:
6.2 Sequences 205Ageneralgeometricp
Page 227 and 228:
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:
Page 249 and 250:
Page 251 and 252:
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:
Page 283 and 284:
Example8.8 IfB =( ) 123andC=456⎛
Page 285 and 286:
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:
Page 319 and 320:
Itfollows thatso that(2−λ)(4−
Page 321 and 322:
Page 323 and 324:
Page 325 and 326:
Page 327 and 328:
8.12 Analysis of electrical network
Page 329 and 330:
Page 331 and 332:
Page 333 and 334:
8.13 Iterative techniques for the s
Page 335 and 336:
Page 337 and 338:
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:
Page 389 and 390:
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:
Page 399 and 400:
Page 401 and 402:
Page 403 and 404:
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:
Page 417 and 418:
Page 419 and 420:
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:
Page 431 and 432:
Page 433 and 434:
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:
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:
Page 467 and 468:
Page 469 and 470:
Page 471 and 472:
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:
Page 549 and 550:
Page 551 and 552:
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:
Page 565 and 566:
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:
Page 573 and 574:
Page 575 and 576:
Page 577 and 578:
Page 579 and 580:
19.5 Second-order linear equations
Page 581 and 582:
19.6 Constant coefficient equations
Page 583 and 584:
Page 585 and 586:
Page 587 and 588:
Page 589 and 590:
Page 591 and 592:
thatis,β = 332The required particu
Page 593 and 594:
Page 595 and 596:
Page 597 and 598:
Page 599 and 600:
Page 601 and 602:
Page 603 and 604:
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:
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:
Page 617 and 618:
Page 619 and 620:
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
Page 651 and 652:
21.4 Properties of the Laplace tran
Page 653 and 654:
(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:
Page 675 and 676:
X(s)= s3 −3s 2 −4s+6s 2 (s 2
Page 677 and 678:
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:
Page 693 and 694:
Page 695 and 696:
21.13 Laplace transforms of some sp
Page 697 and 698:
21.13.2 Periodicfunctions21.13 Lapl
Page 699 and 700:
Review exercises 21 6792 Find the L
Page 701 and 702:
22 Differenceequationsandtheztransf
Page 703 and 704:
22.2 Basic definitions 68322.2.2 Th
Page 705 and 706:
22.2 Basic definitions 685an inhomo
Page 707 and 708:
22.3 Rewriting difference equations
Page 709 and 710:
22.4 Block diagram representation o
Page 711 and 712:
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
Page 721 and 722:
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:
Page 733 and 734:
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
Page 741 and 742:
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
Page 765 and 766:
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
Page 777 and 778:
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:
Page 801 and 802:
Page 803 and 804:
24.9 The discrete Fourier transform
Page 805 and 806:
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:
Page 819 and 820:
Page 821 and 822:
24.15 Discrete convolution and corr
Page 823 and 824:
Page 825 and 826:
Page 827 and 828:
Page 829 and 830:
Page 831 and 832:
Page 833 and 834:
Page 835 and 836:
Page 837 and 838:
Page 839 and 840:
Page 841 and 842:
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:
Page 859 and 860:
Page 861 and 862:
25.7 Maximum and minimum points of
Page 863 and 864:
Page 865 and 866:
Page 867 and 868:
Review exercises 25 8474 Find allfi
Page 869 and 870:
26 VectorcalculusContents 26.1 Intr
Page 871 and 872:
26.3 The gradient of a scalar field
Page 873 and 874:
(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
Page 887 and 888:
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:
Page 905 and 906:
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:
Page 913 and 914:
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:
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--
show all

082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?