An Introduction to Numerical Methods. A MatLab Approach [4th ed.]

Contents......Page 3
Preface......Page 8
ABOUT MATLAB and MATLAB GUI (Graphical User Inter- face)......Page 11
AN INTRODUCTION TO MATLAB......Page 12
TAYLOR SERIES......Page 25
EXERCISE SET 1.3......Page 29
COMPUTER PROBLEM SET 1.3......Page 31
FLOATING-POINT ARITHMETIC......Page 32
EXERCISE SET 2.1......Page 35
ROUND-OFF ERRORS......Page 37
EXERCISE SET 2.2......Page 39
COMPUTER PROBLEM SET 2.2......Page 40
TRUNCATION ERROR......Page 41
EXERCISE SET 2.3......Page 42
INTERVAL ARITHMETIC......Page 43
EXERCISE SET 2.4......Page 47
Roots of Equations......Page 49
THE BISECTION METHOD......Page 50
EXERCISE SET 3.1......Page 54
COMPUTER PROBLEM SET 3.1......Page 57
FIXED POINT ITERATION......Page 58
EXERCISE SET 3.2......Page 61
THE SECANT METHOD......Page 65
EXERCISE SET 3.3......Page 66
COMPUTER PROBLEM SET 3.3......Page 69
NEWTON’S METHOD......Page 70
EXERCISE SET 3.4......Page 75
COMPUTER PROBLEM SET 3.4......Page 79
CONVERGENCE OF THE NEWTON AND SECANT METHODS......Page 80
EXERCISE SET 3.5......Page 81
MULTIPLE ROOTS AND THE MODIFIED NEWTON METHOD......Page 82
EXERCISE SET 3.6......Page 86
NEWTON’S METHOD FOR NONLINEAR SYSTEMS......Page 88
EXERCISE SET 3.7......Page 92
APPLIED PROBLEMS FOR CHAPTER 3......Page 94
System of Linear Equations......Page 100
MATRICES AND MATRIX OPERATIONS......Page 101
EXERCISE SET 4.1......Page 103
NAIVE GAUSSIAN ELIMINATION......Page 104
EXERCISE SET 4.2......Page 109
COMPUTER PROBLEM SET 4.2......Page 111
GAUSSIAN ELIMINATION WITH SCALED PARTIAL PIV- OTING......Page 112
EXERCISE SET 4.3......Page 118
COMPUTER PROBLEM SET 4.3......Page 123
LU DECOMPOSITION......Page 125
EXERCISE SET 4.4......Page 134
COMPUTER PROBLEM SET 4.4......Page 138
ITERATIVE METHODS......Page 139
EXERCISE SET 4.5......Page 147
COMPUTER PROBLEM SET 4.5......Page 151
APPLIED PROBLEMS FOR CHAPTER 4......Page 152
Interpolation......Page 159
POLYNOMIAL INTERPOLATION THEORY......Page 160
EXERCISE SET 5.1......Page 161
NEWTON’S DIVIDED-DIFFERENCE INTERPOLATING POLYNOMIAL......Page 162
EXERCISE SET 5.2......Page 167
COMPUTER PROBLEM SET 5.2......Page 172
THE ERROR OF THE INTERPOLATING POLYNOMIAL......Page 173
EXERCISE SET 5.3......Page 176
LAGRANGE INTERPOLATING POLYNOMIAL......Page 178
EXERCISE SET 5.4......Page 181
APPLIED PROBLEMS FOR CHAPTER 5......Page 183
Interpolation with Spline Functions......Page 186
PIECEWISE LINEAR INTERPOLATION......Page 187
EXERCISE SET 6.1......Page 190
COMPUTER PROBLEM SET 6.1......Page 192
QUADRATIC SPLINE......Page 193
EXERCISE SET 6.2......Page 195
COMPUTER PROBLEM SET 6.2......Page 196
NATURAL CUBIC SPLINES......Page 197
EXERCISE SET 6.3......Page 205
COMPUTER PROBLEM SET 6.3......Page 209
APPLIED PROBLEMS FOR CHAPTER 6......Page 211
Method of Least-Squares......Page 213
LINEAR LEAST-SQUARES......Page 214
EXERCISE SET 7.1......Page 217
LEAST-SQUARES POLYNOMIAL......Page 220
EXERCISE SET 7.2......Page 227
NONLINEAR LEAST-SQUARES......Page 228
EXERCISE SET 7.3......Page 231
APPLIED PROBLEMS FOR CHAPTER 7......Page 236
ANALYSIS OF SINGLE-VARIABLE FUNCTIONS......Page 239
EXERCISE SET 8.1......Page 241
LINE SEARCH METHODS......Page 242
EXERCISE SET 8.2......Page 254
MINIMIZATION USING DERIVATIVES......Page 255
COMPUTER PROBLEM SET 8.3......Page 258
APPLIED PROBLEMS FOR CHAPTER 8......Page 259
NUMERICAL DIFFERENTIATION......Page 261
EXERCISE SET 9.1......Page 266
RICHARDSON’S FORMULA......Page 268
EXERCISE SET 9.2......Page 270
COMPUTER PROBLEM SET 9.2......Page 273
APPLIED PROBLEMS FOR CHAPTER 9......Page 274
Numerical Integration......Page 277
TRAPEZOIDAL RULE......Page 278
EXERCISE SET 10.1......Page 282
SIMPSON’S RULE......Page 287
EXERCISE SET 10.2......Page 292
COMPUTER PROBLEM SET 10.2......Page 296
ROMBERG ALGORITHM......Page 298
EXERCISE SET 10.3......Page 303
COMPUTER PROBLEM SET 10.3......Page 304
GAUSSIAN QUADRATURE......Page 305
EXERCISE SET 10.4......Page 311
COMPUTER PROBLEM SET 10.4......Page 315
APPLIED PROBLEMS FOR CHAPTER 10......Page 316
INTRODUCTION......Page 321
QUADRATURE RULES......Page 324
EXERCISE SET 11.2......Page 333
THE SUCCESSIVE APPROXIMATION METHOD......Page 334
EXERCISE SET 11.3......Page 335
SCHMIDT’s METHOD......Page 336
VOLTERRA-TYPE INTEGRAL EQUATIONS......Page 338
EXERCISE SET 11.5......Page 342
APPLIED PROBLEMS FOR CHAPTER 11......Page 344
Numerical Methods for ODEs......Page 346
EULER’S METHOD......Page 347
EXERCISE SET 12.1......Page 350
COMPUTER PROBLEM SET 12.1......Page 352
ERROR ANALYSIS......Page 353
EXERCISE SET 12.2......Page 357
HIGHER-ORDER TAYLOR SERIES METHODS......Page 358
EXERCISE SET 12.3......Page 360
RUNGE-KUTTA METHODS......Page 362
EXERCISE SET 12.4......Page 369
COMPUTER PROBLEM SET 12.4......Page 373
MULTISTEP METHODS......Page 376
ADAMS-BASHFORTH METHODS......Page 377
EXERCISE SET 12.6......Page 383
COMPUTER PROBLEM SET 12.6......Page 385
PREDICTOR-CORRECTOR METHODS......Page 386
ADAMS-MOULTON METHODS......Page 387
EXERCISE SET 12.8......Page 390
COMPUTER PROBLEM SET 12.8......Page 393
NUMERICAL STABILITY......Page 395
EXERCISE SET 12.9......Page 397
HIGHER-ORDER EQUATIONS AND SYSTEMS OF DIFFERENTIAL EQUATIONS......Page 398
EXERCISE SET 12.10......Page 402
COMPUTER PROBLEM SET 12.10......Page 403
IMPLICIT METHODS AND STIFF SYSTEMS......Page 405
PHASE PLANE ANALYSIS: CHAOTIC DIFFERENTIAL EQUATIONS......Page 407
EXERCISE SET 12.12......Page 411
APPLIED PROBLEMS FOR CHAPTER 12......Page 413
Boundary-Value Problems......Page 420
FINITE-DIFFERENCE METHODS......Page 421
EXERCISE SET 13.1......Page 425
COMPUTER PROBLEM SET 13.1......Page 427
SHOOTING METHODS......Page 428
EXERCISE SET 13.2......Page 436
APPLIED PROBLEMS FOR CHAPTER 13......Page 440
BASIC THEORY......Page 444
EXERCISE SET 14.1......Page 448
THE POWER METHOD......Page 449
THE QUADRATIC METHOD......Page 452
EXERCISE SET 14.3......Page 460
EIGENVALUES FOR BOUNDARY-VALUE PROBLEMS......Page 461
BIFURCATIONS IN DIFFERENTIAL EQUATIONS......Page 464
EXERCISE SET 14.5......Page 467
APPLIED PROBLEMS FOR CHAPTER 14......Page 469
Dynamical Systems & Chaos......Page 470
A REVIEW OF LINEAR ORDINARY DIFFERENTIAL EQUATIONS......Page 471
EXERCISE SET 15.1......Page 473
DEFINITIONS AND THEORETICAL CONSIDERATIONS......Page 474
EXERCISE SET 15.2......Page 480
TWO-DIMENSIONAL SYSTEMS......Page 481
EXERCISE SET 15.3......Page 492
CHAOS......Page 493
EXERCISE SET 15.4......Page 497
LAGRANGIAN DYNAMICS......Page 498
EXERCISE SET 15.5......Page 503
COMPUTER PROBLEM SET 15.5......Page 504
APPLIED PROBLEMS FOR CHAPTER 15......Page 505
PDEs......Page 508
PARABOLIC EQUATIONS......Page 509
EXERCISE SET 16.1......Page 516
HYPERBOLIC EQUATIONS......Page 520
EXERCISE SET 16.2......Page 524
ELLIPTIC EQUATIONS......Page 527
EXERCISE SET 16.3......Page 531
NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS......Page 533
EXERCISE SET 16.4......Page 539
INTRODUCTION TO THE FINITE-ELEMENT METHOD......Page 540
EXERCISE SET 16.5.1......Page 546
EXERCISE SET 16.5.2......Page 551
APPLIED PROBLEMS FOR CHAPTER 16......Page 552
Refs......Page 554
A.1 Limits and continuity......Page 559
A.3 Integration......Page 560
MatLab Built-in Functions......Page 562
Text MatLab Functions......Page 566
D.1 Roots of Equations......Page 568
D.2 System of Linear Equations......Page 570
D.4 The Method of Least Squares......Page 571
D.5 Integration......Page 572
D.6 Differentiation......Page 573
D.8 Boundary-Value Problems......Page 574
D.9 Numerical Methods for PDEs......Page 575
Answers......Page 578
Index......Page 611