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

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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