CONTENTS 。i 13 BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS 471 13.1 Polar Coordinates 472 13.2 Polar and Cylindrical Coordinates 477 13.3 Spherical Coordinates 483 CHAPTER 13 IN REVIEW 486 14 INTEGRAL TRANSFORMS 488 14.1 Error Function 489 14.2 Laplace Transform 490 14.3 Fourier Integral 498 14.4 Fourier Transforms 504 CHAPTER 14 IN REVIEW 510 15 NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS 511 15.1 Laplace's Equation 512 15.2 Heat Equation 517 15.3 Wave Equation 522 CHAPTER 15 IN REVIEW 526 APPENDICES Gamma Function APP-1 I Matrices APP-3 Laplace Transforms APP-21 Answers for Selected Odd-Numbered Problems ANS-1 Index I-1CONTENTS ● ix 13 BOUNDARY-VALUE PROBLEMS IN OTHER COORDINATE SYSTEMS 471 13.1 Polar Coordinates 472 13.2 Polar and Cylindrical Coordinates 477 13.3 Spherical Coordinates 483 CHAPTER 13 IN REVIEW 486 14 INTEGRAL TRANSFORMS 488 14.1 Error Function 489 14.2 Laplace Transform 490 14.3 Fourier Integral 498 14.4 Fourier Transforms 504 CHAPTER 14 IN REVIEW 510 15 NUMERICAL SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS 511 15.1 Laplace’s Equation 512 15.2 Heat Equation 517 15.3 Wave Equation 522 CHAPTER 15 IN REVIEW 526 APPENDICES I Gamma Function APP-1 II Matrices APP-3 III Laplace Transforms APP-21 Answers for Selected Odd-Numbered Problems ANS-1 Index I-1