Advanced Calculus for Applications

Advanced Calculus for Applications......Page 2 Preface......Page 4 Contents......Page 7 CHAPTER 1 Ordinary Differential Equations......Page 12 CHAPTER 2 The Laplace Transform......Page 62 CHAPTER 3 Numerical Methods for Solving Ordinary Differential Equations......Page 104 CHAPTER 4 Series Solutions of Differential Equations: Special Functions......Page 130 CHAPTER 5 Boundary-Value Problems and Characteristic-Function Representations......Page 198 CHAPTER 6 Vector Analysis......Page 273 CHAPTER 7 Topics in Higher-Dimensional Calculus......Page 346 CHAPTER 8 Partial Differential Equations......Page 387 CHAPTER 9 Solutions of Partial Differential equations of Mathematical Physics......Page 437 CHAPTER 10 Functions of a Complex Variable......Page 520 Appendix A......Page 628 Appendix B......Page 630 Answers to Problems......Page 632 Index......Page 648