| Chapter 1 First-order differential equations 1.1 Introduction 1.2 First-order linear differential equations 1.3 The Van Meegeren art forgeries 1.4 Separable equations 1.5 Population models 1.6 The spread of technological innovations 1.7 An atomic waste disposal problem 1.8 The dynamics of tumor growth， mixing problems， and orthogonal trajectories 1.9 Exact equations， and why we cannot solve very many differential equations 1.10 The existence-uniqueness theorem； Picard iteration 1.11 Finding roots of equations by iteration 1.11.1 Newton‘s method 1.12 Difference equations， and how to compute the interest due on your student loans 1.13 Numerical approximations； Euler‘s method 1.13.1 Error analysis for Euler‘s method 1.14 The three term Taylor series method 1.15 An impwoved Euler method 1.16 The Runge-Kutta method 1.17 What to do in practice Chapter 2 Second-order linear differential equations 2.1 Algebraic properties of solutions 2.2 Linear equations with constant coefficients 2.3 The nonhomogeneous equation 2.4 The method of variation of parameters 2.5 the method of judicious guessing …… Chapter 3 Systems of differential equations Chapter 4 Qualitative theory of differential equations Chapter 5 Separation of varibles and Fourier series Chapter 6 Sturm-Liouville boundary value problems Appendix A Some simple facts concerning functions of several variables Appendix B Sequences and series Appendix C C Programs Answers to odd-numbered dexercises Index |
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