Introduction to Partial Differential Equations with MATLAB (Hardcover, 1998. Corr. 2nd)

Chapter 1. Preliminaries Chapter 2. First-Order Equations: Method of characteristics for linear equations; nonlinear conservation laws; weak solutions; shock waves; numerical methods. Chapter 3. Diffusion: Diffusion on the line; maximum principle; fundamental solution of the heat equation; Burgers' equation; numerical methods. Chapter 4. Boundary Value Problems for the Heat Equation: Separation of variables; eigenfunction expansions; symmetric boundary conditions; long-time behavior. Chapter 5. Waves Again: Gas dynamics; the nonlinear string; linearized model; the linear wave equation without boundaries; boundary value problems on the half-line and finite interval; conservation of energy;numerical methods; nonlinear Klein-Gordon equation. Chapter 6. Fourier Series and Fourier Transform: Fourier series; Fourier transform and the heat equation; discrete Fourier transform; fast Fourier transform. Chapter 7. Dispersive Waves and the Schrodinger Equation: Method of stationary phase; dispersive equation (group velocity and phase velocity); Schrodinger equation; spectrum of the Schrodinger operator. Chapter 8. The Heat and Wave Equations in Higher Dimensions: Fundamental solution of heat equation; eigenfunctions for the disk and rectangle; Kirchoff's formula for the wave equation; nodal curves; conservation of energy; the Maxwell equations. Chapter 9. Equilibrium: Harmonic functions; maximum principle; Dirichlet problem in the disk and rectangle; Poisson kernel; Green's functions; variational problems and weak solutions. Chapter 10. Numerical Methods in Higher Dimensions: Finite differences; finite elements; Galerkin methods, A reaction-diffusion equation. Chapter 11. Epilogue: Classification Appendix A: Recipes and Formulas Appendix B: Elements of MATLAB Appendix C: References Appendix D: Solutions to Selected Problems Appendix E: List of Computer Programs Index