Applied Partial Differential Equations – Richard Haberman – 4th Edition

1. Heat Equation.
2. Method of Separation of Variables.
3. Fourier Series.
4. Vibrating Strings and Membranes.
5. Sturm-Liouville Eigenvalue Problems.
6. Finite Difference Numerical Methods for Partial Differential Equations.
7. Partial Differential Equations with at Least Three Independent Variables.
8. Nonhomogeneous Problems.
9. Green's Functions for Time-Independent Problems.
10. Infinite Domain Problems—Fourier Transform Solutions of Partial Differential Equations.
11. Green's Functions for Wave and Heat Equations.
12. The Method of Characteristics for Linear and Quasi-Linear Wave Equations.
13. A Brief Introduction to Laplace Transform Solution of Partial Differential Equations.
14. Topics: Dispersive Waves, Stability, Nonlinearity, and Perturbation Methods.