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1. Heat Equation. 2. Method of Separation of Variables. 3. Fourier Series. 4. Vibrating Strings and Membranes. 5. Sturm-Liouville Eigenvalue Problems. 6. Partial Differential Equations with at Least Three Independent Variables. 7. Nonhomogenous Problems. 8. Green's Functions for Time-Independent Problems. 9. Infinite Domain Problems -- Fourier Transform Solutions of Partial Differential Equations. 10. Green's Functions for Time-Dependent Problems. 11. The Method of Characteristics for Linear and Quasi-Linear Wave Equations. 12. A Brief Introduction to Laplace Transform Solution of Partial Differential Equations. 13. An Elementary Discussion of Finite Different Numerical Methods for Partial Differential Equations. Selected Answers to Starred Exercises. Bibliography. Index.