Solution Techniques for Elementary Partial Differential Equations

Of the many available texts on partial differential equations (PDEs), most are too detailed and voluminous, making them daunting to many students. In sharp contrast, Solution Techniques for Elementary Partial Differential Equations is a no-frills treatment that explains completely but succinctly some of the most fundamental solution methods for PDEs. After a brief review of elementary ODE techniques and discussions on Fourier series and Sturm-Liouville problems, the author introduces the heat, Laplace, and wave equations as mathematical models of physical phenomena. He then presents a number of solution techniques and applies them to specific initial/boundary value problems for these models. Discussion of the general second order linear equation in two independent variables follows, and finally, the method of characteristics and perturbation methods are presented.Most students seem to like concise, easily digestible explanations and worked examples that let them see the techniques in action. This text offers them both. Ideally suited for independent study and classroom tested with great success, it offers a direct, streamlined route to competence in PDE solution techniques.

Contents

Preface

1. Ordinary Differential Equations: Brief Revision
2. Fourier Series
3. Sturm-Liouville Problems
4. Three Fundamental Equations of Mathematical Physics
5. The Method of Separation of Variables
6. Linear Nonhomogeneous Problems
7. The Method of Eigenfunction Expansion
8. The Fourier Transformations
9. The Laplace Transformation
10. The Method of Green's Functions
11. General Second-Order Linear Partial Differential Equations with Two Independent Variables
12. The Method of Characteristics
13. Perturbation and Asymptotic Methods

Appendix
Bibliography
Index