This introductory text on partial differential equations interates modern and classical techniques for solving PDEs, at a level suitable for undergraduates. The author complements the classical topic of Fourier series with modern finite element methods. The result is an up-to-date, flexible approach to solving PDEs, which both faculty and students should find rewarding. Linear algebra is a key component of the text, providing a framework for both computing solutions and for understanding the theoretical basis of the methods. While techniques are emphasized over theory, the methods are presented in a mathematically sound fashion, developing a strong foundation for further study. Numerous exercises and examples involve meaningful experiments with realistic physical parameters, allowing students to use physical intuition to understand the qualitative features of the solutions.
Table of Contents
Preface; 1. Classification of differential equations; 2. Models in one dimension; 3. Essential linear algebra; 4. Essential ordinary differential equations; 5. Boundary value problems in Statics; 6. Heat flow and diffusion; 7. Waves; 8. Problems in multiple spatial dimensions; 9. More about Fourier series; 10. More about finite element methods; Appendix A; Appendix B; Appendix C; Bibliography; Index.
Mark S. Gockenbach is an Associate Professor of Mathematical Sciences at Michigan Technological University. He earned his PhD from Rice University in 1994, and has held faculty positions at Indiana University, University of Michigan, and Rice University. His research interests include inverse problems, computational optimisation, and mathematical software.