Mark Gockenbach is Professor and Chair of the Department of Mathematical Sciences at Michigan Technological University. He is the author of Partial Differential Equations: Analytical and Numerical Methods (SIAM, 2002) and Understanding and Implementing the Finite Element Method (SIAM, 2006). His research interests include inverse problems in partial differential equations and numerical methods and software for large-scale optimization problems.
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Description
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. First-order PDEs and the method of characteristics; 9. Green's functions; 10. Sturm-Liouville eigenvalue problems; 11. Problems in multiple spatial dimensions; 12. More about Fourier series; 13. More about finite element methods; Appendix A. Proof of Theorem 3.47; Appendix B. Shifting the data in two dimensions; Bibliography; Index.
'I love this book and look forward to using it as a text in the future ... It's the first truly modern approach that I've seen in a PDE text.' Maeve McCarthy, MAA Online