Partial Differential Equations
2nd Edition
- Author: Mark S. Gockenbach
- Date Published: December 2010
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
- format: Hardback
- isbn: 9780898719352
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Undergraduate courses on partial differential equations (PDEs) have traditionally been based on the Fourier series method for analysing and solving PDEs. What this textbook offers is a fresh approach; the traditional method taught alongside the modern finite element method. Both powerful methods are introduced to the reader and emphasised equally. A further beneficial feature of the book is that it uses the language of linear algebra, in particular in emphasising the role of best approximation in function spaces and the idea of an eigenfunction expansion. Its inclusion of realistic physical experiments for many examples and exercises will make the book appealing to science and engineering students, as well as students of mathematics. This second edition has a broader coverage of PDE methods and applications than the first, with the inclusion of chapters on the method of characteristics, Green's functions, Sturm–Liouville problems and a section on finite difference methods.
Read more- Tutorials are provided that explain the features of MATLAB, Mathematica and Maple which are useful for the material in the book
- The text includes thorough expositions of the background material from linear algebra and ordinary differential equations
- The only prerequisite is a course in ordinary differential equations
Reviews & endorsements
'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
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×Product details
- Edition: 2nd Edition
- Date Published: December 2010
- format: Hardback
- isbn: 9780898719352
- length: 674 pages
- dimensions: 261 x 183 x 35 mm
- weight: 1.3kg
- contains: 150 b/w illus.
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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. 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.-
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