| Title: | Applied Partial Differential Equations |
| Authors: | Logan, J. David |
| Keywords: | Partial Differential Equations Mathematics |
| Issue Date: | 2015 |
| Publisher: | Springer |
| Abstract: | The main part of the text is the first four chapters, which cover the essential concepts. Specifically, they treat first- and second-order equations on bounded and unbounded domains and include transform methods (Laplace and Fourier), characteristic methods, and eigenfunction expansions (separation of variables); there is considerable material on the origin of PDEs in the natural sciences and engineering. Two additional chapters, Chapter 5 and Chapter 6, are short introductions to applications of PDEs in biology and to numerical computation of solutions. The text offers flexibility to instructors who, for example, may want to insert topics from biology or numerical methods at any time in the course. A brief appendix reviews techniques from ordinary differential equations. Sections marked with an asterisk (*) may safely be omitted. The mathematical ideas are strongly motivated by physical problems, and the exposition is presented in a concise style accessible to students in science and engineering. The emphasis is on motivation, methods, concepts, and interpretation rather than formal theory. |
| Description: | Partial differential equations (PDEs) is a topic worthy of your study. It is a subject about differential equations involving unknown functions of sev- eral variables; the derivatives are partial derivatives. As such, it is a subject that is intimately connected with multivariable calculus. To be successful you should have a good command of the concepts in the calculus of several vari- ables. So keep a calculus text nearby and review concepts when needed. The same comments apply to elementary ordinary differential equations (ODEs). An appendix at the end of the book reviews basic solution techniques for ODEs. If you wish to consult other sources, the texts by Farlow (1993) and Strauss (1994) are good choices. A mathematics book must be read with a pencil and paper in hand. Ele- mentary books fill in most steps in the exposition, but more advanced books leave many details to the reader. This book has enough detail so that you can follow the discussion, but pencil and paper work is required in some portions. Verifying all the statements and derivations in a text is a worthwhile endeavor and will help you learn the material. Many students find that studying PDEs provides an opportunity to hone their skills and reinforce concepts in calculus and differential equations. Further, studying PDEs increases your understand- ing of physical principles in a monumental way. The exercises are the most important part of this text, and you should try to solve most of them. Some require routine analytical calculations, but others require careful thought. We learn mathematics by doing mathematics, even when we are stymied by a problem. The effort put into a failed attempt will help you sort out the concepts and reinforce the learning process. View the exercises as a challenge and resist the temptation to give up. It is also a good habit to write up your solutions in a clear, concise, logical form. Good writing entails good thinking, and conversely. |
| URI: | http://localhost:8080/xmlui/handle/123456789/186 |
| ISBN: | 978-3-319-12493-3 |
| Appears in Collections: | ARTS & SCIENCE |
| File | Description | Size | Format | |
|---|---|---|---|---|
| 2015_Book_AppliedPartialDifferentialEqua.pdf | 2.51 MB | Adobe PDF | View/Open |
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