Introduction to Partial Differential Equations and Hilbert Space Methods
Author | : Karl E. Gustafson |
Publisher | : Courier Corporation |
Total Pages | : 492 |
Release | : 1999-01-01 |
ISBN-10 | : 0486612716 |
ISBN-13 | : 9780486612713 |
Rating | : 4/5 (16 Downloads) |
Book excerpt: This volume offers an excellent undergraduate-level introduction to the main topics, methods, and applications of partial differential equations. Chapter 1 presents a full introduction to partial differential equations and Fourier series as related to applied mathematics. Chapter 2 begins with a more comprehensive look at the principal method for solving partial differential equations — the separation of variables — and then more fully develops that approach in the contexts of Hilbert space and numerical methods. Chapter 3 includes an expanded treatment of first-order systems, a short introduction to computational methods, and aspects of topical research on the partial differential equations of fluid dynamics. With over 600 problems and exercises, along with explanations, examples, and a comprehensive section of answers, hints, and solutions, this superb, easy-to-use text is ideal for a one-semester or full-year course. It will also provide the mathematically inclined layperson with a stimulating review of the subject's essentials.