Introduction to Partial Differential Equations and Hilbert Space Methods

• Publisher:   Dover Publications
• Number Of Pages:   480
• Publication Date:   1997-07-10
• ISBN-10 / ASIN:   0486612716
• ISBN-13 / EAN:   9780486612713

Excellent undergraduate/graduate-level introduction presents full introduction to the subject and to the Fourier series as related to applied mathematics, considers principal method of solving partial differential equations, examines first-order systems, computation methods, and much more. Over 600 problems and exercises, with answers for many. Ideal for a one-semester or full-year course.

Having just taken this course from Professor Gustafson, I can say, with complete support from everyone in every PDEs class he's taught as of yet, that this book leaves a lot to be desired. There is absolutely no mention of separation of variables, the section on greens functions forgets to mention at all what they're used for, and further how to do anything with them, and numerous other grave omissions. I feel a more apt title would be: "An overview of PDE's for the advanced student, and interesting applications." So perhaps, for the right teacher this will be a fine book, but beware, you are going to have a lot of work filling in the large gaps the book leaves. Also, thought this has no bearing on the quality of the book, he has a strange obsession with the number 3.

This is an excellent book for the beginning engineer/scientist as well as the more experienced technical person. I will use this as a reference in the class I teach on Mathematical Methods for Electromagnetic Theory.

I recently taught a one-semester course out of this text, having chosen Gustafson's book after a careful review of most of the standard introductory PDE texts. The feature which distinguishes this text from its competitors is its organization, which is based upon the author's belief in the pedagogical style of reinforcement through repetition. Within the first 50 pages, the reader has already seen a first treatment of (i) separation of variables and Fourier techniques, (ii) Green's functions, and (iii) variational (or energy) methods. One then repeatedly studies each of these standard solution techniques in greater depth at later points in the text. By contrast, with many alternative texts one can read 300 pages and still know nothing about Green's functions or variational techniques. Additionally, Gustafson writes so clearly that the text could be used for independent study. His selection of problems (3 Problems and 3 Exercises at the end of each section)reflects careful, deliberate choices. One is not overwhelmed with endless pages of repetitious "drill" exercises. Instead, each problem has a definite purpose and illustrates an important point. This text is a masterpiece, and Dover is to be congratulated for keeping it in print.

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