Introduction to partial differential equations and Hilbert space methods

By Karl E. Gustafson

Book Overview

This text covers all the major concepts and techniques in an elementary and clear style and explores some fields usually dealt with only in the advanced literature, also in a simplified manner. This edition includes new discussions on the three basic numerical methods, an introduction to computational fluid dynamics, and an introduction to Lie group methods for partial differential equations. All topics are treated as brief descriptions of needed results, not as condensed short courses. The text's practical approach will motivate students to pursue many areas of study, such as Fourier series, complex analysis, Lebesgue integration and functional analysis.

• Format: Hardcover
• Language: English
• ISBN: 0471832278
• ISBN13: 9780471832270
• Release Date: January 1987
• Publisher: See Description
• Length: 430 Pages
• Weight: 1.60 lbs.
• Dimensions: 9.4" x 1.0" x 6.5"

Customer Reviews

review 1

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.

Unique Organization

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.