Introduction to Partial Differential Equations and Hilbert Space Methods

Rating:
Summary: Unique Organization
Review: 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.