In 362 pages, the author conveys a good deal of information about first- and second-order ordinary and partial differential equations and their connections to integral equations. The material was developed in classes at the College of William and Mary and at Oxford. The style is somewhat formal, but the topics are handled well, with examples, clear diagrams, and exercises to illuminate and supplement the text. There are no references to using technology and no answers/solutions to exercises appear at the back of the book.
This text assumes a previous course in ordinary differential equations, although some basic material is included in the Appendix. (These days, Chapter 15, on Phase-Plane Analysis, may be considered review material as well.) A very brief sketch of important results in single and multivariable calculus is given in Chapter 0. Linear algebra is introduced where required and an introduction to complex function methods is provided at key places in the text. The author provides different paths through the material via a schematic presentation of the book’s contents and helpful discussions of the interdependence of the chapters. The book ends with a 48-item bibliography.
In contrast to most modern first courses in differential equations, virtually all applications of the material are concerned with classical problems of mathematical physics. For instance, only as an exercise in the last chapter does Volterra’s predator-prey model appear.
As the publisher’s blurb asserts, this is “analysis for applications” and this well-written text is suitable for physicists, economists, chemists, and any student interested in acquiring a working knowledge of applied analysis.