Basic Partial Differential Equations

by David D. Bleecker, George Csordas (University of Hawaii at Manoa)

For students with three semesters of calculus, this book is self-contained. In particular, Section 1.1 contains a complete treatment of the relevant types of ordinary differential equations. No previous course in ordinary differential equations or linear algebra is necessary. There are approximately 280 examples worked out in detail, and 600 exercises ranging from routine to challenging. Answers to selected problems appear in the back of the book. Rigorous proofs of nearly all results used are given after ample physical motivation. The book documents extensive applications, heat conduction, wave propagation, vibrations of strings, square drums, round drums, spheres and manifolds, traffic flow shocks, evolution of population densities, fluid flow, electrostatics, minimal surfaces, gravitation, quantum mechanics (including the determination of the bound states of the hydrogen atom). Convenient summaries appear at the end of each section. Theorems and definitions are clearly off-set in boxes. The book contains 97 figures, illustrations and tables (graphs of mathematical functions of one or several variables were computer generated.).

735 pages, Hardcover

First published May 1, 1992

Reviews

[Tom Schulte · Rating 4 out of 5]

... The tight integration of the material show the work and effort the authors put in to creating this PDEs text. I have always felt the first PDEs text for a student should challenge the student’s earlier calculus text in size. This is an excellent text for a student’s first deep dive into this important, fundamental topic. It has the breadth and heft covering basic and advanced topics in the subject. It is unusual in my experience to see a work of this scope assigned as a university text for PDEs, so I advise the wise to consider this as a supplement.

See my full review up at MathDL Reviews.