This is a text for students with a calculus background and basic familiarity with ODEs; linear algebra is not required. The work starts with a cursory review of ODEs. After that, the book is self-contained to a point that makes it a candidate for a couple of semesters of coursework or the equivalent in independent study.
There are nearly 300 detailed examples, often supported with complete proofs or supporting remarks. There are roughly twice as many exercises that support the material. Double-lined boxes highlight important theorems throughout. The chapters conclude with a succinct summary of key points and methods prior to the exercises for which selected answers appear in the back. The book also contains nearly one hundred figures, illustrations and tables.
At over 700 pages, the work offers itself as a complete PDE introduction. Part of the length comes from the authors methodically laying out the material in detailed exposition stitched together with motivations, sometimes arising from practical applications. Among the physical motivations used are heat conduction, waves, vibrations on strings and drums, traffic and fluid flow, electrostatics, and gravity. There are also some quantum mechanics applications in the final chapter.
The tight integration of the material show the work and effort the authors put in to creating this textbook. I have always felt the first PDEs text 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.
Tom Schulte teaches mathematics at Oakland Community College in Michigan.
1. Review and Introduction of Contents
2. First-Order PDEs
3. The Heat Equation
4. Fourier Series and Sturm-Liouville Theory
5. The Wave Equation
6. Laplace's Equation
7. Fourier Transforms
8. Numerical Solutions of PDEs - An Introduction
9. PDEs in Higher Dimensions