Covers analytical techniques for solving single equation ODEs and some PDEs and is organized as 50 lectures. This is a good book for anyone who has already taken a one semester undergrad course on differential equations. The book claims all you need is calculus, but this claim is completely unrealistic as the authors skim through the contents of a differential equations course all in the first 46 pages!

This sentence in the preface pretty much indicates who the intended audience is: "Like any other mathematical book, it does contain some theorems and their proofs". LOL. And true there aren't many theorems and of those theorems that are stated a good portion lack a proof. This book doesn't cover numerical methods nor uses anything requiring knowledge of linear algebra (eg, inner products and norms are used but you don't need to know what a vector space is). What is covered include series solutions, various special functions, Green's function, perturbation techniques, boundary value/Sturm Liouville, and solving PDEs centered around seperation of variables technique. Many exercises and hints/answers at the end of each chapter.

There is one thing I really don't like about this book: If you aren't going to prove a major theorem, at least give a reference or have a section in the chapter for "further reading". All we get are statements along the lines of "the reason is beyond the scope of this book" or "this is too difficult to cover here" or "this requires advanced concepts"; no elaboration, no reference.

Скачать книгу бесплатно (pdf, 2.43 Mb)

---

Читать «Ordinary and Partial Differential Equations: With Special Functions, Fourier Series, and Boundary Value Problems (Universitext)»