Introduction to Mathematical Physics

After many years, I have finished a graduate level textbook and reference work on mathematical physics with the mundane title "Introduction to Mathematical Physics". Some features that distinguish this book from the standard books (Mathews and Walker, Arfken, etc) that we have been using for many years are, among others: 1. A modern view of tangent vectors and differential forms is introduced at an early stage (chapter 3). The appearance of the Jacobian determinant in multi-dimensional integrals and the manipulations of partial derivatives in thermodynamics, are two elementary applications that are much simpler in this view than in traditional presentations. 2. Several important examples of nonlinear equations are presented, and stability analysis introduced. Also an elementary discussion of solitons. I hope to expand this discussion if the book should reach a second edition. 3. Chapters on finite groups (chapter 9) and Lie groups and algebras (chapter 10). 4. The treatment of the classical linear problems involving Laplace's equation is sharply reduced. While the standard special functions (Legendre polynomials, spherical harmonics, Bessel functions) are introduced and described, the treatment is fairly brief. The book is published by Wiley-VCH. The table of contents and a complete chapter 1 can be downloaded from the Wiley web site. Also the index, if you follow the link to the online version of the book. You can also read much of the book online through Google(R). If you Google(R) on "Introduction to Mathematical Physics" Vaughn an early link will be to the Google books site. The book is also available from the usual online booksellers. A collection of problem solutions (not complete) for instructors who adopt the book for a course is available from the publisher. There is a page of errata for the book. Please e-mail me questions, comments, corrections and any other feedback. Thanks, Mike