Methods of Mathematical Physics (Cambridge Mathematical Library) 3rd Edition, Kindle Edition

I was turned on to this book decades ago by one of my professors. The book bursts with useful material, but the organization is poor, the explanations almost nil, and the problems remote. (Indeed, most of the "drill" problems that the book provides are from British university honors' examinations in mathematics on which applicants are expected to score 15%.) If you are looking for a strong, harmonious collection of advanced techniques in advanced analysis, harmonic functions, and many aspects of operational calculus, you would do better to read "Applied Analysis" by the immortal Cornelius Lanczos.

The preface to the first edition of this book starts by saying it will provide an account of those parts of pure mathematics that find an application in at least two branches of physics. This sets the tone for a volume that sets the tools of mathematical physics on a solid, rigorous foundation, from tensors to multiple integrals, from functions of a complex variable to Fourier analysis, with a thorough coverage in the last ten chapters of differential equations including the wave and diffusion equations, and the Bessel, Hypergeometric, Legendre and Elliptic functions. The style is crisp and precise throughout, without any of the hand-waving that is all too common in some mathematical methods courses.If you apply a method from this book to a problem, you will know exactly what conditions are required for it to be valid, and there is little in this book that is not still useful, despite the 60 years since its first edition.