I'm looking for a comprehensive mathematical physics book for self-study. My ideal book would have some of these qualities: - lots of applications, examples, problems and solutions (or available solutions) - not focused on rigor - interesting to read (maybe with some history too?) - ideally it would prep me for jumping right into reading recent publications - good for reference And it would have some of these subjects: - vector calculus, integration techniques (and/or other relevant calculus) - complex analysis, conformal mappings, sums, series and sequences - linear algebra, eigenvalues/vectors, rotations, tensors - Fourier Analysis, Laplace Transforms - linear and partial differential equations, Sturm-Liouville theory, Green's functions - nonlinear dynamics, chaos, numerical methods, graph theory - prob/stats, bayes stats and other useful stats (like markov chains, regression, etc) - topology, differential geometry, group theory, renormalization and other advanced topics Obviously that's a lot of material; it's not listed in any order of importance. Does anybody have any suggestions? The book I'm looking at right now is Mathematical Techniques by Jordan and Smith. It has quite a few of these subjects, but I want some better opinions. And if I didn't mention any particular positive aspect of a book for self-study (or an important modern subject), feel free to add your input. Also, I'm at the beginning half of grad school, if it makes a difference.