- #1

Cygnus_A

- 34

- 2

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.