Comprehensive math-physics books for self-study

[Cygnus_A]

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.

 

[Greg Bernhardt]

You may find some information here
https://www.physicsforums.com/threads/how-to-self-study-mathematics.804404/

 

[Cygnus_A]

That is certainly helpful. I've always been good at asking myself questions, but I've never been systematic about it.

Maybe I'll pick up one of those books by Gelfand. I could imagine myself leisurely doing basic exercises.

 

[vanhees71]

My newest favorite is

Sadri Hassani, Mathematical Physics, 2nd Edition, Springer 2013
DOI 10.1007/978-3-319-01195-0

 

[Cygnus_A]

At first glance it looks good, thanks :)

 

[Frimus]

Sadri Hassani, Mathematical Physics, 2nd Edition, Springer 2013

At first glance it looks good, thanks :)

Beware of Kindle edition of the book. It doesn't display some special characters.

 

[vanhees71]

Why should one have the Kindle edition. I've the book in good old paper and as a pdf ebook. The latter is great to carry around with my laptop and tablet, the latter to really study.

 

[Cygnus_A]

Yeah, Kindle's lack of ability to put up figures and equations in PDFs was the main reason that I didn't buy it.