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Intro Math Comprehensive math-physics books for self-study

  1. Apr 7, 2015 #1
    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.
  2. jcsd
  3. Apr 7, 2015 #2
    You may find some information here
    https://www.physicsforums.com/threads/how-to-self-study-mathematics.804404/ [Broken]
    Last edited: May 7, 2017
  4. Apr 7, 2015 #3
    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.
  5. Apr 8, 2015 #4


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    My newest favorite is

    Sadri Hassani, Mathematical Physics, 2nd Edition, Springer 2013
    DOI 10.1007/978-3-319-01195-0
  6. Apr 9, 2015 #5
    At first glance it looks good, thanks :)
  7. Apr 10, 2015 #6
    Beware of Kindle edition of the book. It doesn't display some special characters.
  8. Apr 10, 2015 #7


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    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.
  9. Apr 10, 2015 #8
    Yeah, Kindle's lack of ability to put up figures and equations in PDFs was the main reason that I didn't buy it.
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