Comprehensive math-physics books for self-study

In summary, the conversation is about finding a comprehensive mathematical physics book for self-study. The ideal book should have lots of applications, examples, and problems with solutions, as well as cover various subjects such as vector calculus, complex analysis, and nonlinear dynamics. The book mentioned for consideration is Mathematical Techniques by Jordan and Smith, but the individual is open to other suggestions. One suggestion is Sadri Hassani's Mathematical Physics, but there is a caution about the Kindle edition's display of special characters.
  • #1
Cygnus_A
34
2
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.
 
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  • #2
You may find some information here
https://www.physicsforums.com/threads/how-to-self-study-mathematics.804404/
 
Last edited:
  • #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.
 
  • #4
My newest favorite is

Sadri Hassani, Mathematical Physics, 2nd Edition, Springer 2013
DOI 10.1007/978-3-319-01195-0
 
  • #5
At first glance it looks good, thanks :)
 
  • #6
vanhees71 said:
Sadri Hassani, Mathematical Physics, 2nd Edition, Springer 2013
Cygnus_A said:
At first glance it looks good, thanks :)
Beware of Kindle edition of the book. It doesn't display some special characters.
 
  • #7
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.
 
  • #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.
 

Related to Comprehensive math-physics books for self-study

1. What makes a comprehensive math-physics book suitable for self-study?

A comprehensive math-physics book for self-study should have clear and concise explanations, a wide range of practice problems, and detailed solutions to those problems. It should also cover all the necessary topics and concepts in a logical and organized manner.

2. Are there any recommended comprehensive math-physics books for self-study?

Yes, there are many highly recommended books for self-study in math and physics. Some popular options include "Mathematical Methods in the Physical Sciences" by Mary L. Boas, "The Feynman Lectures on Physics" by Richard Feynman, and "Calculus" by Michael Spivak.

3. Can I use a comprehensive math-physics book for self-study even if I am not a scientist?

Yes, absolutely. These books can be beneficial for anyone who wants to improve their understanding of math and physics, regardless of their background or profession. However, some books may assume prior knowledge in these subjects, so it's essential to choose a book that aligns with your current level of understanding.

4. How long does it take to complete a comprehensive math-physics book for self-study?

The time it takes to complete a comprehensive math-physics book for self-study varies depending on the individual's pace and commitment. It also depends on the length and complexity of the book. Some people may finish a book in a few months, while others may take a year or longer.

5. Are there any online resources that can supplement a comprehensive math-physics book for self-study?

Yes, there are many online resources, such as lecture videos, practice problems, and interactive simulations, that can enhance your learning while using a comprehensive math-physics book for self-study. These resources can provide additional explanations and examples, making it easier to grasp difficult concepts.

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