Mathematical Methods book for Undergraduate

[Septim]

Greetings everyone,

I am posting this question here since I cannot post it in the math and science learning materials section of the forum. My question is that sometimes in physics I get into a lot of involved math particularly linear algebra, Hilbert space, partial differential equations and complex analysis I want to brush up my skills in these areas by self studying a mathematical methods book. Do you have any recommendations for these kind of books?

I currently own "Mathematical Methods for Students of Physics and Related Fields" by Hassani and a calculus and a linear algebra book. However sometimes these books are not sufficient and I need one which includes a detailed derivation of the properties of spherical harmonics and stuff related to group theory in quantum mechanics for example.

After some search I found that the book by Hassani has a sequel named "Mathematical Physics: a Modern Introduction to its Foundations", there is a short book by Susan Lea named "Mathematics for Physicists" and yet another book "A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry" by Peter Szekeres. Actually some of these books lack some topics that the others have in them, that is what makes me confused. I would be happy to hear your opinions on this topic because I need to see the proof of every claim that a book makes.

 

[micromass]

If you want a deep understanding of the mathematics, then you'll need to read mathematics books. Mathematical methods book will only give a superficial understanding (although that is usually enough to be able to do physics).

Certainly if you want a proof of every claim a book makes. If you want that, then you'll need to go to math books for sure.

 

[Septim]

Thanks for the reply. My point was that there should be a good balance between theory and application, some of the books are heavily biased towards applications, I do not want that and too involved math is difficult for me to understand since I do not have a formal training in math. Do you have a suggestion for where to start? Does Hassani's book provide a good balance between theory and application?

 

[alissca123]

Hassani is the one you're looking for! It's not as rigorous as a pure math book, but it is certainly not the typical hand-wavy math methods book. Szekeres is also a great book though...

 

[Septim]

Thanks for the recommendations, I would either buy Hassani or Szekeres yet I am confused among these two could you further elaborate on these books?

Thanks