Mathematical Methods book for Undergraduate

In summary: These books will get you started with the basics, but if you want to really get a deep understanding of the mathematics you'll need to read more mathematics books.
  • #1
Septim
167
6
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.
 
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  • #2
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.
 
  • #3
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?
 
  • #4
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...
 
  • #5
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
 

What is the purpose of a Mathematical Methods book for Undergraduate?

A Mathematical Methods book for Undergraduate is designed to provide students with the necessary mathematical tools and techniques to solve problems in various fields such as physics, engineering, economics, and more. It covers a wide range of topics including calculus, linear algebra, differential equations, and probability.

Is a Mathematical Methods book necessary for Undergraduate study?

While it is not a requirement for all undergraduate programs, a Mathematical Methods book can be very helpful in understanding and applying mathematical concepts in various courses. It can also serve as a valuable reference for future studies and career pursuits.

What should I look for in a good Mathematical Methods book for Undergraduate?

A good Mathematical Methods book should have clear explanations and examples, a variety of practice problems, and applications to real-world problems. It should also cover a wide range of topics and provide step-by-step solutions to problems.

How can a Mathematical Methods book improve my problem-solving skills?

A Mathematical Methods book can improve your problem-solving skills by teaching you different mathematical techniques and strategies. It can also help you develop critical thinking and analytical skills, as well as the ability to apply mathematical concepts to practical situations.

Can a Mathematical Methods book be used as a self-study tool?

Yes, a Mathematical Methods book can be a useful self-study tool for students who want to improve their mathematical skills or review concepts on their own. However, it is recommended to also seek guidance from a teacher or tutor when needed to fully understand the material.

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