Recommended Quantum Physics and Maths book?

[bubblewrap]

Hi, I'm currently in high school but I know several university maths and physics (just a little)
I want to know about

Maths:
Lagrangian and Hamiltonian
Fourier Transform (I self-studied Fourier series)
Differential Equations (only know one way to solve them, I think its the most basic one)
Gaussian Function and its properties (like multiplying two of them and making a one with a p I couldn't find anything related to it online)
Surface Integrals and more on integrals (like Cantor Integrals)

Physics:
Quantum Mechanics(I've learned the basics so I want something that's understandable (with proofs would be nice) but not too easy but then not too hard as well. So I guess I want introductory Quantum Mechanics Book with a little rigor)
Relativity: Understandable one with a lot of contents (exercise questions too)

If anyone could find a good book please let me know.
Thanks in advance

 

[KSG4592]

Those are pretty advanced subjects. If you are only in high school I would suggest that it would be more beneficial to gain a firm grounding in your maths and physics from the basics up than to jump straight into a book about Lagrangians or differential equations. A thorough understanding of calculus is necessary.

 

[bubblewrap]

I did do a lot of basic calculus and did year one university mathematics and physics is that okay?

 

[bubblewrap]

Those are pretty advanced subjects. If you are only in high school I would suggest that it would be more beneficial to gain a firm grounding in your maths and physics from the basics up than to jump straight into a book about Lagrangians or differential equations. A thorough understanding of calculus is necessary.

Forgot to press 'reply'

 

[verty]

Try these if you like. I definitely prefer non-standard books, I dislike the ascetic quality that many modern books have.

1. Braun, "Differential Equations and their Applications". Looks like it covers a lot and rigorously but not in the standard way.
2. Holland, "Applied Analysis by the Hilbert Space Method". Looks quirky and very relevant for the modern QM.

I've removed the third suggestion I had here, it's not because I think it was a bad book to choose but I want to step away from these forums for a while and this is a good time to do it. These two seem to fit what you requested very nicely and I leave it up to you which books you want to buy.