Looking to learn Maths required for understanding of Physics

[Sir Bryan]

So I am in my senior year of a Computer Engineering degree. I've always been interested in physics but never really thought to study it in depth. I've always read a lot of popular physics books, the kind for the lay person and all they do is leave me asking "why". They explain all of these marvelous ideas from different fields of physics but never give the details, which of course is not their intention. However I am not content anymore without knowing those details. I want to learn more physics, at least to the point where I can start to read physics papers and journals and actually understand them.

The dilemma I'm at now is that I do not have the mathematical knowledge required to pursue this to much effect. I'm looking to fill the gaps of my Mathematical ignorance so that I can begin to really study some physics. From the math courses I have had and the books I already own I feel I still need more maths to be successful. I want to be able to get through a rigorous self study of modern Physics, with Quantum Mechanics, Relativity, Particle Physics and the like.

I've taken three levels of Calculus, covering topics from basic differentiation and integrations, to multiple integration, surface and line integrals, basic Vector calculus (Stokes theorem, Divergence theorem, and Green's Theorem mostly) and have also had one course in Differential Equations, which admittedly was not my strong suit.

So I guess mostly what I'm asking is, given this mathematical background and the goals I have in mind, where do you recommend I begin my mathematical studies? What topics would be most vital for me to cover, and what books would you recommend I purchase to begin my studies?

 

[UltrafastPED]

The most important course will be linear algebra; this should be an upper level course based on proofs. Here you will learn how to think about abstract vector spaces as well as how to solve eigenvalue problems ... this is most of the mathematics required for QM. The rest is differential equations, but you only need to know how to solve a few special types - find a good book on "Mathematical Physics" and study those chapters.

You will probably also want to take the "Mathematical Physics" course ... there are a lot of odds and ends that can be picked up there.

If you have more time take complex analysis (but not real analysis), and perhaps a course in partial differential equations ...

If you think you will be writing computer programs for simulations, etc. then a good course in numerical analysis will be worth while - but learn the other stuff first!

 

[Sir Bryan]

Thanks for that. I am actually taking a Linear Algebra course, exactly as you described, next semester. Ill be especially sure to take good notes and study well. Next fall is my last semester so I don't have a lot of oppurtunity to take any more maths courses on top of that so the rest will be self study but I am pretty good at that.