So far I have taken the intro Calculus based Physics courses and got A in both of them, however, I plan on taking more advanced physics courses? So far, from my research, the upper level physics courses are: mechanics, electromagnetism, thermodynamics and quantum mechanics? My question is, what would be the math prerequisites for these higher level math courses? When I took intro Calculus based physics, much of it was algebra and trigonometry, with simple differentiation and integration, and using those methods to derive the formulas. How different are things in higher level physics courses? Will it just be plugging and chugging with algebra or will it be more involved with Calculus? I understand that you have to understand the concepts more, but I find it more interesting how the math is used.
You definitely need Multivariate Calculus and Differential Equations as a base. Most physics majors also take a Mathematical Physics course or a couple of other math courses, such as linear algebra and statistics or special functions.
Upper level physics is all about vector Calculus and solving differential equations and boundary value problems.