I am very interested in physics and am planning to self studying it. But for this I need to be mature in various areas of math. So I want to know what is the order in which I need to learn the math required for working my way through classical physics covering mechanics, electrodynamics etc. and then maybe special and general relativity.
I want to know how much calculus is required and apart from calculus, the other math I need to master like linear algebra, Fourier series etc.
Also, can someone please recommend good books for the math. Is Khan academy good enough for calculus?
I have not found any satisfactory answers for this question on physics stack exchange and hence am asking this here.
Best Answer
You will need to study Calculus, Real Analysis, Differential Geometry certainly.
For calculus I would recommend M.Spivak-Calculus. And then for a more advanced calculus book Spivak-Calculus on Manifolds. For Real Analysis W.Rudin-Principles of Mathematical Analysis and Stein,Shakarchi-Real Analysis. For Differential Geometry Do Carmo-Differential Geometry of Curves and Surfaces, Riemannian Geometry.
Some algebra probably would be necessary. Introduction to Algebra by Cameron is a good reference.