Learning math for physics

Question

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.

Answer 1

Whatever the path you follow, sooner or latter you'll going to meet the famous "variational calculus", which is a fundamental tool for the applications you have in mind. So plan your ascend in math (and physics) always taking a look what it is saying in that calculus.

Answer 2

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.

Answer 3

Consider getting a good CAS (such as Mathematica, the one I'm familiar with and perhaps the best) and use it not just to do calculations, but to write tutorials or essays on the material you are learning. These might include symbolic derivations and proofs all done by calculation and using definitions, axioms and algorithms that you implement. The notebook tutorials would also include textual discussion, presentations and examples, static or active. There is nothing like actually using and manipulating the various objects that the mathematicians talk about so they become familiar and your own. (Mathematicians seem to be so darn smart that they do a lot of this in their head!) Also by this method you can build up an active capability to do the math and not just be doing ephemeral calculations.

Also remember that although physicists are quick to acknowledge their debt to the mathematicians, the feeling is not always reciprocated. Consider the question of how you attach numbers to physical phenomena. It takes a physical device, often invented by an experimental physicist and perfected by an engineer, to do that.