Where do I start in math for physics comprehension?

[mpatryluk]

I am looking to work my way through classical physics and into more complex modern physics topics.

I try to learn from a combination of internet resources and textbooks, but on the internet I find them often using terminology which is too mathematically advanced for me.

Some examples are:
-Hilbert space
-Lagrangian/Hamiltonian
-Fourier transforms

And when i try to research these topics online, I don't have the necessary context or experience to understand the vocabulary that explains them, i.e. terminology like "a structure on a set" or other vocabulary that is too vague for me to understand (because I don't have the experience to know which context the words should be taken in).

I've learned up to calculus/trig, and am starting work on linear algebra, but I'd like to know which topics I can study which will give me the math literacy I need to understand concepts like the above mentioned. Ideally resources that introduce me to the vocabulary without presuming prior knowledge.

Thanks!

 

[jedishrfu]

When I went to school, I had Calc 1,2,3, Advanced Calculus, linear algebra and Diff Eqns and that was sufficient to study Classical Mechanics from Marion or from Goldstein, E and M Theory and Quantum Mechanics. For self-study you probably need to study them in that order too as QM depends on some CM and EM concepts.

I also took Tensor Analysis and that helped with the notation.

 

[mpatryluk]

Thank you so much, I'll do it in that order then!

 

[jedishrfu]

For me, the Lagrangisn formulation in CM was the coolest thing I had ever encountered. Consider how you've studied Newtonian physics and used force diagrams and vector math to solve your problems which can get very involved to determine the motion of the system.

It never occurs to you that there is this underlying principle call Least Action that says things move is a way to expend the least amount of energy and from simply accounting for the energy of the system and taking its difference in T-V and doing some math determine the motion. It was very profound for me.