I'm an graduate level in engineering physics, finishing my 1st year. This is what i have so far in math:
Calculus (single and multivariable)
Line integrals, green's theorem, vector fields.
Linear Algebra
Series
And this is what ill have next year:
Differential equations
Fourier series
Fourier and laplace transform, complex functions and vector calculus.
My questions are: Am i ready to begin studying differential geometry, or should i wait a little bit longer? (I have a little bit of experience with analysis, but isn't anything very worth mentioning) i'm interested in studying differential geometry at home, so any other topics i didn't mentioned up there and you think is important to know before start thinking about DG, you're welcome to say. Also, i have another question: Are there any good sources of video-lectures and materials (such as notes, exercises, practice exams) that you guys can point me for start in DG? I tried MIT OCW but i couldn't find anything.
Thank you guys!
I would say get three books. Any university multivariable calculus book (which usually hand wave details to make things accessible, but are very useful for attaching high-level theory to basic examples), Tu's book on manifolds, O'Neill's elementary differential geometry and O'Neill's semi-riemannian geometry. Although the latter is fairly advanced, since you're a physicist this is a great book for you to see where all the mathematics is heading.