I'm a sophomore at Rensselaer Polytechnic Institute and I'm taking MATH 4600 which is Advanced Calculus. I love the class and it is very interesting, we're taking what we learned in Multivariable Calculus, but just at a much higher level. However, my teacher does a lot of proofs behind why it's true and a lot of theory. I am having trouble understanding the proofs of the implicit theorem, the inversion theorem, and even just partial derivatives. I know how to do the problems with actual examples, it's just the theory that's a little weak and I really want to improve on it to fully appreciate it a lot more. Thanks to anyone who could help give me pointers to understand the proofs a lot more!