I need help taking notes on vector calculus. Can you find the theorems and equations for the following topics? and explain how to apply them and when to use it?

-implicit value theorem, inverse function theorem, double/triple integrals, polar, cylindrical, spherical coordinates, change of variables, line integrals, surface integrals and parametric surfaces, stokes and divergence theorem.

https://books.google.com/books?id=LiRLJf2m_dwC&printsec=frontcover&dq=vector+calculus+5th+edition&hl=en&sa=X&ved=0ahUKEwiU0MDM_q7aAhVM_oMKHeu7BE4Q6wEIKDAA#v=snippet&q=divergence&f=false