# Is it possible to derive/learn rigorously the theorems of vector analysis without differential forms?

I'm in Calc III without any linear algebra experience, so differential forms are a bit too high level for me right now. But, I want to know the reason behind all these theorems.

For example, why does $\dfrac{\partial Q}{\partial x} - \dfrac{\partial P}{\partial y}$ appear as the integrand in Green's Theorem? Could you derive this and the integrands in the other theorems without using the exterior derivative of differential forms?

Also, if you know of any books/resources for this type of level please let me know.

• There is no need for abstract differential forms and exterior derivatives to obtain Green's formula, all can be done completely within the one-dimensional calculus. – A.Γ. Oct 16 '15 at 11:16
• In fact, the concept of differential forms is natural; need not be intimidated by the fact that differential forms usually appear later. – Megadeth Oct 16 '15 at 11:37