Theorems of Vector Calculus

Abstract

One of the more intimidating parts of vector calculus is the wealth of so-called fundamental theorems: i. The Gradient Theorem1 ii. Green’s Theorem iii. Stokes’ Theorem iv. The Divergence Theorem Understanding when and how to use each of these can be confusing and overwhelming. The following discussion is meant to give some insight as to how each of these theorems are related. Our guiding principle will be that the four theorems above arise as generalizations of the Fundamental Theorem of Calculus.