ABSTRACT
Vector calculus deals with the differentiation and integration of vector fields in two- and three-dimensional space. This chapter considers important concepts such as the different types of line integrals and then how closed line integrals can be equivalent to double integrals over a region known as Green's theorem. The magnitude of a vector is given by the square root of all the components squared and added together. Just as the fundamental theorems of calculus and line integrals turn line integrals into a calculation of the function at end points, Green's theorem turns an area integral into an integral around a boundary line of the area. There are different ways to find the normal vectors to different surfaces.
