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Calculus III - Notes
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## Line Integrals

In this section we are going to start looking at Calculus with vector fields (which we’ll define in the first section).  In particular we will be looking at a new type of integral, the line integral and some of the interpretations of the line integral.  We will also take a look at one of the more important theorems involving line integrals, Green’s Theorem.

Here is a listing of the topics covered in this chapter.

Vector Fields  In this section we introduce the concept of a vector field.

Line Integrals  Part I  Here we will start looking at line integrals.  In particular we will look at line integrals with respect to arc length.

Line Integrals  Part II  We will continue looking at line integrals in this section.  Here we will be looking at line integrals with respect to x, y, and/or z.

Line Integrals of Vector Fields  Here we will look at a third type of line integrals, line integrals of vector fields.

Fundamental Theorem for Line Integrals  In this section we will look at a version of the fundamental theorem of calculus for line integrals of vector fields.

Conservative Vector Fields  Here we will take a somewhat detailed look at conservative vector fields and how to find potential functions.

Green’s Theorem  We will give Green’s Theorem in this section as well as an interesting application of Green’s Theorem.

Curl and Divergence  In this section we will introduce the concepts of the curl and the divergence of a vector field.  We will also give two vector forms of Green’s Theorem.

 Area and Volume Revisited Previous Section Next Section Vector Fields Multiple Integrals Previous Chapter Next Chapter Surface Integrals

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