Unit 4 Introduction

In our last unit we move up from two to three dimensions. Now we will have three main objects of study:

1. Triple integrals over solid regions of space.
2. Surface integrals over a 2D surface in space.
3. Line integrals over a curve in space.

As before, the integrals can be thought of as sums and we will use this idea in applications and proofs.

We'll see that there are analogs for both forms of Green's theorem. The work form will become Stokes' theorem and the flux form will become the divergence theorem (also known as Gauss' theorem). To state these theorems we will need to learn the 3D versions of div and curl.

Part A

In this part we will learn to compute triple integrals over regions in space. We will learn to do this in three natural coordinate systems: rectangular, cylindrical and spherical.

» Session 74: Triple Integrals: Rectangular and Cylindrical Coordinates
» Session 75: Applications and Examples
» Session 76: Spherical Coordinates
» Session 77: Triple Integrals in Spherical Coordinates
» Session 78: Applications: Gravitational Attraction
» Problem Set 10