18.02SC | Fall 2010 | Undergraduate

# Multivariable Calculus

## 4. Triple Integrals and Surface Integrals in 3-Space

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### 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: Triple Integrals

Part B: Flux and the Divergence Theorem

Part C: Line Integrals and Stokes’ Theorem

Exam 4

Physics Applications

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## Course Info

Fall 2010
##### Learning Resource Types
Simulations
Exams with Solutions
Problem Sets with Solutions
Lecture Videos
Lecture Notes