18.02SC | Fall 2010 | Undergraduate

# Multivariable Calculus

4. Triple Integrals and Surface Integrals in 3-Space

## Part C: Line Integrals and Stokes' Theorem

« Previous | Next »

In this part we will extend Green’s theorem in work form to Stokes’ theorem. For a given vector field, this relates the field’s work integral over a closed space curve with the flux integral of the field’s curl over any surface that has that curve as its boundary.

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Do practice problems
• Use the solutions to check your work

### Problem Set

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes and examples
• Watch a recitation video

### Lecture Video

#### Video Excerpts

Clip: Line Integrals in Space

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

Line Integrals in Space (PDF)

### Problems and Solutions

Problems: Work Along a Space Curve (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes and examples

### Lecture Video

#### Video Excerpts

Clip: Gradient Fields and Potential Functions

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

### Problems and Solutions

Problems: Gradient Fields and Potential Functions (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Watch a recitation video

### Lecture Video

#### Video Excerpts

Clip: Curl in 3D

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

Del Notation (PDF)

Physical Meaning of Curl (PDF)

### Examples

Testing for a Conservative Field (PDF)

### Problems and Solutions

Problems: Curl in 3D (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Read course notes and examples
• Watch a recitation video

### Lecture Video

#### Video Excerpts

Clip: Stokes’ Theorem

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

Stokes’ Theorem (PDF)

### Problems and Solutions

Problems: Stokes’ Theorem (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes

### Lecture Video

#### Video Excerpts

Clip: Proof of Stokes’ Theorem

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

Proof of Stokes’ Theorem (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Watch a recitation video

### Lecture Video

#### Video Excerpts

Clip: Example

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

### Examples

Extended Stokes’ Theorem (PDF)

### Problems and Solutions

Problems: Extended Stokes’ Theorem (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Watch two recitation videos

### Lecture Video

#### Video Excerpts

Clip: Simply Connected Regions, Topology

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

Some Topological Questions (PDF)

### Problems and Solutions

Problems: Simply Connected Regions (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes
• Watch a recitation video

### Lecture Video

#### Video Excerpts

Clip: Stokes’ Theorem and Surface Independence

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

### Problems and Solutions

Problems: Surface Independence (PDF)

Solutions (PDF)

« Previous | Next »

« Previous | Next »

### Overview

In this session you will:

• Watch a lecture video clip and read board notes

### Lecture Video

#### Video Excerpts

Clip: Summary of Multiple Integration

The following images show the chalkboard contents from these video excerpts. Click each image to enlarge.

« Previous | Next »

## Course Info

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