18.02SC | Fall 2010 | Undergraduate

Multivariable Calculus

3. Double Integrals and Line Integrals in the Plane

Part B: Vector Fields and Line Integrals

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A vector field attaches a vector to each point. For example, the sun has a gravitational field, which gives its gravitational attraction at each point in space. The field does work as it moves a mass along a curve. We will learn to express this work as a line integral and to compute its value.

In physics, some force fields conserve energy. Such conservative fields are determined by their potential energy functions. We will define what a conservative field is mathematically and learn to identify them and find their potential function.

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Overview

In this session you will:

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

Problems Set

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Overview

In this session you will:

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

Lecture Video

Video Excerpts

Clip: Work and Line Integrals

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

Work and Line Integrals (PDF)

Problems and Solutions

Problems: Work and Line Integrals (PDF)

Solutions (PDF)

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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: Geometric Approach

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

Geometric Approach (PDF)

Problems and Solutions

Problems: Geometric Approach to Line Integrals (PDF)

Solutions (PDF)

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« 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
• Watch another lecture video clip and read board notes

Lecture Video

Video Excerpts

Clip: Fundamental Theorem

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

Fundamental Theorem (PDF)

Lecture Video

Video Excerpts

Clip: An Important Non-Conservative Field

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

Problems and Solutions

Problems: Fundamental Theorem for Line Integrals (PDF)

Solutions (PDF)

Problems: Line Integrals of Vector Fields (PDF)

Solutions (PDF)

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« 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

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

Problems and Solutions

Problems: Identifying Gradient Fields and Exact Differentials (PDF)

Solutions (PDF)

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« 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: Potential Functions

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

Potential Functions and Exact Differentials (PDF)

Problems and Solutions

Problems: Identifying Potential Functions (PDF)

Solutions (PDF)

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Course Info

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