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.

» Session 56: Vector Fields
» Session 57: Work and Line Integrals
» Session 58: Geometric Approach
» Session 59: Example: Line Integrals for Work
» Session 60: Fundamental Theorem for Line Integrals
» Session 61: Conservative Fields, Path Independence, Exact Differentials
» Session 62: Gradient Fields
» Session 63: Potential Functions
» Session 64: Curl
» Problem Set 8

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Course Info

As Taught In
Fall 2010
Learning Resource Types
Exams with Solutions
Problem Sets with Solutions
Lecture Videos
Lecture Notes