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