# Vector Calculus Independent Study Path

## Unit 5: Vector Fields

A vector field is a function which associates a vector to every point in
space. Vector fields are everywhere in nature, from the wind (which
has a velocity vector at every point) to gravity (which exerts a force
vector at every point) to the gradient of any scalar field (for example,
the gradient of the temperature field assigns to each point a vector
which says which direction to travel if you want to get hotter).
In this unit, you will learn:

- How to graph a vector field.
- How to tell if a path is a flow line for a velocity or acceleration
vector field.
- How to tell if a vector field is conservative.
- How to take the curl and divergence of a vector field.
- How to prove that the curl of a conservative vector field is the
zero vector, and how to prove that the divergence of a curl field is zero.

For more detailed instructions, see the Xdvi
or PDF pages.
## Suggested Procedure

- Read and do some problems from
- Rogers Chapters 19 and 21,
- Marsden and Tromba third edition sections 3.3, 3.4, 3.5, and 8.3,
or
- Marsden and Tromba fourth edition sections 4.3, 4.4, and 8.3

- Take the Sample Test, Xdvi or PDF.
- Take a unit test.

Vector Calculus Independent Study Path |
Vector Calculus Index |
World Web Math Main Page

watko@athena.mit.edu
Last modified July 28, 1998