# 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