Pages similar to: Vector field overview
- Vector fields as fluid flow
Interpretation of vector fields as velocity fields of fluids. - The idea of the divergence of a vector field
Intuitive introduction to the divergence of a vector field. Interactive graphics illustrate basic concepts. - Subtleties about divergence
Counterexamples illustrating how the divergence of a vector field may differ from the intuitive appearance of the expansion of a vector field. - The idea of the curl of a vector field
Intuitive introduction to the curl of a vector field. Interactive graphics illustrate basic concepts. - Subtleties about curl
Counterexamples illustrating how the curl of a vector field may differ from the intuitive appearance of a vector field's circulation. - The components of the curl
Illustration of the meaning behind the components of the curl. - Divergence and curl notation
Different ways to denote divergence and curl. - Divergence and curl example
An example problem of calculating the divergence and curl of a vector field. - Introduction to a line integral of a vector field
The concepts behind the line integral of a vector field along a curve are illustrated by interactive graphics representing the work done on a magnetic particle. The graphics motivate the formula for the line integral. - Alternate notation for vector line integrals
An alternative notation for the line integral of a vector field is introduced. - Line integrals as circulation
Definition of circulation as the line integral of a vector field around a closed curve. - Vector line integral examples
Example of calculating line integrals of vector fields. - The idea behind Green's theorem
Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field. - An introduction to conservative vector fields
An introduction to the concept of path-independent or conservative vector fields, illustrated by interactive graphics. - How to determine if a vector field is conservative
A discussion of the ways to determine whether or not a vector field is conservative or path-independent.
Back to: Vector field overview