Pages similar to: The components of the curl
- 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. - 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. - The idea behind Green's theorem
Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field. - The definition of curl from line integrals
How the curl of a vector field is defined by line integrals representing circulation. - Calculating the formula for circulation per unit area
A sketch of the proof for the formula for the component of the curl of a vector field. - A path-dependent vector field with zero curl
A counterexample showing how a vector field could have zero curl but still fail to be conservative or path-independent. - The idea behind Stokes' theorem
Introduction to Stokes' theorem, based on the intuition of microscopic and macroscopic circulation of a vector field and illustrated by interactive graphics. - 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. - Vector field overview
An overview introducing the basic concept of vector fields in two or three dimensions. - Vector fields as fluid flow
Interpretation of vector fields as velocity fields of fluids. - Line integrals as circulation
Definition of circulation as the line integral of a vector field around a closed curve. - When Green's theorem applies
A discussion of situations where you are allowed to use Green's theorem. - Green's theorem with multiple boundary components
How Green's theorem applies even to regions with holes in them - The curl of a gradient is zero
Calculation showing that the curl of a gradient is zero. - A conservative vector field has no circulation
How a conservative, or path-independent, vector field will have no circulation around any closed curve. - Proper orientation for Stokes' theorem
The importance of orientating the surface and its boundary correctly when using Stokes' theorem. - Stokes' theorem examples
Examples illustrating how to use Stokes' theorem.
Back to: The components of the curl