Pages similar to: When Green's theorem applies
- The idea behind Green's theorem
Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field. - Green's theorem with multiple boundary components
How Green's theorem applies even to regions with holes in them - 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 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. - Line integrals as circulation
Definition of circulation as the line integral of a vector field around a closed curve. - Other ways of writing Green's theorem
Small variations in the way you can write Green's theorem - Using Green's theorem to find area
A trick to use Green's theorem to calculate the area of a region - Green's theorem examples
Examples of using Green's theorem to calculate line integrals - The definition of curl from line integrals
How the curl of a vector field is defined by line integrals representing circulation. - A conservative vector field has no circulation
How a conservative, or path-independent, vector field will have no circulation around any closed curve. - 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 fundamental theorems of vector calculus
A summary of the four fundamental theorems of vector calculus and how the link different integrals.
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