Math Insight

Pages similar to: Other ways of writing Green's theorem

• The idea behind Green's theorem
  Introduction to Green's theorem, based on the intuition of microscopic and macroscopic circulation of a vector field.
• 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
• 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
• 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 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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