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Unit: Green's, Stokes', and the divergence theorems

Formal definitions of div and curl (optional reading)

Learn
Why care about the formal definitions of divergence and curl?
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Formal definition of divergence in two dimensions
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Formal definition of divergence in three dimensions
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Formal definition of curl in two dimensions
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Formal definition of curl in three dimensions
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Green's theorem (videos)

Learn
Green's theorem proof (part 1)
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Green's theorem proof (part 2)
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Green's theorem example 1
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Green's theorem example 2
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Green's theorem (articles)

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Green's theorem
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Green's theorem examples
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2D divergence theorem

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Constructing a unit normal vector to a curve
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2D divergence theorem
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Conceptual clarification for 2D divergence theorem
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Stokes' theorem (videos)

Learn
Stokes' theorem intuition
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Green's and Stokes' theorem relationship
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Orienting boundary with surface
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Orientation and stokes
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Conditions for stokes theorem
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Stokes example part 1
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Stokes example part 2
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Stokes example part 3
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Stokes example part 4
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Evaluating line integral directly - part 1
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Evaluating line integral directly - part 2
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Stokes' theorem (articles)

Learn
Stokes' theorem
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Stokes' theorem examples
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Stokes' theorem and the fundamental theorem of calculus
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3D divergence theorem (videos)

Learn
3D divergence theorem intuition
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Divergence theorem example 1
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Explanation of example 1
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Divergence theorem (articles)

Learn
2D divergence theorem
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3D divergence theorem
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3D divergence theorem examples
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Proof of Stokes' theorem

Learn
Stokes' theorem proof part 1
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Stokes' theorem proof part 2
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Stokes' theorem proof part 3
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Stokes' theorem proof part 4
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Stokes' theorem proof part 5
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Stokes' theorem proof part 6
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Stokes' theorem proof part 7
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Types of regions in three dimensions

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Type I regions in three dimensions
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Type II regions in three dimensions
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Type III regions in three dimensions
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Divergence theorem proof

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Divergence theorem proof (part 1)
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Divergence theorem proof (part 2)
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Divergence theorem proof (part 3)
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Divergence theorem proof (part 4)
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Divergence theorem proof (part 5)
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About this unit

Here we cover four different ways to extend the fundamental theorem of calculus to multiple dimensions. Green's theorem and the 2D divergence theorem do this for two dimensions, then we crank it up to three dimensions with Stokes' theorem and the (3D) divergence theorem.