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Green's, Stokes', and the divergence theorems

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Why care about the formal definitions of divergence and curl?Formal definition of divergence in two dimensionsFormal definition of divergence in three dimensionsFormal definition of curl in two dimensionsFormal definition of curl in three dimensions
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Green's theorem proof (part 1)Green's theorem proof (part 2)Green's theorem example 1Green's theorem example 2
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Green's theoremGreen's theorem examples
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Constructing a unit normal vector to a curve2D divergence theoremConceptual clarification for 2D divergence theorem
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Stokes' theorem intuitionGreen's and Stokes' theorem relationshipOrienting boundary with surfaceOrientation and stokesConditions for stokes theoremStokes example part 1Stokes example part 2Stokes example part 3Stokes example part 4Evaluating line integral directly - part 1Evaluating line integral directly - part 2
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Stokes' theoremStokes' theorem examplesStokes' theorem and the fundamental theorem of calculus
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3D divergence theorem intuitionDivergence theorem example 1Explanation of example 1
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2D divergence theorem3D divergence theorem3D divergence theorem examples
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Stokes' theorem proof part 1Stokes' theorem proof part 2Stokes' theorem proof part 3Stokes' theorem proof part 4Stokes' theorem proof part 5Stokes' theorem proof part 6Stokes' theorem proof part 7
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Type I regions in three dimensionsType II regions in three dimensionsType III regions in three dimensions
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Divergence theorem proof (part 1)Divergence theorem proof (part 2)Divergence theorem proof (part 3)Divergence theorem proof (part 4)Divergence theorem proof (part 5)

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.