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

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Formal definitions of div and curl (optional reading)

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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

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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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Practice
Simple, closed, connected, piecewise-smooth practiceGet 3 of 4 questions to level up!
Circulation form of Green's theoremGet 3 of 4 questions to level up!

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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Practice
Normal form of Green's theoremGet 3 of 4 questions to level up!

Quiz 1

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Stokes' theorem

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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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Practice
Orientations and boundariesGet 3 of 4 questions to level up!
Stokes' theoremGet 3 of 4 questions to level up!

Stokes' theorem (articles)

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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

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3D divergence theorem intuition
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Divergence theorem example 1
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Explanation of example 1
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Practice
The divergence theoremGet 3 of 4 questions to level up!

Divergence theorem (articles)

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2D divergence theorem
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3D divergence theorem
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3D divergence theorem examples
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Quiz 2

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Proof of Stokes' theorem

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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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Unit test

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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.