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

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Possible mastery points

Formal definitions of div and curl (optional reading)

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Green's theorem

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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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2D divergence theorem

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Practice

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

Quiz 1

Level up on the above skills and collect up to 240 Mastery points

Stokes' theorem

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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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3D divergence theorem

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Practice

The divergence theoremGet 3 of 4 questions to level up!

Divergence theorem (articles)

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Quiz 2

Level up on the above skills and collect up to 240 Mastery points

Proof of Stokes' theorem

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Types of regions in three dimensions

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Divergence theorem proof

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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.