18.02SC | Fall 2010 | Undergraduate

Multivariable Calculus

4. Triple Integrals and Surface Integrals in 3-Space

Part B: Flux and the Divergence Theorem

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Here we will extend Green’s theorem in flux form to the divergence (or Gauss’) theorem relating the flux of a vector field through a closed surface to a triple integral over the region it encloses. Before learning this theorem we will have to discuss the surface integrals, flux through a surface and the divergence of a vector field.

» Session 79: Vector Fields in Space
» Session 80: Flux Through a Surface
» Session 81: Calculating Flux; Finding ndS
» Session 82: ndS for a Surface z = f(x, y)
» Session 83: Other Ways to Find ndS
» Session 84: Divergence Theorem
» Session 85: Physical Meaning of Flux; Del Notation
» Session 86: Proof of the Divergence Theorem
» Session 87: Diffusion Equation
» Problem Set 11

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Course Info

As Taught In
Fall 2010
Learning Resource Types
Exams with Solutions
Problem Sets with Solutions
Lecture Videos
Lecture Notes