18.02SC | Fall 2010 | Undergraduate

Multivariable Calculus

4. Triple Integrals and Surface Integrals in 3-Space

Part C: Line Integrals and Stokes' Theorem

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In this part we will extend Green’s theorem in work form to Stokes’ theorem. For a given vector field, this relates the field’s work integral over a closed space curve with the flux integral of the field’s curl over any surface that has that curve as its boundary.

» Session 88: Line Integrals in Space
» Session 89: Gradient Fields and Potential Functions
» Session 90: Curl in 3D
» Session 91: Stokes’ Theorem
» Session 92: Proof of Stokes’ Theorem
» Session 93: Example
» Session 94: Simply Connected Regions; Topology
» Session 95: Stokes’ Theorem and Surface Independence
» Session 96: Summary of Multiple Integration
» Problem Set 12

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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