Stokes' Theorem (three dimensions)
(1.3 hours to learn)
Summary
Stokes' Theorem is a theorem relating a line integral along the boundary of a surface to the integral of curl over the surface. It can be seen as a three-dimensional generalization of Green's Theorem.
Context
This concept has the prerequisites:
- surface integrals (Stokes' Theorem is a theorem about surface integrals.)
- line integrals (Stokes' Theorem is a theorem about line integrals.)
- Green's Theorem (Stokes' Theorem is a generalization of Green's Theorem.)
- determinant (The determinant is used as a mnemonic for the definition of curl.)
Goals
- Know the definition of curl in three dimensions
- Know the statement of Stokes' Theorem (in three dimensions)
- Prove Stokes' Theorem (in three dimensions)
- Be able to use Stokes' Theorem to compute line integrals and surface integrals
Core resources (read/watch one of the following)
-Free-
→ MIT Open Courseware: Multivariable Caclulus (2010)
Video lectures for MIT's introductory multivariable calculus class.
-Paid-
→ Multivariable Calculus
An introductory multivariable calculus textbook.
Location:
Section 15.7, "Stokes' Theorem," pages 1065-1070
See also
-No Additional Notes-