Divergence Theorem
(1.1 hours to learn)
Summary
The Divergence Theorem is a theorem relating the flux across a surface to the integral of the divergence over the interior. It can be seen as a three-dimensional generalization of Green's Theorem.
Context
This concept has the prerequisites:
- surface integrals (The Divergence Theorem is a theorem about surface integrals.)
- partial derivatives (The definition of divergence includes partial derivatives.)
- multiple integrals (The Divergence Theorem includes a triple integral.)
Goals
- Know the definition of divergence
- Know the statement of the Divergence Theorem in three dimensions
- Prove the Divergence Theorem in three dimensions
- Be able to apply the Divergence Theorem to calculate flux across a surface
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 15.6, "The Divergence Theorem," pages 1057-1063
See also
-No Additional Notes-