(1.1 hours to learn)
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.
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.)
- 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)
→ MIT Open Courseware: Multivariable Caclulus (2010)
Video lectures for MIT's introductory multivariable calculus class.
→ Multivariable Calculus
An introductory multivariable calculus textbook.
Location: Section 15.6, "The Divergence Theorem," pages 1057-1063
-No Additional Notes-
- create concept: shift + click on graph
- change concept title: shift + click on existing concept
- link together concepts: shift + click drag from one concept to another
- remove concept from graph: click on concept then press delete/backspace
- add associated content to concept: click the small circle that appears on the node when hovering over it
- other actions: use the icons in the upper right corner to optimize the graph placement, preview the graph, or download a json representation