# 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-