What is Divergence Theorem?
Divergence Theorem states that,
“Surface integral of the normal of the vector point function P over a closed surface is equal to the volume integral of the divergence of P under the closed surface”.
What is Divergence?
Divergence of a vector field is defined as the vector operation which results in the scalar field calculating the rate of change of flux. The divergence is denoted by the symbol ∇ or div(vector).
For a vector field P:
Divergence of P(x, y) in 2-D, P = P1i + P2j is given by:
∇P(x, y) =
Divergence of P(x, y) in 3-D, P = P1i + P2j + P3k is given by:
∇P(x, y, z) =
Learn more about, Divergence and Curl
Divergence Theorem
Divergence Theorem is one of the important theorems in Calculus. The divergence theorem relates the surface integral of the vector function to its divergence volume integral over a closed surface.
In this article, we will dive into the depth of the Divergence theorem including the divergence theorem statement, divergence theorem formula, Gauss Divergence theorem statement, Gauss Divergence theorem formula, and Gauss Divergence Theorem proof.
We will also go through some points on Gauss’s Divergence theorem vs Green’s theorem, solve some examples, and answer some FAQs related to the divergence theorem.
Table of Content
- What is Divergence Theorem?
- Divergence Theorem Formula
- Gauss Divergence Theorem
- Proof of Gauss Divergence Theorem
- Gauss’s Divergence Theorem vs. Green’s Theorem