Let (S) be a closed surface and (V) the enclosed volume. Prove Green's first and second identities,
Question:
Let \(S\) be a closed surface and \(V\) the enclosed volume. Prove Green's first and second identities, respectively.
a. \(\int_{S} \phi abla \psi \cdot \mathbf{n} d S=\int_{V}\left(\phi abla^{2} \psi+abla \phi \cdot abla \psi\right) d V\).
b. \(\int_{S}[\phi abla \psi-\psi abla \phi] \cdot \mathbf{n} d S=\int_{V}\left(\phi abla^{2} \psi-\psi abla^{2} \phi\right) d V\).
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
A Course In Mathematical Methods For Physicists
ISBN: 9781138442085
1st Edition
Authors: Russell L Herman
Question Posted: