| 释义 |
Divergence TheoremA.k.a. Gauss's Theorem. Let  be a region in space with boundary  . Then
 | (1) |
 be a region in the plane with boundary  .
 | (2) |
 satisfies certain constraints, simplified forms can be used. If  where  is a constant vector  , then
 | (3) |
 | (4) |
 | (5) |
 | (6) |
 , and  must vary with  so that cannotalways equal zero. Therefore,
 | (7) |
 , where is a constant vector , then
 | (8) |
References
Arfken, G. ``Gauss's Theorem.'' §1.11 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 57-61, 1985. |