Tutorial 6: Gauss Divergence Theorem
Question PDF
Class Recording
- By using divergence theorem, find where and is a cube bounded by , , .
Solution
- Evaluate where and is a closed boundary of paraboloid and plane . Use divergence theorem to simplify the derivation. Hint: use cylindrical coordinate.
Solution
Now convert to cylindrical coordinate (recall that , , , ). For paraboloid, the volume is bounded by , , . Hence,
- By using divergence theorem, find where and is a closed surface of hemisphere and . Hint: use spherical coordinate.
Solution
Now convert to spherical coordinate (recall that , , , ). For the given hemisphere, the volume is bounded by , , . Hence,
- Solve , where is the boundary of , and . Use divergence theorem to simplify the derivation.
Solution
- Use the divergence theorem to evaluate the surface integral , where and is the closed surface of the hemisphere , .
Solution
- Verify the divergence theorem for over the region bounded by , and .
Solution
On , , ,
On , , ,
On , ,