Detailed solution to Problem Set 41 Exercise 3
- Question:
- Find the exterior differential (aka exterior derivative)
of the following exterior differential form:
2xy dx +
3yz dy +
4xz dz.
- Solution:
- d ∧
(2xy dx +
3yz dy +
4xz dz) =
d(2xy) ∧ dx +
d(3yz) ∧ dy +
d(4xz) ∧ dz =
(2y dx + 2x dy) ∧
dx +
(3z dy + 3y dz) ∧
dy +
(4z dx + 4x dz) ∧
dz =
2y dx ∧ dx +
2x dy ∧ dx +
3z dy ∧ dy +
3y dz ∧ dy +
4z dx ∧ dz +
4x dz ∧ dz =
0 − 2x dx ∧ dy +
0 − 3y dy ∧ dz +
4z dx ∧ dz + 0 =
−2x dx ∧ dy +
4z dx ∧ dz −
3y dy ∧ dz.
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