Question 1
Let Φ be a differential
k-form and Ψ be a differential
l-form on a domain
D ⊂ R
n and let
d(Φ∧Ψ) ∈
Fm(
D). Express m in terms of
k and
l.◦ m =
k l ◦ m =
k + l◦ m =
k l + 1
◦ m =
k + l + 2
◦ m =
k + l + 1
Question 2
Let Φ = 4xzsin
2(y) dy∧dz + z(2y + sin(2y)) dz∧dx + (yz - 2z
2) dx∧dy. Find dΦ.
◦ (y - 8z) dx∧dy∧dz
◦ (y - 4zcos(2y)) dx∧dy∧dz
◦ (8z - y) dx∧dy∧dz
◦ y
◦ ydx∧dy∧dz