Integral Theorems Flashcards
1
Q
Divergence Theorem
A
delta . F integrated over the volume dV
=
F . dS integrated over the closed surface
(dS = n^dA)
2
Q
Stokes Theorem
A
delta x F . dS integrated over the closed surface
F . dr integrated over the enclosing curve
(dS=n^dA)
3
Q
Area Element: Spherical Polar Coordinates
A
r^2 sin(θ) dθdΦ
4
Q
Area Element: Plane Polar Coordinates
A
r drdθ
5
Q
Area Element: Cartesian Coordinates
A
dxdy
6
Q
Parameterisation of a circle of radius r
A
r(t) = (rcos(t),rsin(t),0)
7
Q
Parameterisation of a sphere of radius r
A
r(θ,Φ) = ( rsinθcosΦ , rsinθsinΦ , rcosθ ) [given]
0 < θ < pi, 0 < Φ < 2pi [not given]
8
Q
General Formula for Area Element
A
¦ dr/du x dr/dv ¦ dudv
