Differential Operators Flashcards
1
Q
v(t) =
A
dr(t)/dt
2
Q
a(t) =
A
dv(t)/dt = d^2 r(t)/dt^2
3
Q
Continuity equation
A
∇ j + d/dt p = 0
4
Q
Parameterise r
A
via u
r = (cosu,sinu,0)
5
Q
cylindrical limits
A
0 < Φ < 2π
6
Q
spherical limits
A
0 < Φ < 2π
0 < θ < π
7
Q
cylindrical coordinates
A
ρ = √x^2+y^2
Φ = arctan(y/x)
z
8
Q
spherical coordinates
A
ρ = √x^2+y^2 + z^2
Φ = arctan(y/x)
θ = arctan(√x^2+y^2 / z)
9
Q
∇ · (b × c)
A
∇ · (b × c) =∇(b) · (b × c) + ∇(c) · (b × c)
= c · (∇(b) × b) − ∇(c) · (c × b)
= c · (∇ × b) − b · (∇ × c)
10
Q
Solenoidal
A
∇ . a = 0
11
Q
Irrotational
A
∇ x a = 0
12
Q
to find the positions of the sources and sinks
A
find the divergence twice then = 0
13
Q
electrostatic force
A
F = - ∇V
14
Q
velocity or speed =
A
dr/dt
15
Q
directional derivative
A
∇aΦ = (∇Φ).a
