Geography Reference
In-Depth Information
C.2
INTEGRAL THEOREMS
(a) Divergence theorem:
B
·
n
dA
=
V
·
B
dV
A
V
where V is a volume enclosed by surface A and
n
is a unit normal on A.
(b) Stokes' theorem:
B
·
d
l
=
(
V
×
B
)
·
n
dA
A
where A is a surface bounded by the line traced by the position vector
l
and
n
is a
unit normal of A.
C.3
VECTOR OPERATIONS IN VARIOUS COORDINATE SYSTEMS
(a) Cartesian coordinates: (x, y, z)
Coordinate
Symbol
Velocity component
Unit vector
Eastward
x
u
i
Northward
y
v
j
Upward
z
w
k
i
∂
∂
∂y
+
k
∂
∂z
∇
=
∂x
+
j
∂u
∂x
+
∂v
∂y
∇·
V
=
∂v
∂x
−
∂u
∂y
k
·
∇
×
V
)
=
(
∂
2
∂x
2
∂
2
∂y
2
2
∇
h
=
+
