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PHY2061
R. D. Field
Department of Physics
grad_1.doc
Univesity of Florida
Gradient of a Scalar Function
Let
f(x,y,z)
be a
scalar function
of position and let
z
dz
y
dy
x
dx
r
d
ˆ
ˆ
+
+
=
!
"
be an infinitesimal displacement vector.
Directional derivative:
−
+
+
+
=
→
dr
z
y
x
f
dz
z
dy
y
dx
x
f
r
d
df
dr
)
,
,
(
)
,
,
(
lim
0
"
The directional derivative depends on the point (x,y,z) and the direction
of
r
d
"
.
Gradient:
The
gradient
of a scalar
function f(x,y,z) is a
vector
whose
magnitude is the
maximum directional
derivative
at the point being considered
and whose direction is the direction of
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This note was uploaded on 05/31/2011 for the course PHY 2061 taught by Professor Fry during the Spring '08 term at University of Florida.
 Spring '08
 FRY
 Physics

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