The Gradient
The gradient plays an important role in heat conduction and in
other areas of applied mathematics. Feel free to explore our Gradient module,
for more information.
From calculus we know that for a given function
, at the point
the gradient of
in two dimensional Cartesian coordinates has the form:
Equation
2
is a vector perpendicular to the contour curve,
, which contains the point.
Equation (1.1) defines
, the gradient of
. The magnitude of
,
, is the maximum rate of change of
at that point, and the direction of
is the direction in which that maximum rate
of change occurs (in other words, the direction in which
increases most rapidly with
displacement).
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