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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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