Gradient

In vector calculus, the gradient of a scalar field is a

Related Topics:
Vector calculus - Scalar field

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vector field which points in the direction of the greatest rate

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of change of the scalar field, and whose magnitude is the greatest rate of change.

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More rigorously, the gradient of a function from the Euclidean space Rn to R is the best linear approximation to that function at any particular point in Rn. To that extent, the gradient is a particular case of the Jacobian.

Related Topics:
Function - Euclidean space - Linear approximation - Jacobian

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In the case of a real-valued function of a single variable, the gradient is simply the derivative, or, for a linear function, the slope of the line.

Related Topics:
Derivative - Linear function - Slope

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The word gradient is sometimes used synonymously with grade, meaning the inclination of a surface along a given direction. One can obtain the grade by taking the dot product of the vector gradient with the unit vector in the direction of interest. The magnitude of the gradient is also sometimes referred to as just the gradient.

Related Topics:
Grade - Surface - Dot product

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