Gradient

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

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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.

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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.

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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.

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Vector calculus: Vector calculus is a field of mathematics concerned with multivariate real analysis of vectors in two or more dimensions. It consists of a suite of formulas and problem solving techniques very useful for engineering and physics....

Scalar field: In mathematics and physics, a scalar field associates a scalar to every point in space. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure....

Function: In general (not in the mathematical but in the engineering sense), a function is a goal-oriented property of an entity. The carrier of a function is a process; therefore, is possible to realise the same function using different physical processes, and one process can be a carrier of multiple funct...

Gradient related Images and Photos (experimental)

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