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/gray"dee euhnt/, n.1. the degree of inclination, or the rate of ascent or descent, in a highway, railroad, etc.2. an inclined surface; grade; ramp.3. Physics.a. the rate of change with respect to distance of a variable quantity, as temperature or pressure, in the direction of maximum change.b. a curve representing such a rate of change.4. Math. a differential operator that, operating upon a function of several variables, results in a vector the coordinates of which are the partial derivatives of the function. Abbr.: grad. Symbolically appearing as a downward pointing triangle.adj.5. rising or descending by regular degrees of inclination.6. progressing by walking; stepping with the feet as animals do.7. of a type suitable for walking or running, as the feet of certain birds; gressorial.[1635-45; < L gradient- (s. of gradiens), prp. of gradi to walk, go, equiv. to grad- walk + -i- thematic vowel + -ent- -ENT]
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In mathematics, a differential operator applied to a three-dimensional vector-valued function to yield a vector whose three components are the partial derivatives of the function with respect to its three variables.The symbol for gradient is ∇. Thus, the gradient of a function f, written grad f, or ∇f, is ∇f = ifx + jfy + kfz where fx, fy, and fz are the first partial derivatives of f and the vectors i, j, and k are the unit vectors of the vector space. If in physics, for example, f is a temperature field (giving the temperature at every point in a space), ∇f is the direction of the heat-flow vector in the field.* * *
Universalium. 2010.
