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gradient

gradient


gra·di·ent  (grd-nt)
n. Abbr. grad.
1. A rate of inclination; a slope.
2. An ascending or descending part; an incline.
3. Physics The rate at which a physical quantity, such as temperature or pressure, increases or decreases relative to change in a given variable, especially distance.
4. Mathematics A vector having coordinate components that are the partial derivatives of a function with respect to its variables.
5. Biology A series of progressively increasing or decreasing differences in the growth rate, metabolism, or physiological activity of a cell, organ, or organism.
[Perhaps grade + -ient, as in quotient.]
gradient [ˈgreɪdɪənt]
n
1. (Engineering / Civil Engineering) Also called (esp US) grade a part of a railway, road, etc., that slopes upwards or downwards; inclination
2. (Engineering / Civil Engineering) Also called (esp US and Canadian) grade a measure of such a slope, esp the ratio of the vertical distance between two points on the slope to the horizontal distance between them
3. (Physics / General Physics) Physics a measure of the change of some physical quantity, such as temperature or electric potential, over a specified distance
4. (Mathematics) Maths
a.  (of a curve) the slope of the tangent at any point on a curve with respect to the horizontal axis
b.  (of a function, f(x, y, z)) the vector whose components along the axes are the partial derivatives of the function with respect to each variable, and whose direction is that in which the derivative of the function has its maximum value. Usually written: grad f, #X2207;f or #X2207;f Compare curl [11] divergence [4]
adj
sloping uniformly
[from Latin gradiēns stepping, from gradī to go]
gradient  (grd-nt)
1. The degree to which something inclines; a slope. A mountain road with a gradient of ten percent rises one foot for every ten feet of horizontal length.
2. The rate at which a physical quantity, such as temperature or pressure changes over a distance.
3. A operator on scalar fields yielding a vector function, where the value of the vector evaluated at any point indicates the direction and degree of change of the field at that point.
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gradient
The gradient on the left is gentle enough for trees to take root. The gradient on the right is too steep.


gradient  /gredint/  n. 1 the degree of change in a slope, as in a road: The railroad rises in a small gradient. 2 a rate of change, as in temperature: The pressure gradient in the water heater is rising. gradient
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