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The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance

{a} walking, proceeding, advancing

moving or advancing by steps

Moving by steps; walking; as, gradient automata

The rate of increase or decrease of a variable magnitude, or the curve which represents it; as, a thermometric gradient

A variation in some quantity with respect to another In the context of NMR, a magnetic field gradient is a variation in the magnetic field with respect to distance [Chapter 7]

the property possessed by a line or surface that departs from the horizontal; "a five-degree gradient"

Pressure difference the term "gradient" is used to specify the difference in blood pressure before and after a blockage or stenosis The gradient is a pressure difference (calculated by subtracting the higher pressure before a blockage from the lower pressure beyound the blockage) The severity of a blockage and the impact on circulation hemodynamics can be estimated by the magnitude of the gradient This is particularly useful in estimating the severity of obstructive heart valve conditions

The slope or rate of increase or decrease in the elevation of a surface; usually expressed as a percentage

An expression of slope or an angle of slope Gradient may be expressed as a fraction or percentage, for example, 1/50 (1 in 50) metres indicates that the elevation changes (rises or falls) by one metre in a horizontal distance of 50 metres (or a 2% grade)

a graded change in the magnitude of some physical quantity or dimension

Adapted for walking, as the feet of certain birds

1 The space rate of decrease of a function Of a function in three space dimensions, the vector normal to surfaces of constant value of the function and directed toward decreasing values, with magnitude equal to the rate of decrease of the function in this direction The gradient of a function f is denoted by -f (without the minus sign in the older literature), and is itself a function of both space and time The ascendant is the negative of the gradient See del-operator

Of a function y = f(x) or the graph of such a function, the rate of change of y with respect to x, that is, the amount by which y changes for a certain (often unit) change in x

{i} slope, incline; rate of ascent or descent

(1) A measure of slope (soil- or water-surface) in meters of rise or fall per meter of horizontal distance (2) More general, a change of a value per unit of distance, e g the gradient in longshore transport causes erosion or accretion (3) With reference to winds or currents, the rate of increase or decrease in speed, usually in the vertical; or the curve that represents this rate

the spatial rate of change of an observable in the direction of maximum rate of increase (as in temperature gradient)

The steepness of a slope as measured in degrees, percentage, or as a distance ratio (rise/run)

A gradient is a slope, or the degree to which the ground slopes. a gradient of 1 in 3 The courses are long and punishing, with steep gradients. a slope or a degree of slope, especially in a road or railway American Equivalent: grade. 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

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