“gradient”的概念、定义、翻译、参考文献-科学参考

gradient

Physics

1. The slope of a line. In Cartesian coordinates, a straight line y = mx+c, has a gradient m. For a curve, y=f(x), the gradient at a point is the derivative dy/dx at that point, i.e. the slope of the tangent to the curve at that point.

2. See gradient operator.

Mathematics

The vector obtained by applying the differential operator del, $\nabla = i \frac{\partial}{\partial x} + j \frac{\partial}{\partial y} + k \frac{\partial}{\partial z}$ , to a scalar function of position ϕ‎(r). This gives the gradient of ϕ‎ as grad $ϕ = \nabla ϕ = i \frac{\partial ϕ}{\partial x} + j \frac{\partial ϕ}{\partial y} + k \frac{\partial ϕ}{\partial z} .$ The gradient of ϕ‎ points in the direction in which ϕ‎ is increasing fastest. See also curl, divergence.

Chemical Engineering

The slope of a line on a graph. In Cartesian coordinates, the general equation of a straight line is y = mx + c where m is the gradient or slope and c is the intercept on the y-axis. The gradient at some point on a curve can be found from the derivative $d y / d x$ at that point. The gradient is therefore the tangent to the curve.

Internet

The gradual transition from one colour to another colour in a graphic image, usually a background colour.

Geology and Earth Sciences

The rate of change of a function (e.g. elevation pressure or temperature), at right angles to the isolines.

单词	gradient
释义	gradient Physics 1. The slope of a line. In Cartesian coordinates, a straight line y = mx+c, has a gradient m. For a curve, y=f(x), the gradient at a point is the derivative dy/dx at that point, i.e. the slope of the tangent to the curve at that point. 2. See gradient operator. Mathematics The vector obtained by applying the differential operator del, $\nabla = i \frac{\partial}{\partial x} + j \frac{\partial}{\partial y} + k \frac{\partial}{\partial z}$ , to a scalar function of position ϕ‎(r). This gives the gradient of ϕ‎ as grad $ϕ = \nabla ϕ = i \frac{\partial ϕ}{\partial x} + j \frac{\partial ϕ}{\partial y} + k \frac{\partial ϕ}{\partial z} .$ The gradient of ϕ‎ points in the direction in which ϕ‎ is increasing fastest. See also curl, divergence. Chemical Engineering The slope of a line on a graph. In Cartesian coordinates, the general equation of a straight line is y = mx + c where m is the gradient or slope and c is the intercept on the y-axis. The gradient at some point on a curve can be found from the derivative $d y / d x$ at that point. The gradient is therefore the tangent to the curve. Internet The gradual transition from one colour to another colour in a graphic image, usually a background colour. Geology and Earth Sciences The rate of change of a function (e.g. elevation pressure or temperature), at right angles to the isolines.
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