Gradient vs. Incline

Gradientnoun

A slope or incline.

Gradientnoun

A rate of inclination or declination of a slope.

Gradientnoun

(calculus) 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 equivalently, the inclination to the X axis of the tangent to the curve of the graph.

Gradientnoun

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

Gradientnoun

(analysis) A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇φ

Gradientnoun

A gradual change in color. A color gradient; gradation.

Gradientadjective

Moving by steps; walking.

Gradientadjective

Rising or descending by regular degrees of inclination.

Gradientadjective

Adapted for walking, as the feet of certain birds.

Gradientadjective

Moving by steps; walking; as, gradient automata.

Gradientadjective

Rising or descending by regular degrees of inclination; as, the gradient line of a railroad.

Gradientadjective

Adapted for walking, as the feet of certain birds.

Gradientnoun

The rate of regular or graded ascent or descent in a road; grade.

Gradientnoun

A part of a road which slopes upward or downward; a portion of a way not level; a grade.

Gradientnoun

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

Gradientnoun

The variation of the concentration of a chemical substance in solution through some linear path; also called concentration gradient; - usually measured in concentration units per unit distance. Concentration gradients are created naturally, e.g. by the diffusion of a substance from a point of high concentration toward regions of lower concentration within a body of liquid; in laboratory techniques they may be made artificially.

Gradientnoun

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

Gradientnoun

the property possessed by a line or surface that departs from the horizontal;

Gradient

In vector calculus, the gradient of a scalar-valued differentiable function f of several variables is the vector field (or vector-valued function) ∇ f {\displaystyle \nabla f} whose value at a point p {\displaystyle p} is the vector whose components are the partial derivatives of f {\displaystyle f} at p {\displaystyle p} . That is, for f : R n → R {\displaystyle f\colon \mathbb {R} ^{n}\to \mathbb {R} } , its gradient ∇ f : R n → R n {\displaystyle \nabla f\colon \mathbb {R} ^{n}\to \mathbb {R} ^{n}} is defined at the point p = ( x 1 , … , x n ) {\displaystyle p=(x_{1},\ldots ,x_{n})} in n-dimensional space as the vector: ∇ f ( p ) = [ ∂ f ∂ x 1 ( p ) ⋮ ∂ f ∂ x n ( p ) ] .

Inclineverb

(transitive) To bend or move (something) out of a given plane or direction, often the horizontal or vertical.

Inclineverb

(intransitive) To slope.

Inclineverb

To tend to do or believe something, or move or be moved in a certain direction, away from a point of view, attitude, etc.

Inclinenoun

A slope.

Inclineverb

To deviate from a line, direction, or course, toward an object; to lean; to tend; as, converging lines incline toward each other; a road inclines to the north or south.

Inclineverb

Fig.: To lean or tend, in an intellectual or moral sense; to favor an opinion, a course of conduct, or a person; to have a propensity or inclination; to be disposed.

Inclineverb

To bow; to incline the head.

Inclineverb

To cause to deviate from a line, position, or direction; to give a leaning, bend, or slope to; as, incline the column or post to the east; incline your head to the right.

Inclineverb

To impart a tendency or propensity to, as to the will or affections; to turn; to dispose; to influence.

Inclineverb

To bend; to cause to stoop or bow; as, to incline the head or the body in acts of reverence or civility.

Inclinenoun

An inclined plane; an ascent or descent; a grade or gradient; a slope.

Inclinenoun

an elevated geological formation;

Inclinenoun

an inclined surface or roadway that moves traffic from one level to another

Inclineverb

have a tendency or disposition to do or be something; be inclined;

Inclineverb

bend or turn (one's ear) towards a speaker in order to listen well;

Inclineverb

lower or bend (the head or upper body), as in a nod or bow;

Inclineverb

be at an angle;

Inclineverb

make receptive or willing towards an action or attitude or belief;