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Gradient vs. Incline — What's the Difference?

Gradient vs. Incline — What's the Difference?

Difference Between Gradient and Incline

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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 ) ] .

Incline

To cause (someone) to have a certain tendency
Dispose.

Gradient

A rate of inclination; a slope.

Incline

To dispose (someone) to have a certain preference or opinion or to take a course of action
I'm inclined to agree with you. Are you inclined to go to out tonight?.

Gradient

An ascending or descending part; an incline.
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Incline

To cause to lean, slant, or slope
"Galileo ... inclined the plane and rolled brass balls down it" (George Johnson).

Gradient

(Physics) The rate at which a physical quantity, such as temperature or pressure, changes in response to changes in a given variable, especially distance.

Incline

To bend or lower in a nod or bow
I inclined my head in acquiescence.

Gradient

(Mathematics) A vector having coordinate components that are the partial derivatives of a function with respect to its variables.

Incline

To be disposed to a certain preference, opinion, or course of action
Some researchers incline toward a different view of the problem.

Gradient

(Biology) A series of progressively increasing or decreasing differences in the growth rate, metabolism, or physiological activity of a cell, organ, or organism.

Incline

To deviate from the horizontal or vertical; slant
When the path inclined steeply, it became difficult to continue hiking.

Gradient

A slope or incline.

Incline

To lower or bend the head or body, as in a nod or bow.

Gradient

A rate of inclination or declination of a slope.

Incline

An inclined surface; a slope or gradient
The car rolled down the incline.

Gradient

The ratio of the rates of change of a dependent variable and an independent variable, the slope of a curve's tangent.

Incline

(transitive) To bend or move (something) out of a given plane or direction, often the horizontal or vertical.
He had to incline his body against the gusts to avoid being blown down in the storm.
The people following the coffin inclined their heads in grief.

Gradient

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

Incline

(intransitive) To slope.
Over the centuries the wind made the walls of the farmhouse incline.

Gradient

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

Incline

To tend to do or believe something, or move or be moved in a certain direction, away from a point of view, attitude, etc.
He inclines to believe anything he reads in the newspapers.
I'm inclined to give up smoking after hearing of the risks to my health.

Gradient

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

Incline

A slope.
To reach the building, we had to climb a steep incline.

Gradient

Moving by steps; walking.

Incline

A portal of a subway tunnel.

Gradient

Rising or descending by regular degrees of inclination.
The gradient line of a railroad

Incline

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.

Gradient

Adapted for walking, as the feet of certain birds.

Incline

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.
Their hearts inclined to follow Abimelech.
Power finds its balance, giddy motions ceaseIn both the scales, and each inclines to peace.

Gradient

Moving by steps; walking; as, gradient automata.

Incline

To bow; to incline the head.

Gradient

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

Incline

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.
Incline thine ear, O Lord, and hear.

Gradient

Adapted for walking, as the feet of certain birds.

Incline

To impart a tendency or propensity to, as to the will or affections; to turn; to dispose; to influence.
Incline my heart unto thy testimonies.
Incline our hearts to keep this law.

Gradient

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

Incline

To bend; to cause to stoop or bow; as, to incline the head or the body in acts of reverence or civility.
With due respect my body I inclined.

Gradient

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

Incline

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

Gradient

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

Incline

An elevated geological formation;
He climbed the steep slope
The house was built on the side of the mountain

Gradient

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.

Incline

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

Gradient

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

Incline

Have a tendency or disposition to do or be something; be inclined;
She tends to be nervous before her lectures
These dresses run small
He inclined to corpulence

Gradient

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

Incline

Bend or turn (one's ear) towards a speaker in order to listen well;
He inclined his ear to the wise old man

Incline

Lower or bend (the head or upper body), as in a nod or bow;
She inclined her head to the student

Incline

Be at an angle;
The terrain sloped down

Incline

Make receptive or willing towards an action or attitude or belief;
Their language inclines us to believe them

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