Slope vs. Gradient

Slopenoun

An area of ground that tends evenly upward or downward.

Slopenoun

The degree to which a surface tends upward or downward.

Slopenoun

(mathematics) The ratio of the vertical and horizontal distances between two points on a line; zero if the line is horizontal, undefined if it is vertical.

Slopenoun

(mathematics) The slope of the line tangent to a curve at a given point.

Slopenoun

The angle a roof surface makes with the horizontal, expressed as a ratio of the units of vertical rise to the units of horizontal length (sometimes referred to as run).

Slopenoun

A person of Chinese or other East Asian descent.

Slopeverb

(intransitive) To tend steadily upward or downward.

Slopeverb

(transitive) To form with a slope; to give an oblique or slanting direction to; to incline or slant.

Slopeverb

To try to move surreptitiously.

Slopeverb

(military) To hold a rifle at a slope with forearm perpendicular to the body in front holding the butt, the rifle resting on the shoulder.

Slopeadjective

(obsolete) Sloping.

Slopeadverb

(obsolete) slopingly

Slopenoun

An oblique direction; a line or direction including from a horizontal line or direction; also, sometimes, an inclination, as of one line or surface to another.

Slopenoun

Any ground whose surface forms an angle with the plane of the horizon.

Slopenoun

The part of a continent descending toward, and draining to, a particular ocean; as, the Pacific slope.

Slopeadjective

Sloping.

Slopeadverb

In a sloping manner.

Slopeverb

To form with a slope; to give an oblique or slanting direction to; to direct obliquely; to incline; to slant; as, to slope the ground in a garden; to slope a piece of cloth in cutting a garment.

Slopeverb

To take an oblique direction; to be at an angle with the plane of the horizon; to incline; as, the ground slopes.

Slopeverb

To depart; to disappear suddenly.

Slopenoun

an elevated geological formation;

Slopenoun

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

Slopeverb

be at an angle;

Slopenoun

a surface of which one end or side is at a higher level than another; a rising or falling surface

Slopenoun

a difference in level or sideways position between the two ends or sides of a thing

Slopenoun

a part of the side of a hill or mountain, especially as a place for skiing

Slopenoun

the gradient of a graph at any point.

Slopenoun

the mutual conductance of a valve, numerically equal to the gradient of one of the characteristic curves of the valve.

Slopenoun

a person from East Asia, especially Vietnam.

Slopeverb

(of a surface or line) be inclined from a horizontal or vertical line; slant up or down

Slopeverb

place or arrange in a sloping position

Slopeverb

move in an idle or aimless manner

Slopeverb

leave unobtrusively, typically in order to evade work or duty

Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. Slope is often denoted by the letter m; there is no clear answer to the question why the letter m is used for slope, but its earliest use in English appears in O'Brien (1844) who wrote the equation of a straight line as and it can also be found in Todhunter (1888) who wrote it as .Slope is calculated by finding the ratio of the to the between (any) two distinct points on a line.

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 ) ] .