Inclination vs. Gradient

A physical tilt or bend.

Example: ‘The inclination of his head increased and he awoke with a start.’;

A slant or slope.

Example: ‘The road up to the house had a steep inclination.’;

A mental tendency.

Example: ‘His inclination to drink escalated to alcoholism.’;

(geometry) The angle of intersection of a reference plane

Example: ‘The astronomer calculated the inclination of the equator or ecliptic of Earth and the orbital planes of each visible heavenly body.’; ‘Artillery must take account of a weapon's precise inclination.’;

(obsolete) A person or thing loved or admired.

The act of inclining, or state of being inclined; a leaning; as, an inclination of the head.

A direction or tendency from the true vertical or horizontal direction; as, the inclination of a column, or of a road bed.

A tendency towards another body or point.

The angle made by two lines or planes; as, the inclination of the plane of the earth's equator to the plane of the ecliptic is about 23° 28´; the inclination of two rays of light.

A leaning or tendency of the mind, feelings, preferences, or will; propensity; a disposition more favorable to one thing than to another; favor; desire; love.

Example: ‘A mere inclination to a thing is not properly a willing of that thing.’; ‘How dost thou find the inclination of the people?’;

A person or thing loved or admired.

Decantation, or tipping for pouring.

an attitude of mind especially one that favors one alternative over others;

Example: ‘he had an inclination to give up too easily’; ‘a tendency to be too strict’;

(astronomy) the angle between the plane of the orbit and the plane of the ecliptic stated in degrees

(geometry) the angle formed by the x-axis and a given line (measured counterclockwise from the positive half of the x-axis)

(physics) the angle that a magnetic needle makes with the plane of the horizon

that toward which you are inclined to feel a liking;

Example: ‘her inclination is for classical music’;

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

Example: ‘the tower had a pronounced tilt’; ‘the ship developed a list to starboard’; ‘he walked with a heavy inclination to the right’;

a characteristic likelihood of or natural disposition toward a certain condition or character or effect;

Example: ‘the alkaline inclination of the local waters’; ‘fabric with a tendency to shrink’;

the act of inclining; bending forward;

Example: ‘an inclination of his head indicated his agreement’;

A slope or incline.

A rate of inclination or declination of a slope.

(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.

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

(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

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

Moving by steps; walking.

Example: ‘gradient automata’;

Rising or descending by regular degrees of inclination.

Example: ‘the gradient line of a railroad’;

Adapted for walking, as the feet of certain birds.

Moving by steps; walking; as, gradient automata.

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

Adapted for walking, as the feet of certain birds.

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

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

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

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

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

Example: ‘a five-degree 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 ) ] .