What are gradients?

Answer 1

Gradient is commonly used to describe the measure of the slope (also called steepness, fall or incline) of a straight line. In the UK it is the usual term for the inclination of a surface along a given direction, which is usually called the grade in the U.S.A. Given a surface, the grade (inclination) of the surface in a particular direction given a unit vector is the dot product of the vector gradient with that vector.

A generalization of these concepts is the gradient in vector calculus; and this article will be mostly about this vector gradient. The gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change.
A generalization of the gradient, for functions which have vectorial values, is the Jacobian.

Answer 2

Gradient is commonly used to describe the measure of the slope (also called steepness, fall or incline) of a straight line. In the UK it is the usual term for the inclination of a surface along a given direction, which is usually called the grade in the U.S.A. Given a surface, the grade (inclination) of the surface in a particular direction given a unit vector is the dot product of the vector gradient with that vector.

A generalization of these concepts is the gradient in vector calculus; and this article will be mostly about this vector gradient. The gradient of a scalar field is a vector field which points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change.
A generalization of the gradient, for functions which have vectorial values, is the Jacobian.

Answer 3

gradient
One entry found for gradient.


Main Entry: gra·di·ent
Pronunciation: 'grA-dE-&nt
Function: noun
Etymology: Latin gradient-, gradiens, present participle of gradi
1 a : the rate of regular or graded ascent or descent : INCLINATION b : a part sloping upward or downward
2 : change in the value of a quantity (as temperature, pressure, or concentration) with change in a given variable and especially per unit distance in a specified direction
3 : the vector sum of the partial derivatives with respect to the three coordinate variables x, y, and z of a scalar quantity whose value varies from point to point
4 : a graded difference in physiological activity along an axis (as of the body or an embryonic field)
5 : change in response with distance from the stimulus

Answer 4

To keep the answer simple, if you're are talking about a graphics program, a gradient is one of the tools you can use to shade with a color, thus giving the object a three dimensional feel.

Answer 5

the degree of inclination, or the rate of ascent or descent, in a highway, road, river, etc and The degree of inclination of a riverbed, usually described as the number of feet the river drops per mile.

Answer 6

Algebrical operation which means the partial derivee in each of the three directions.

Answer 7

grad V = dv/dx ax+ dv/dy ay + dv/dz az