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  1. Copilot Answer

    Gradient - Wikipedia

    • The gradient, represented by the blue arrows, denotes the direction of greatest change of a scalar function. The values of the function are represented in greyscale and increase in value from white (low) to dark (high). See more

    Overview

    In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) whose value at a point gives the direction and the rate of fastest increase. The gradie… See more

    Motivation

    Consider a room where the temperature is given by a scalar field, T, so at each point (x, y, z) the temperature is T(x, y, z), independent of time. At each point in the room, the gradient of T at that point will show the di… See more

    Definition

    The gradient (or gradient vector field) of a scalar function f(x1, x2, x3, …, xn) is denoted ∇f or ∇→f where ∇ (nabla) denotes the vector differential operator, del. The notation grad f is also commonly used to represen… See more

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