In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field
where … See more

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

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

The gradient is closely related to the total derivative (total differential) : they are transpose (dual) to each other. Using the convention that vectors in are represented by column vectors, and that covectors (linear maps ) … See more

A level surface, or isosurface, is the set of all points where some function has a given value.
If f is differentiable, then the dot product (∇f )x ⋅ v of the gradient at a point x with a vector v giv… See more