Vector Field

Every general vector field can be defined through component functions such that: $F(x,y,z)=M(x,y,z)i+N(x,y,z)j+P(x,y,z)k$

Gradient Field

The gradient vector of a differentiable scalar-valued function at a point gives the direction of greatest increase of the function.

$$\nabla f=\frac{\partial f}{\partial x}i+\frac{\partial f}{\partial y}j+\frac{\partial f}{\partial z}k$$

Related

• Conservative Vector Fields