Calculus questions

[pray4mojo]

What exactly are directional derivatives and gradient vectors? I understand how to do the problems but I don't know how they're applicable.

 

[dowxp]

basically to take the gradient of a function is to find the "slope" of the function in a direction, or vector. note a gradient does not have to be position, for ex, in solid state physics, you can take the gradient of doping density to find the diffusion current. (i think).

 

[Peetoeng]

It's been too many moons since I read calculus. But, let me chip in.

A slope of a 2D curve is straight forward, right. But a slope of a 3D surface? At a given point on the surface, assuming the derivative exists, there are many possible slopes which lie on a plane. So, these slopes, directional derivatives, are then expressed in terms of the normal vectors of the said plane.

Please double check tho!