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Calculus questions

pray4mojo

pray4mojo

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