For this equation, does vector u have to be an unit vector? I checked some online resources and all of them convert u into an unit vector when calculating.
keenan
does vector u have to be an unit vector?
NO! :-)
Absolutely not. The directional derivative makes perfect sense for any vector, independent of its magnitude. There may indeed be cases where you care only about the derivative with respect to a unit vector. But there are very clear-cut important examples where you actually want the derivative with respect to a non-unit vector (or vector field). For instance, in fluid mechanics you often want to know how fast a quantity is changing with respect to the fluid velocity, which is not unit.
I would be very careful of anything you read online, including our own course website. The absolute best resource for determining whether something is right or wrong is your own brain and rational thought process.
For this equation, does vector u have to be an unit vector? I checked some online resources and all of them convert u into an unit vector when calculating.
NO! :-)
Absolutely not. The directional derivative makes perfect sense for any vector, independent of its magnitude. There may indeed be cases where you care only about the derivative with respect to a unit vector. But there are very clear-cut important examples where you actually want the derivative with respect to a non-unit vector (or vector field). For instance, in fluid mechanics you often want to know how fast a quantity is changing with respect to the fluid velocity, which is not unit.
I would be very careful of anything you read online, including our own course website. The absolute best resource for determining whether something is right or wrong is your own brain and rational thought process.