Differentiation of Vectors: What It Actually Means to DIfferentiate a Vector-Valued Function!

[snnwstt]

In 5:16 you hinted that you won't consider derivative of a function taking a vector as argument. But in 9:01 we are doing just that, isn't it?




Ok, the "function" in 9:01, the "limit", is almost like the identity function, but you probably know how Engineers like to tickle Mathematicians (for all the times Mathematicians tickle us) . :-)

[evankalis]

Such a cool little fact that allows for some quick back of the napkin work on predicting say velocity at a point in a video or somwthing like that. It is also nice for a position vector function that doesnt have a closed form seen in an analysis class.

[punditgi]

Love these videos! A real inspiration. ❤🎉😊

[aleksandarjankovski]

Elegant, indeed, both the idea and the explanation.

[DivineScaleOfGod]

Even though differentiation of functions having vectors as arguments is weird to think about you can still make an intuitive approach to it geometrically and see where the errors first occur.

[tanmaygupta]

I cannot wait to teach this to someone!!

[robharwood]

Hi Prof.! A few of your recent videos in this series, including this one, do not yet appear in your 'complete playlist'. Hopefully it's not too hard to add them to it.

[bjkhadka]

Is there a good way to understand continuity around a vector of a vector valued function? It's easy to see how limits work with scalar values with continuity of points in the x, y plane but hard to picture for resultant vectors from a change in t, "around" another vector. Also seems to beg the question how we would know if there is a uniform instantaneous change for a vector of a vector valued function as the distance between it and any other vector from an increase in t, approaches zero.

[davidhand]

f(u), the scalar-valued function of a vector, is exactly what a scalar field is. What's the problem with taking its derivative, i.e. gradient?

[KaiseruSoze]

Or you can define a derivative as [ f(x+1) - f( x-1 ) ]/[ (x+1) -- (x-1)] And no limit . the concept is the same but it's symmetric and uses the smallest number of the whole numbers. You don't need calculus.

[TekCroach]

Actually, what he is trying to say is the very obvious idea behind just about any differentiation. I don't see any specialty here.

[ivan]

Promised to explain, but didn't, asking to watch the next video. Click bait, dislike.