I found this video is really helpful for my studying about calculus 2 in uni. Could you share that geogebra animation, I really want to learn more about animating in geogebra! After all, thank you so much for your work!

@DrMcCrady

2 ай бұрын

Glad it was helpful! Sure here’s the Geogebra link. www.geogebra.org/m/e7vztr4d

If the directional derivative is the scalar product with a turning unitary vector, it's mean that 2 points which have the same gradient on 2 different curve will have necessarly the same directional derivative in each direction at that given point ? Probably because the 2 different curve are the same LOCALLY ? -- altough intuitively I would think it could be different and depend on the law of evolution of it's own curve.

@DrMcCrady

Ай бұрын

Yes looks like you’re on the right track. If gradient f at (a,b) has the same value as gradient g at (c,d), then locally f and g look the same, and if u is any unit vector, then the directional derivative for f at (a, b) in the direction of u will match the directional derivative for g at (c,d) in the direction of u. This is because the directional derivative is just the scalar product of the gradient with u.

thanks man

How did you do the animation?

@DrMcCrady

Жыл бұрын

I used Geogebra. It’s crazy how much it can do for free.

thank you!!!!!

@DrMcCrady

3 ай бұрын

Glad it was helpful!

spend 2 hours trying to figure out why gradient is perpendicular to slope

@DrMcCrady

9 ай бұрын

Not bad, sucks when you’ve got other stuff to do, but putting that time in will pay off. Glad to hear the video was helpful!

@user-er5hj1jw7b

Ай бұрын

Is the gradient vector really perpendicular to slope ? He is in the plane X-Y and his magnitude is the slope of the surface curve at the given point ? if we take this magnitude for the component in Z, we have a vector perpendicular, let's say rather normal, to the surface curve ?