Gradient and contour maps

Cool!

Super insightful! Thank you, Mr. Grant!

very nice, thank you

I think he is 3b1b 😁😁

thanks bro, helped a lot

Gradient is always perpendicular to contour line ,if I move in direction tengential to contour then f(x,y) will remain same .

tyyyyyyyyyyyyyyyyyyyyyy

I am Granted with profound mathematical knowledge

Anybody has the link of video about contour map?

I don't know if it's just because I was first taught this in college without any visualization, but I'm really struggling to find value/intuition with these graphs. Are they useful? Would it be bad to entirely ignore all graphs?

The gradient is the same as the jacobian right?

I don't understand why the red vectors in the center of the contour maps longer?

I don't know if you really have a grasp of the unbelievable service you are providing for all those working in mathematics correlated field, such as engineers as myself, but that don't really deal with a given math topic in a daily basis and, once in a while, need to deal with a research or job problem that demands refreshing a given subject. I don't even want to think how much time it would take for me to go through a classical text book (first I would need to find a good one on the topic) and get all these reviews, intuitions and even new concepts by myself. I will definitely look for patreon or any other funding way to support you guys. Thank you, so much.

Basically the same heuristic but flipped around: in order to minimize the change in the output, we should move in the direction of our current contour line (its tangent). So in order to maximize the change in the output, we should move perpendicular to the contour line, as any other direction will have a component in the direction of the contour line. We get the most bang for our buck by moving perpendicular to the contour line.

I can't believe how clear your explanations are. Thank you!

Amazingly intuitive. Thank you to the presenter for being a fantastic educator!

why contour lines should always be parallel.

wow top

It reminds me of orthogonality of Electric fields with the equipotentials

I did dofe, of course I know about contour lines.

Hey, aren't the red vectors the shorter ones and the blue vectors the longer ones? For this function, the gradient gets larger in magnitude as you move away from the origin of the input space.

Thank you all so much!

Genius. Thanks for your existence.

we got 5 years
and thats all we got

Wait, since the graph has contour lines. What happens if you rescale everything upwards and make the shape 3d?
How will the final shape look like? :O

Amaziiiiiiiiing

please make more videos on how to draw contour maps!

Perfect example!
That made the whole mathematical explanation into a very good visual concept. Thank you so much!

The guy has a cool pointer, doesn't he?

Seventh! Thumbs up!

Lol I thought this was a video on contouring, makeup wise... Lol I'm dumb

Wait...I know that voice...is that 3Blue1Brown? I didn't expect to see you in a Khan Academy video!

Sixth

Third

second

First