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if you show only the definition without walking through, I would rather read articles.

Good video! Just a minor thing: at 2:55, the movement of the point doesn't match given equations. It should be at the origin for t=-infty, go to the left side at infty as t goes to 0-, jump to the origin for t=0 and then flip to the right part at infty for t=0+, and back to 0 as t goes to +infty. It is therefore not continuous in 0. But we get the idea and it is easy to build the desired mapping from there. 😊

0:54 haha. Unfortunately.

Crazy that this series has so few views, great stuff

Positive curvature (dark matter, synergy) is dual to negative curvature (dark energy). Curvature is dual. Contravariant is dual to covariant -- vectors or functors -- dual basis. Attraction is dual to repulsion -- forces are dual! "Always two there are" -- Yoda.

HOLLY MOLLY! THANK YOU! THANK YOU! THANK YOU!

Can you give a hint how to solve the problem near the end of the lecture, I dont understand how I should use deltas

Just in time! I really needed that! Thanks!

You deserve more subscribers

Your explanation and together with the animations were superb! Thank you for helping me understand this.

AMAZING

The piano song was beautiful

Very helpful video

15:16 the sequence |r_n - s_n| goes to zero, not infinity!!!

you helped me get a 75% on my Differential Geometry Exam and a distinction in the course! Ty so much for this amazing playlist, hope it keeps continuing!!

18 views, glad I'm being recommended this video somehow, seems like I managed to build my youtube algorithm the way I want it to be 😆 nice video, a lot of efforts had to be put in, please continue !

Cool man thanks

Marvelous man...keep.up

7:06 <S(v), v>=<N,r''(0)> that shows the relations to Normal Curvature and 2nd fund.form. This helps!

Fantastic visualizations. Great work! Also great use of manim.

Really? I studied math and know differential geometry. Therefore I know what you are talking of. That is why I can say, that the whole video is merely a sum o quotations of some text book. Watching is worthless.

I wish you would drop the background music. It is both distracting and annoying. Otherwise, your animations are beautiful. Great job.

Thank you. Well done.

Blessed be the algorithm for recommending me this video. Best believe the Diff Geometry Playlist is going in my watch-later list. I'm still an undergraduate, but hopefully in a year or two I could use it as sumplementary material.

These videos are really well made, I hope you make more of them. The explanations are very clear and the visual examples are great

00:03 Smooth functions on surfaces can be defined using charts and composition 01:08 Introduction to tangent planes 02:10 The tangent plane to Sigma at P is obtained by considering the set of older velocity vectors at Time Zero. 03:13 The tangent plane to segment p is contained in the set of velocity vectors of curves passing through b. 04:12 Derivatives of smooth functions for a smooth function f 05:18 The quantity on the left is independent of gamma and depends linearly on the coefficients of w. 06:21 Jacobian is defined as the length of the cross product of partial derivatives 07:20 Differential geometry uses parametrization to integrate over regions in R2.

High quality

At 11:23, in the last line of the Theorem, it should be gamma_{u,v,a,b} instead of phi_{u,v,a,b}. The geodesic curvature should be denoted by k_g, not k_{\gamma}.

amazing series but where are the views? damn algorithm...

Really good tutorial. Thanks for making this.

I don't understand this at all 😎

first comment

This is so well explained!

This is easily the best video I've seen on this topic. Great explanations and the visuals help so much. Great video!

Really well made. Concise and clear explanations.

Like

Love this, especially the stuff about modeling a surface by parallels and meridians

excellent video!

keep on going ! 💯🥳

Hi, I just started using Manim and I was wondering if you could share a piece of code that you used to move the tangent vector T along the curve?

This channel is super underrated, keep it up!

I understood 28.75640274627467015562091% of what you said but I still enjoyed it

I really appreciate you thanks 🌹

you are seriously underrated

Enjoyed this - thank you for making it.

I hope you post a complete course on differential geometry

Good work dude keep going..