Calculus 3 Lecture 12.3/12.5: TNB (Frenet-Serret) Frames, Curvature, Torsion, Encapsulation

Calculus 3 Lecture 12.3/12.5: TNB (Frenet-Serret) Frames, Curvature, and Torsion: Focus on how to compute the TNB Frames as simply as possible and use the results to find the Curvature, Osculating circle, osculating plane, normal plane, and radius of curvature. Formulas are also given including how to perform vector encapsulation for 2-D functions.

[eunuchcommunity]

0:00:00 Curvature
0:21:28 Torsion
0:26:00 Osculating Circle
0:43:00 Example 1
0:56:50 Singing
1:42:22 Example 2
1:56:32 Example 3
2:28:52 Example 4

[diddyxgi]

Professor my fiancé and I really love you! we even named our foster puppy Leonard because of you. Instead of watching netflix at night we watch your videos together(we are classmates). He also says that he loves that you are super muscular and his dream is to train at the gym with you lol. Anyways, I just wanted to thank for all the effort you put to really clarify complicated things to your students and people who watch your videos. We are very thankful to have access to it. You just make it so easy to understand and you really can see where the students can possibly make mistakes and you point it to us even before we notice it. That is talent! I wish my teacher have half of the talent you have. Wish there was a way to do something nice in return. the least we can do is to let you know how awesome you are! God bless you and your family! Thank you so much!!!!

[thebigVLOG]

Some people are Christian, some are Muslim and others are Jewish. Me personally, I'm a Leonardian.

[theproofessayist]

This is the most impactful description I've seen of TNB curvature ever. I remember covering this in Calc 3 section of James Stewart. All I really understood were how the derivations worked and definition of unit tangent, normal, and binormal, but you sir Professor Leonard gave best informal explanation on why we need them. To understand curvilinear motion in moving reference frames and how the arc-length can serve as a parameter that simplifies the calculations immensely. Its always good to see the big picture, cheers.

[lorenzoalloni]

I'm now at my last year of university in Italy and you're actually one of best professor I've ever had. Thanks professor Leonard.

[locolamondanga]

at around minute 15, you forgot to put the magnitude for the derivative of T in the curvature function.

[WithASideOfFries]

I'm praying that you're teaching linear algebra next semester.

[Uncertaintycat]

best part: The Leonard bursting into song at 57:00. no seriously, the technique and explanation throughout not only made me understand on both an intuitive and mathematical level, but saved me from mistake opportunities throughout the calculation. Thanks once again, Mr. The Leonard.

[NguyenDuong-pjqd]

I know this is late, but isn't at 15:00, ||dT/dt|| = ||T'(t)|| instead of just T'(t).
Also, thank for so much for these video lectures!

[kevinhc]

Watching this as a review and I have to say, I've never had a professor even half as good as you. That being said I've had some great professors. Amazing work Leonard!

[wfat]

Ok, Prof. Leonard, you're my professor this summer, since my remote class is not going as well as I hoped. Thank you!

[kennykaijage]

You helped me get a B in calc 2. I wish I found this for calc 1 as I would've done better but now I am ready for the next level. Thank you sir.

[mydsmart]

8 years and this lecture is still relevant, wow

[JesusLopez-yuff]

Professor Leonard, I just want you to know that not only you have help me understand math and the theory at a deeper level, but also have fun during the process. thank you for your wealth of knowledge!!

[mamaslostsoul]

Great Teacher. at 22:30, wish he had mentioned that Torsion is merely existence of change in Bi-Normal, just like Curvature exists with change in Normal. The vector perpendicular to a plane of paper (biNormal), when it starts changing its perpendicularity, Torsion creeps in.

[nandofregoso]

I missed lecture this day at my college. Thank you so much for this!

[fawazalkhelaiwi]

56:52 Come on professor, you know it is against the law to drink and derive. (:

[georgesadler]

Professor Leonard, thank you for another mammoth and lengthy video/lecture on TNB Frames, Curvatures, Torsion and Encapsulation in Multivariable Calculus. From watching the lecture and doing problems, I understand the material from start to finish.This material is useful in Statics, Dynamics, Physics and Applied Mathematics.

[osmanharundundar]

Hocam(Sir) whenever i need sth related with calculus you are the one help me a lot .Thax for everthing

[OVERORLY]

so glad you are doing calc 3 just intime for my summer course