Math 392 Lecture 16 - Stokes' theorem and the beginning of Divergence theorem

Welcome to lecture 16 of Vector Calculus and Linear Algebra!

In this lecture, we cover Stokes' theorem, section 13.8 in Stewart's Essential Calculus, ed 1. We state the theorem and then go through some definitions--including ones that illustrate how in applying Stokes' theorem, we can somehow choose the surface that we want to use. We then move on to introduce section 13.9, the Divergence theorem, we state the theorem and do one example. We will pick up where we left off and finish the Divergence theorem in the next lecture.

[susam]

When someone tries to correct him I'm just like "You feeble-minded creature how dare you question the power of Jhevon?!?!!" 1:06:15 lolll

[PoohBear]

Your the best professor, clear & well explained examples many thanks for  your opencourseware material

[Jhev]

Indeed it was. Her question shows insight.

[vlwlv]

Thank you so much for these lecture videos. My prof. uses ppt for lecture, and I couldn't understand the concept through ppt, so I had to study calculus on my own. So I read the book and do the exercises. I was able to taught myself at the beginning. I was able to keep my grade at high B to low A range. but when we got to vector calculus, I just couldn't do it myself. My grade drops to C b4 the final. I was at the risk of failing the class, because my prof. told us that the final is gonna focus on the vector calculus. I was thinking giving up, not taking the final and just retake the class. But then the Cavalier came back from 1 to 3, and won the NBA final inspired me. Anything is possible. So I decided to give it a try, and take the final. One week b4 the final, I found out your lecture videos on vector calculus. I watched it day and night, taking the notes, again and again. I took the final, I did really well. And luckily, the final score can replace one of the midterm score(the one I failed on the vector calculus). And I got an A for the class in the end. THANK YOU SO MUCH!!! without your videos, I would have fail the class. thank you thank you thank you for recording and uploading these videos. your lecture are so amazing that I watched an hour long video twice, I never imagine I would ever do that even with the movie. now that I'm taking the linear algebra class, I am watching your videos for that too. :P

[manuelsanchez]

I don't know how you put up with that kid all semester -_-

[UnforsakenXII]

I noticed that I started writing my z's the same way you do. Whelp. At least I can no longer confuse with them with twos.

[Surendrarana-fnpe]

Sir plz explain me, that in cone example of Stoke's theorem, how u take curl in second surface . And thank u in advance.

[christiancenturion]

the trick of using a simpler surface to find the vector dS. does that only work for stokes theorem, or could i also apply it when evaluating a surface integral int ( F*dS) ??

[TheOriginal]

What did you mean during the last example with divg. thm around 1:00:00 when you said this is a Type 1. I understand that it is probably a reference to a Calc 3 topic/method, but any elaboration would be greatly appreciated.

[brianzar]

Can I please ask if in 29:59, could you set the integral based on dx dy, instead of polar coordinates, by setting z=0 just like the previous example?
And thanks, you're the man!

[shamirik_]

How about stokes theorem for cirynder and sphere help please sir!!

[kelvinzheng]

at 27:18 you messed up the double angle formula. cos2t is positive