Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007

[@SteveMacAwesome]

These videos have totally increased my understanding of vector calculus - I'm no longer just doing the trick but I'm actually manipulating the maths. Thanks MIT.

[@alexhudson502]

Lecture 1: Dot Product Lecture 2: Determinants Lecture 3: Matrices Lecture 4: Square Systems Lecture 5: Parametric Equations Lecture 6: Kepler's Second Law Lecture 7: Exam Review (goes over practice exam 1a at 24 min 40 seconds) Lecture 8: Partial Derivatives Lecture 9: Max-Min and Least Squares Lecture 10: Second Derivative Test Lecture 11: Chain Rule Lecture 12: Gradient Lecture 13: Lagrange Multipliers Lecture 14: Non-Independent Variables Lecture 15: Partial Differential Equations Lecture 16: Double Integrals Lecture 17: Polar Coordinates Lecture 18: Change of Variables Lecture 19: Vector Fields Lecture 20: Path Independence Lecture 21: Gradient Fields Lecture 22: Green's Theorem Lecture 23: Flux Lecture 24: Simply Connected Regions Lecture 25: Triple Integrals Lecture 26: Spherical Coordinates Lecture 27: Vector Fields in 3D Lecture 28: Divergence Theorem Lecture 29: Divergence Theorem (cont.) Lecture 30: Line Integrals Lecture 31: Stokes' Theorem Lecture 32: Stokes' Theorem (cont.) Lecture 33: Maxwell's Equations Lecture 34: Final Review Lecture 35: Final Review (cont.)

[@onlyonetwin]

the guy who filmed these videos must by now be the best engineer of all times...

[@paris_mars]

The camera work on these lectures is great.

[@DouglasNyback]

It does - there is a generalized Stoke's theorem of which the Divergence Theorem, Green's Theorem, Stoke's theorem as it appears here, and the Fundamental Theorem of Calculus are all special cases. This generalized theorem works in any dimension!

[@KyleBroder]

I have a math degree and I still enjoy these lectures. Auroux is a great lecturer.

[@beastlt12]

Great video. I kept wanted to walk away instead of spending 50 minutes on YT, but each new topic was very relevant. Ended up watching the whole damn thing. Thanks p.s. I agree. That chalk is pretty sweet.

[@mariapuerto5427]

thank you!!!!! so in love with this class :)

[@mcmackerel]

I love these lectures. He makes it so easy.

[@yang22kaka]

Seemed sooo difficult in class today......now i understand why they are so good at MIT. Such a great teacher....Make it look easy.

[@agingerrail123]

This is unfair to your teacher because on any material that you have previously previewed, you would understand it much more quickly. So your teacher acted as a first learning of the material, and this video acted as a second viewing of the material. That is why you feel like it is so much easier to understand.

[@cheungtyrone3615]

However, I watched these videos first and then attend the lectures in my own university only to find that professors at MIT indeed conveys knowledge in a much more easy-to-understand way. I'm not saying that my own professor is inferior to any other professor in academic field; what I want to claim is that my professor frequently and unintentionally complexify the knowledge and in turns scares the students "away" and I think is the point is that lecturers should be reminded that using geometric interpretation or other intuitive approach doesn't contradict with rigorous mathematics.

[@abbasjheir7450]

thank you al lot prof. Denis Auroux... you are a great lecturer

[@TheFaceOfJohnPants]

48:14 that guy totally knew he was blocking the camera

[@karrotman]

Man I wish my college had those blackboards. Nah, I kid - MIT rocks! I wish I had this professor!

[@banana144]

The ideas for the proof of the Stoke theorem make me remember the way Maxwell argued about the existence of micro currents in a magnetic shell (a kind of imaginary surface) which cancel each other so that they're equal as a single current circumventing the magnet, and thats why you can recreate a magnet with just a single electric current in a loop... then i realized that the Stokes theorem is used in Maxwell equations... wow hehe

[@hangjiang858]

38:08 very impressive proof

[@crazypunisher4066]

what other lectures does this amazing lecturer have?

[@Andyman3k]

EPIC AUTO-BLACKBOARD @ 2:35 And that chalk sounds really soft, the stuff my teacher uses is all hard and you can hear the scratching ;_; Oh and thanks, this is really helpful for my final next week :P

[@gam3fr33k]

Guaranteed everybody watching this has a final tomorrow

[@rosadovelascojosuedavid1894]

No, I don't

[@universalentertainment5028]

dude i am in 9th class learning this for fun

[@AruEsse]

19:40 if you turn the volume down everything he says changes its meaning

[@AnandVL]

Quality teaching!

[@akibmustahid6467]

Top teacher.💯💯 Usually scholars don't teach that well.😅😅😅

[@shakesbeer00]

Thanks.That's gonna be interesting. I was wondering how the concepts such as curl(F) can be extended to high-dimensional scenarios and also whether all the geometrical interpretations remain.

[@hobeypollack]

Do you think he purposefully stopped erasing boards while they were coming down simultaneously so that the students wouldn't cheer? Because throughout the lecture series it seemed to progressively happen less and less which makes me sad.

[@iyanev]

Actually as you seen in the lecture curl is defined as the cross product between the del operator and the vector field.The problem here is that the cross product is defined only in 3D(and 7D ),so I am also wondering how curl generalizes to higher dimension other than 7D

[@00TheVman]

I didn't know it had some special meaning in 7D, but there is a way to cross product n-1 vectors in n-dimensional space. And this may align with the generalized Stokes' Theorem in n-dimensions

[@LouisEmery]

He writes nicely.

[@devanshgarg31]

20:55 Does that.......make sense? hehe

[@TDarkshine]

@HikariOfTheAzureSky Google says France, yes.

[@not_amanullah]

This is helpful ❤️🤍

[@shakesbeer00]

I wonder if Stoke's theorem generalizes well to even higher, say, n, dimensional space.

[@00TheVman]

It does actually, there's a generalized Stokes' Theorem for an n-dimensional surface and (n-1)-dimensional boundary. The thing is, it uses more complicated terms but it aligns with Stokes' on 3D space (and even the Fundamental theorem of calculus in 1D!)

[@hb712]

@@00TheVman the way it was described to me was Stoke’s theorem generalized is “The change of something on the outside is the same as the sum of the change of everything inside” or essentially if you find the change in a boundary it’s the same as the sum of all exterior derivatives, which gives nice formulas in lower dimensions like the Fundamental Thrm of calculus, Stokes, and Divergence

[@audreydaleski1067]

We used m,n, and p.

[@wickedm348]

Genius. Fantastic.

[@paulmoore7964]

question, why does curl come out twice the rotational speed

[@santiagoarce5672]

Theres a problem on the website about this: look ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/3.-double-integrals-and-line-integrals-in-the-plane/part-b-vector-fields-and-line-integrals/session-64-curl/MIT18_02SC_pb_64_comb.pdf

[@not_amanullah]

Thanks ❤️🤍

[@robertoconconi]

I can assure that, he has that frenchy accent specially when saying zero

[@audreydaleski1067]

As viewed from above

[@dokumentaritube]

what is the text book for this course

[@ahmadeldesokey9844]

He is very interesting

[@coreyoakes1792]

yes

[@nateshih]

@fprecoiil math is easy if you have a good professor

[@mohamedatef2383]

kzbin.info/www/bejne/qqvSipubaK1omq8 "Except that at that time we called things M&Ns"

[@shawnnyhus2193]

*pulls into the garage

[@audreydaleski1067]

Cross product is easy.

[@HikariOfTheAzureSky]

is he french?

[@jacobbellavance8545]

Yes, definitely

[@audreydaleski1067]

Cilindet

[@yangyxia]

....a huge lecture hall..but the instructor has to use chalkboard to write notes!!!

[@devanshgarg31]

Is it just me who hears poof everytime he says proof

[@nateshih]

@Brotrr and a sweet ass chalkboard

[@KyleBroder]

I have a math degree and I still enjoy these lectures. Auroux is a great lecturer.