Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007

[@gobbledee55]

Man....MIT student's are lucky to have such professors ...

[@circleoffriends5667]

They got in to MIT. We are lucky they taped it and let us view for free.

[@priyanshubansal6776]

@@circleoffriends5667 but we do not meet with the professors probably and gain more knowledge from him or with other legend professors in the world hope you would understand .

[@tamannashaw2857]

It's not luck... they studied hard to get in there. Takes a lot of determination and consistency to achieve that.

[@kritik3604]

​@@julioforessi1336And, of course, being raised with good nurture.

[@hashim710]

dam this, whenever i see an MIT lecture i admire how those students are so lucky!

[@HKHKKKHHHRHRRRHHforever]

you are lucky to watch it for free

[@johnlin7056]

who else sees double and triple integrals as nested for loops...

[@emenikeanigbogu9368]

This was a perfect way of describing it.

[@pabloarroyo1023]

Hadn’t thought of it that way but it’s a good way to explain it to someone with a bit of coding experience

[@aashsyed1277]

eyuck

[@josephtraverso2700]

This exactly!!! I’m glad to see someone else think of it that way

[@surplusvalue3271]

@@josephtraverso2700 same

[@alinapol]

Denis is the best teacher I have ever seen!

[@prashantdubey6057]

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.)

[@aashsyed1277]

not all heroes wear caps, thanks a buncher!

[@P_Petkov]

that is very satisfying sounding chalk

[@fmar105]

Wow. 2:17, the chalk on the board is very pleasing to the eye.

[@tocaamerillo431]

Despite knowing what he meant, all that talk about doing stuff "in space" made me chuckle not just once.

[@265HITMAN265]

The blackboard and the chalk makes me wanna become a lecturer.

[@AbuMaryamAN]

LOL at the 35min mark, class cheers him for his sick erasing skills!

[@rocco0031]

Eh bien. Si j'avait vu cela avant le 1er semestre... j'aurais eu mon semestre ! Il explique très bien, merci MIT.

[@maxim.aleksa]

35:01 show off!

[@nguyenthingoclam]

A good teacher - Understand easily :) I watched them when I was a student 2th

[@ny1fanta]

@aritrayou then you can use rectangular coordinates. cylindrical method is good when there is a circle (projection) on xy-plane

[@SumanthLazarus]

HAPPY BDAY!

[@the_eternal_student]

He always leaves the problem unfinished.

[@99ludester]

Awesome erasing skills at 35:00

[@Originalimoc]

This professor is also a interesting programmer🤓

[@middlevoids]

The action starts here 35:00

[@aritrayou]

To whoever is developing the courses online - Could u edit the video, right where Prof Auroux explains how to find the x and y limits for the triple integral int(dV)? I understood the z limits but I didn't understand the logic for the x and y limits. If he could add a snippet explaining the limits with a diagram of columns and slices like he did for the double integrals, it would be better. Thanks in advance and GREAT VIDEOS (though u must be tired of getting that sort of comment by now!)

[@joebrinson5040]

Thanks MIT.

[@not_amanullah]

Thanks ❤🤍

[@KOGR11]

which is why you were reviewing your calculas just a year ago.

[@joebrinson5040]

Thanks MIT

[@13Septem13]

@Anonymiusen This course is great. But there are also khanacademy calculus videos, they are great too.

[@quagmire444]

he has a point

[@namo7888]

fantastic!!!

[@aashsyed1277]

average value of a function f(x,y) in a region r is what?

[@aritrayou]

@pedroissler But what happens if the volume is defined by a bunch of intersecting planes? Same method?

[@Random-sm5gi]

24:37 shouldn’t the reason for being half be because we define theta strictly? I mean we would get the other half by 180 + theta.

[@yoadknux]

Of course I know how to use it, but I once didn't. Same goes for you. Which is why you shouldn't think people who don't know how to use this method are stupid.

[@topilinkala1594]

Ignorance is not stupidity. Stupidity is if you don't do anything to get rid of your ignorancy. So asking a question, when you are willing to learn, is never a stupid think to do. Asking a question so that you can contradict the answer you get is stupidity.

[@NxyDolli]

Much better than the shit-ass lecturer I had for this module. If only I had discovered this before my exams last year...thank god I still managed to scrape my 2:1 :D

[@GNR214]

what kind of book does the class use?

[@KOGR11]

If I knew why your messages keep coming in, I would try to make them coherent.

[@KOGR11]

I wish I knew or cared for the meaning of life for you.

[@Lordgenome76]

I love these vids... but why do they cheer whenever he erases the board?

[@cropsey.]

Agreed. The less coolest thing on this video is the sick erasing skill of the professor who has the steel balls

[@toastertastic]

Could that eraser be any more chalk-dusty?

[@DoctorQuestionMark]

@HD4WG This is Calc 2. Your argument is invalid.

[@69erthx1138]

@Anonymiusen I was going to wager Moroccan, but six of one and...but his English is clear, so I don't see the need for the subtext.

[@snehatangi6293]

€~Thankyou~$ Thanks a lot...

[@mayankrawat14]

im confused with top z and bottom z can someone help me with it/

[@spirontus]

+M Rawat top z is the concave paraboloid (z=4-x^2-y^2), bottom z is the convex paraboloid (other one), that's the region between those two paraboloids. top one must be greater than the bottom one (if we are in the region), hence the inequality

[@99ludester]

@cb2198 why wouldn't you cheer? (o.O) it's just a thing their students have been doing since 18.01, they get bored i guess...

[@humilitywewantit]

From about 20:00 onward the professor didn't explain clearly how he switched dx.dy to r.dr.d(theta). Could anybody help me? I mean, show me step by step. I'd get so thankful.[iminent=aqC6F9gUWfOB] Noble atitudes deserve recognising.

[@John10086]

Well, I may be 6 years late but in his previous lectures he got this result (dxdy=rdrdθ) by using the Jacobian(|J|), which is the determinant, |Xr Xθ, Yr Yθ| which gives you the relationship: drdθ*|J| = dxdy. and in the case of polar coordinates where x=rcosθ and y=rsinθ, |J| = r. So drdθ*r=dxdy

[@lorenzotrojan]

density in grams per cubic inches???? Weird! He was really in a rush towards the end though...

[@gauravsharma889]

Good

[@JDMaxton1999]

I get what he means, but shouldn't dy actually be chopping in horizontal segments?

[@KOGR11]

simple reason, people make mistakes. Use your own brain at times.

[@KOGR11]

Does it matter whether english is my first language or not? If it was would you feel proud or ashamed? or if its not would you feel disgusted? Just back trace your statements a bit, You are asking why a student is in MIT because you feel the student asked a trivial question.. did you forget that it was a student? and that mistakes are expected from students?.. from MIT or NOT? Or is your brain too slow to use that rational?

[@SathishKumar-qe4nq]

That dora cake tho..

[@Yu2Kal]

@jcgarces85 Denis Auroux

[@maxisjaisi400]

I like puppies too

[@audreydaleski1067]

These are not too difficult.

[@Staab0]

35:05 hahahah

[@sunslayer553]

nerd fight.

[@gena8414]

The students are really stupid. The professor is trying to teach how to setup the limit of the integrals but all the students want to do is to compute it. They keep on suggesting ways to "simplify" the computation missing the point that it is not in the least interest of the professor to actually carry out the integration.

[@HD4WG]

Georgia Tech > MIT Our lectures and Calc 3 class is way harder...

[@wewe-fx6un]

Share a video

[@hetaeramancer]

bro being hard is not flex xD

[@jdavis2921]

I HATE MATH