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

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  • Опубліковано 18 гру 2024

КОМЕНТАРІ • 78

  • @gobbledee55
    @gobbledee55 12 років тому +83

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

    • @circleoffriends5667
      @circleoffriends5667 5 років тому +33

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

    • @priyanshubansal6776
      @priyanshubansal6776 3 роки тому +4

      @@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
      @tamannashaw2857 10 місяців тому +1

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

    • @kritik3604
      @kritik3604 7 місяців тому

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

  • @prashantdubey6057
    @prashantdubey6057 3 роки тому +15

    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
      @aashsyed1277 3 роки тому +1

      not all heroes wear caps, thanks a buncher!

  • @hashim710
    @hashim710 12 років тому +23

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

  • @johnlin7056
    @johnlin7056 7 років тому +131

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

    • @emenikeanigbogu9368
      @emenikeanigbogu9368 4 роки тому +4

      This was a perfect way of describing it.

    • @pabloarroyo1023
      @pabloarroyo1023 3 роки тому +2

      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
      @aashsyed1277 3 роки тому +1

      eyuck

    • @josephtraverso2700
      @josephtraverso2700 2 роки тому +1

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

    • @surplusvalue3271
      @surplusvalue3271 Рік тому +1

      @@josephtraverso2700 same

  • @alinapol
    @alinapol 11 років тому +5

    Denis is the best teacher I have ever seen!

  • @P_Petkov
    @P_Petkov 9 років тому +36

    that is very satisfying sounding chalk

  • @fmar105
    @fmar105 9 років тому +2

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

  • @AbuMaryamAN
    @AbuMaryamAN 10 років тому +39

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

  • @tocaamerillo431
    @tocaamerillo431 11 років тому +7

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

  • @ny1fanta
    @ny1fanta 13 років тому +1

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

  • @rocco0031
    @rocco0031 14 років тому +8

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

  • @maxim.aleksa
    @maxim.aleksa 12 років тому +17

    35:01 show off!

  • @nguyenthingoclam
    @nguyenthingoclam 10 років тому +7

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

  • @265HITMAN265
    @265HITMAN265 13 років тому +5

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

  • @aritrayou
    @aritrayou 13 років тому +6

    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!)

  • @SumanthLazarus
    @SumanthLazarus 10 років тому +3

    HAPPY BDAY!

  • @Originalimoc
    @Originalimoc 6 років тому +4

    This professor is also a interesting programmer🤓

  • @99ludester
    @99ludester 14 років тому +4

    Awesome erasing skills at 35:00

  • @13Septem13
    @13Septem13 14 років тому +2

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

  • @middlevoids
    @middlevoids 6 місяців тому

    The action starts here 35:00

  • @Random-sm5gi
    @Random-sm5gi 3 роки тому +2

    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.

  • @aashsyed1277
    @aashsyed1277 3 роки тому +2

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

  • @the_eternal_student
    @the_eternal_student 2 місяці тому

    He always leaves the problem unfinished.

  • @aritrayou
    @aritrayou 13 років тому +1

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

  • @KOGR11
    @KOGR11 12 років тому

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

  • @namo7888
    @namo7888 9 років тому +2

    fantastic!!!

  • @joebrinson5040
    @joebrinson5040 2 роки тому

    Thanks MIT.

  • @NxyDolli
    @NxyDolli 14 років тому +1

    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

  • @not_amanullah
    @not_amanullah 5 місяців тому

    Thanks ❤🤍

  • @joebrinson5040
    @joebrinson5040 2 роки тому

    Thanks MIT

  • @quagmire444
    @quagmire444 12 років тому

    he has a point

  • @yoadknux
    @yoadknux 12 років тому

    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
      @topilinkala1594 2 роки тому

      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.

  • @GNR214
    @GNR214 13 років тому +1

    what kind of book does the class use?

  • @69erthx1138
    @69erthx1138 15 років тому

    @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.

  • @mayankrawat14
    @mayankrawat14 8 років тому

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

    • @spirontus
      @spirontus 8 років тому +2

      +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

  • @KOGR11
    @KOGR11 12 років тому +1

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

  • @Lordgenome76
    @Lordgenome76 14 років тому +1

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

    • @cropsey.
      @cropsey. 2 роки тому

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

  • @KOGR11
    @KOGR11 12 років тому

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

  • @humilitywewantit
    @humilitywewantit 11 років тому

    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
      @John10086 5 років тому +3

      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

  • @99ludester
    @99ludester 14 років тому

    @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...

  • @toastertastic
    @toastertastic 11 років тому

    Could that eraser be any more chalk-dusty?

  • @snehatangi6293
    @snehatangi6293 11 років тому +3

    €~Thankyou~$
    Thanks a lot...

  • @DoctorQuestionMark
    @DoctorQuestionMark 13 років тому

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

  • @lorenzotrojan
    @lorenzotrojan 14 років тому

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

  • @gauravsharma889
    @gauravsharma889 12 років тому

    Good

  • @KOGR11
    @KOGR11 12 років тому

    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?

  • @KOGR11
    @KOGR11 12 років тому

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

  • @Yu2Kal
    @Yu2Kal 14 років тому

    @jcgarces85 Denis Auroux

  • @JDMaxton1999
    @JDMaxton1999 4 роки тому

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

  • @SathishKumar-qe4nq
    @SathishKumar-qe4nq 6 років тому

    That dora cake tho..

  • @audreydaleski1067
    @audreydaleski1067 2 роки тому

    These are not too difficult.

  • @Staab0
    @Staab0 11 років тому

    35:05 hahahah

  • @maxisjaisi400
    @maxisjaisi400 7 років тому

    I like puppies too

  • @sunslayer553
    @sunslayer553 12 років тому

    nerd fight.

  • @gena8414
    @gena8414 5 років тому +2

    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.

  • @jdavis2921
    @jdavis2921 2 роки тому

    I HATE MATH

  • @HD4WG
    @HD4WG 13 років тому

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