Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07

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  • เผยแพร่เมื่อ 24 ธ.ค. 2024

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  • @kingkongtiger
    @kingkongtiger 12 ปีที่แล้ว +251

    MIT professors teach like their students have no background knowledges, and my professors assume I have learnt all shit already in High school

    • @rajaradi802
      @rajaradi802 4 ปีที่แล้ว +2

      @narak leduop not cheap schools but with the worst education system

    • @theblinkingbrownie4654
      @theblinkingbrownie4654 3 ปีที่แล้ว

      @CAVEMAN these bots are surprisingly common especially in stem channels, idk how youtube hasn't noticed yet.

    • @anindyaroy5692
      @anindyaroy5692 2 ปีที่แล้ว +4

      Exactly! And they also jump from one thing to another, and students fail to understand the connection.

    • @marklestergesta7554
      @marklestergesta7554 ปีที่แล้ว +3

      I feel you

  • @qbtc
    @qbtc ปีที่แล้ว +10

    MIT students are smart and know they are being taught by a great professor here. They even applaud when he figures out the blackboard buttons.

    • @jesusk1358
      @jesusk1358 10 ชั่วโมงที่ผ่านมา

      It is very strange how they keep clapping for that. I think it is insulting.

  • @narutouzumakix9201
    @narutouzumakix9201 6 ปีที่แล้ว +109

    this guy is really good at the 3D drawings

    • @Dawatehaq786
      @Dawatehaq786 4 ปีที่แล้ว

      Trigonometry for AS and A level student th-cam.com/video/-WzZRx4vVxI/w-d-xo.html
      Subscribe please

    • @yabannamba7678
      @yabannamba7678 2 ปีที่แล้ว

      Sal Khan is the goat at it but he's good too

  • @TheCrappyaccount
    @TheCrappyaccount 12 ปีที่แล้ว +28

    I love MIT so much for all of these free lectures. I have watched all of physics, this and electronics and circuits.

  • @katee808
    @katee808 14 ปีที่แล้ว +67

    Jesus Christ he's great at teaching. I now understand the difference between spending $50,000 per year and $10,000 per year. At least they're paying for the tuition so I get to watch these videos for free.

  • @ChristianCentury2000
    @ChristianCentury2000 2 ปีที่แล้ว +15

    Thank you MIT for posting these excellent courses online! The professors are great! The lectures are very well done!

  • @koenrad
    @koenrad 10 ปีที่แล้ว +64

    Much easier to understand now that I have a second person explaining it, what a great professor! Also helps that I can rewind and listen however many times I want :p.

    • @justinyeo1428
      @justinyeo1428 9 ปีที่แล้ว +1

      Yup. I also wish I had that professor.

    • @rajaradi802
      @rajaradi802 4 ปีที่แล้ว +1

      Hey you look like Sheldon

  • @83jeffa
    @83jeffa 8 ปีที่แล้ว +56

    this guy is a master chalk operator

    • @Dawatehaq786
      @Dawatehaq786 4 ปีที่แล้ว

      Trigonometry for AS and A level student th-cam.com/video/-WzZRx4vVxI/w-d-xo.html
      Subscribe please

    • @WilliamTaylor-rr6zw
      @WilliamTaylor-rr6zw 4 ปีที่แล้ว +10

      @@Dawatehaq786 bro shut up

  • @awowoosas
    @awowoosas 8 ปีที่แล้ว +26

    All these videos are REALLLY REALLY helpful. Thank you so much, MIT!

  • @vishnureddy3977
    @vishnureddy3977 7 ปีที่แล้ว +21

    That sine graph is amazing.

  • @SimmySimmy
    @SimmySimmy 5 ปีที่แล้ว +20

    One of the reasons I truly like this awesome teacher is he always erase three pieces of blackboards in a row, so I get a chance to skip

  • @ccosm4587
    @ccosm4587 9 ปีที่แล้ว +174

    these kids applaud at the strangest things

    • @ddude957
      @ddude957 5 ปีที่แล้ว +3

      seems you haven't been to college

    • @slackbabo3858
      @slackbabo3858 5 ปีที่แล้ว +22

      @@ddude957 I have and we don't typically applaud the professors

    • @Dawatehaq786
      @Dawatehaq786 4 ปีที่แล้ว +1

      Trigonometry for AS and A level th-cam.com/video/-WzZRx4vVxI/w-d-xo.html
      Subscribe please

    • @aashsyed1277
      @aashsyed1277 3 ปีที่แล้ว

      meh im a 9 year old

  • @syedaliraza3476
    @syedaliraza3476 10 หลายเดือนก่อน +1

    Incredible lecture. Professor Denis Auroux is brilliant. He says his drawings on the board aren’t on point but they are way beyond great.

  • @MrCavitysChessCorner
    @MrCavitysChessCorner 12 ปีที่แล้ว +7

    Phenomenal lecture. Merci beaucoup Professor Auroux!

  • @GNARGNARHEAD
    @GNARGNARHEAD 12 ปีที่แล้ว +2

    just in-case anyone was wondering the program he used to generate those parabola is 3D-XplorMath its a really fun program relatively easy to use its even how i generated my display picture :)

    • @alyasker2194
      @alyasker2194 4 ปีที่แล้ว +1

      thnx a lot that was really helpful :)

  • @MarioS-v7b
    @MarioS-v7b ปีที่แล้ว

    Thanks to MIT for posting this and other math videos. For a math hobbyist these videos are an excellent resource for deepening the knowledge about math. Prof Auroux is really awesome.

  • @Filipe8496
    @Filipe8496 14 ปีที่แล้ว +2

    This is the best teacher I ever seen. :D

  • @imegatrone
    @imegatrone 13 ปีที่แล้ว +3

    I Really Like The Video From Your Level curves; partial derivatives; tangent plane approximation

  • @sac12389
    @sac12389 11 ปีที่แล้ว +5

    and the sidewalk chalk is a great idea. I sit in the second (out of 4) row in my calc 3 class and often can't tell what is being written on the green board. also green boards are a terrible idea.

  • @cristh2311
    @cristh2311 11 ปีที่แล้ว +7

    I hope most of you noticed that at 42:21 we were dealing with a "toilet function" ;)

    • @cristh2311
      @cristh2311 8 ปีที่แล้ว

      +Mei Yifu I guess someone didn't notice ^^

    • @cristh2311
      @cristh2311 8 ปีที่แล้ว

      +Mei Yifu look at how the function is drawn.

    • @cristh2311
      @cristh2311 8 ปีที่แล้ว

      +Mei Yifu :D
      this math is old good night stories for me now. I am quite far in my masters now, physics.
      I just couldnt resist commenting about it at the time ^^

    • @cristh2311
      @cristh2311 8 ปีที่แล้ว

      +Mei Yifu Yes, in minimum period. I started in Summer Semester 2013, wanna see my grades? I have 3 and half years of them :)

  • @inuyashalivesbaby
    @inuyashalivesbaby 15 ปีที่แล้ว +2

    omg.... I know this is stupid, but I have to say it. That movable board is awesome man!!! Go MIT!!!

  • @hassanhb9605
    @hassanhb9605 5 ปีที่แล้ว +3

    Wow , Wow ! What an amazing explanation ... i felt like Multivariate Calculus is very easy as opposite of usual

  • @skylarshi1040
    @skylarshi1040 ปีที่แล้ว +1

    lifesaver and im going to cross register every math class at mit. dont know why my professor assume im smarter than mit students

  • @BareClause
    @BareClause 11 ปีที่แล้ว +1

    I'll add this to my watch later list, because I am going to need this when I do Mathematical Methods at UWA next year.

    • @maxsash
      @maxsash 8 ปีที่แล้ว +7

      I don't think so. They say they will but they never come back.

    • @BareClause
      @BareClause 5 หลายเดือนก่อน

      @@maxsash I ended up getting a phd bitch

  • @karigucio
    @karigucio 6 ปีที่แล้ว +3

    i appreciate this guys 3D drawing skills

  • @iyanev
    @iyanev 11 ปีที่แล้ว +1

    Why does everybody hates Taylor's Series.They are a live saver and allow you to do so much with a little work.

  • @Intellects0
    @Intellects0 หลายเดือนก่อน

    In our Hindu Culture we treat Teachers far above then God and parents ,. I don't what is name of this professor but his teaching style is very good , ❤

  • @hanzellmo
    @hanzellmo 14 ปีที่แล้ว +4

    Spivak's calculus might be to confusing for someone that's starting, but is an awesome book.

  • @ishandave3542
    @ishandave3542 9 ปีที่แล้ว +39

    god please name lectures by the topics!!!!

    • @mitocw
      @mitocw  9 ปีที่แล้ว +28

      +Ishan Dave Sorry, all of our early videos are titled like this (thousands of them, so the odds of us going back through to change them aren't very high). We changed how we named them starting in 2012. To get a list of topics, see the course on MIT OpenCourseWare at: ocw.mit.edu/18-02F07.

    • @ishandave3542
      @ishandave3542 9 ปีที่แล้ว +14

      ***** please there is no need for sorry.I am under great debt from professors from MIT especially professor walter lewin he is my favorite professor of all time he came to my college last year I am sad that I didn't have the chance to meet him.

    • @tripp3468
      @tripp3468 8 ปีที่แล้ว +1

      Jesus dude, learn how to spell.

    • @ishandave3542
      @ishandave3542 8 ปีที่แล้ว +6

      I edited the comment ,seems fine to me now English is not my first language.

    • @saminzawad4677
      @saminzawad4677 6 ปีที่แล้ว +1

      ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/

  • @marklestergesta7554
    @marklestergesta7554 ปีที่แล้ว

    Thank you MIT ❤️❤️❤️

  • @jogaserbia
    @jogaserbia 14 ปีที่แล้ว +1

    Awesome videos. Just to let everyne know, you can donate to the open course ware through their website. Also, you can buy books through amazon where MIT gets money. I dontated because I really believe in what they are trying to achieve.

  • @venkatesh-ke9ff
    @venkatesh-ke9ff 5 ปีที่แล้ว

    your teaching is supper, sir, i never see before such knowledge any professor

  • @mohammadfallahzade2110
    @mohammadfallahzade2110 4 ปีที่แล้ว

    he is a legend
    thanks MIT

  • @silentweapon
    @silentweapon 12 ปีที่แล้ว

    I feel so fucking lost during my calculus class, and enlightened right away after watching this video. THANKS SO MUCH!

  • @SUBASHCD
    @SUBASHCD 6 ปีที่แล้ว

    25:37 Horizontal lines plotted is incorrect?

  • @josephlee392
    @josephlee392 5 ปีที่แล้ว

    At 43:46, what if you chose a different slice in the xz plane? Wouldn't df/dx change because you would get different curves? Or, would all the curves be the same general shape: a parabola, making it not change after all? Thanks.

    • @axxxyxxxx5233
      @axxxyxxxx5233 10 หลายเดือนก่อน

      If u take horizontal slice for z=c the slope will be same for any vertical slice y=k

  • @AdrielGreene
    @AdrielGreene 12 ปีที่แล้ว +1

    This was so enlightening!

  • @orangasli2943
    @orangasli2943 2 ปีที่แล้ว

    Ok now we understand x axis when plotting against y axis is actually looking at an object from the top..
    If we add the z axis we can understand that object little bit more

  • @TheJesseWu
    @TheJesseWu 12 ปีที่แล้ว +4

    That's some nice handwriting.

  • @iitjee3813
    @iitjee3813 3 ปีที่แล้ว +1

    24:09

  • @TheTranceWhale
    @TheTranceWhale 11 ปีที่แล้ว +2

    Is Taylor really that unpopular? (@ 38:20)
    We tend to use 'taylor' as a verb: "Doesn't integrate? Just taylor that shit."

    • @malihareza4754
      @malihareza4754 4 ปีที่แล้ว

      In a previous lecture the whole class gasped when the professor mentions Taylor series. So it's coming from there.

  • @ZbladeVX
    @ZbladeVX 11 ปีที่แล้ว

    Great lecture but itd be cool if the camera movenment is less. He writes reasonably clear and very neat. Great prof too

  • @nchaconn79
    @nchaconn79 15 ปีที่แล้ว

    This is fantastic, very clear explanations. I'm currently taking Calculus 3 in Summer session and I work a full time (40 hours per week) so I have no life... well Calc 3 is my currently life. But I love it

  • @A3abbadq8
    @A3abbadq8 14 ปีที่แล้ว

    Great Lecture!! Helped me a lot.

  • @elamvaluthis7268
    @elamvaluthis7268 2 ปีที่แล้ว

    Basics of vector calculus understands properly.

  • @yhmd777
    @yhmd777 7 ปีที่แล้ว

    It's a great video because I can review what I learned this year

  • @priyanksharma1124
    @priyanksharma1124 6 ปีที่แล้ว

    Amazing pedagogy

  • @JinxiLiu-e2b
    @JinxiLiu-e2b หลายเดือนก่อน

    beautiful, ty

  • @suffixable
    @suffixable 9 ปีที่แล้ว +6

    such an awesome professor. MI,T could you also upload single variable calculus lectures from him. The one you have, right now, is very confusing.

    • @proghostbusters1627
      @proghostbusters1627 4 ปีที่แล้ว +1

      I can't see what you mean. Prof. Jerison is fricking great.

    • @semjoneschweiler2229
      @semjoneschweiler2229 10 หลายเดือนก่อน

      Strongly disagree, Prof. Jerison did a great job in my opinion.

  • @somnathmondal724
    @somnathmondal724 4 ปีที่แล้ว

    If I don't get any point in a small region of topographic map of a mountain, it indicates there is no peak . Is this true ??

  • @benjames2266
    @benjames2266 8 ปีที่แล้ว +1

    What graphing program were they using to plot the graphs and contour plots?

    • @mitocw
      @mitocw  8 ปีที่แล้ว +2

      The course occasionally relies on a series of specially written interactive math applets ("mathlets"), which let you visualize and experiment with various concepts seen in lecture. See the course on MIT OpenCourseWare for the mathlets and more course materials at ocw.mit.edu/18-02F07.

  • @datagus
    @datagus 14 ปีที่แล้ว

    Well, goodbye to my old calculus teacher!!! Welcome MIT!!!!!!!!!!

  • @aashsyed1277
    @aashsyed1277 3 ปีที่แล้ว

    what is a relation in 3 d?????

  • @k0fdark
    @k0fdark 15 ปีที่แล้ว

    Thanks this is very helpful, my fav teacher :D

  • @not_amanullah
    @not_amanullah 6 หลายเดือนก่อน

    This is helpful ❤️🤍

  • @alinapol
    @alinapol 11 ปีที่แล้ว

    great lecture

  • @ДімаКрасько-с7м
    @ДімаКрасько-с7м 7 ปีที่แล้ว

    Are graphs build in Mapple? Recognized the commands, that were used

  • @not_amanullah
    @not_amanullah 6 หลายเดือนก่อน

    Thanks ❤🤍

  • @rebeccalee120
    @rebeccalee120 6 ปีที่แล้ว

    This is what we learn in 4 classes of same length

  • @dnm25
    @dnm25 15 ปีที่แล้ว +2

    41:26 differenti-able :D
    5/5

  • @LAnonHubbard
    @LAnonHubbard 13 ปีที่แล้ว

    Brilliant stuff.

  • @LauroKirsch
    @LauroKirsch 15 ปีที่แล้ว

    This helped me a lot!

  • @sebastiandiazvivas613
    @sebastiandiazvivas613 3 ปีที่แล้ว

    How I would wish to stay at MIT studying right now

  • @AndresGomez-pw4fs
    @AndresGomez-pw4fs 4 ปีที่แล้ว

    what's the program he's using for plotting the functions??

  • @somebodyhere3160
    @somebodyhere3160 3 ปีที่แล้ว

    9:35

  • @zyrohnmng
    @zyrohnmng 12 ปีที่แล้ว

    You still have to admit...it is cool, common or not...it. is. epic.

  • @elamvaluthis7268
    @elamvaluthis7268 2 ปีที่แล้ว

    Very nice.

  • @fermixx
    @fermixx 15 ปีที่แล้ว

    any to recommend me?

  • @eafindme
    @eafindme 12 ปีที่แล้ว +1

    Arrr, finally I found a key to understand multivariables! My lecturer is just screwing it up! I couldn't understand it even I study by myself. Is worth a waste of 46 minutes on watching this recording!

  • @xinyuli9423
    @xinyuli9423 3 ปีที่แล้ว

    44:42 "Applied math is just physics with different notation" LMAO

  • @kindalindaable
    @kindalindaable 8 ปีที่แล้ว

    Thanks sooo much!!

  • @hellomate639
    @hellomate639 13 ปีที่แล้ว

    @inuyashalivesbaby
    There are boards like that at my school.
    Not that special of a device. Common at large universities.

  • @Souliee
    @Souliee 15 ปีที่แล้ว +1

    Hes really good at explaining, not like my professor :

  • @realcirno1750
    @realcirno1750 8 หลายเดือนก่อน

    there was no tangent plane

  • @fermixx
    @fermixx 15 ปีที่แล้ว

    im doing distance learning and this guy is saving my ass.
    you cant imagine how hard is to learn calculus 2 from a book ! (or BAD book).
    Its easier for me to hear this french talking in english than to read the book which is written in my mother tongue (spanish), so figure it out !
    thanks dude !

  • @gautamgopal3517
    @gautamgopal3517 3 ปีที่แล้ว

    Anyone else Bingewatching all these lectures?

  • @inuyashalivesbaby
    @inuyashalivesbaby 13 ปีที่แล้ว

    @hellomate639
    Good for you and your university. :)

  • @eldernos
    @eldernos 5 หลายเดือนก่อน

    That dude sure can draw a sin curve.

  • @jacklyons5888
    @jacklyons5888 11 หลายเดือนก่อน

    things are now getting exciting :P vectors are bleh

  • @themastershadowx
    @themastershadowx 15 ปีที่แล้ว

    i think it's obviously seen that he is from france as he pronounce "r" with french pronunciation

  • @soubhadramaiti1996
    @soubhadramaiti1996 6 ปีที่แล้ว +1

    I've watched and really enjoyed the previous lectures, but I have some doubts regarding this lecture.... what I have learnt from the book by J. Coley is totally opposite (interchanged) to what professor explained about Contour plot and Level curves...... Hoping for anyone's kind reply. Thank you.

  • @yuhanwang7122
    @yuhanwang7122 6 ปีที่แล้ว +4

    Applied math, which is the same thing as physics but with different notations. Comedy gold.

  • @robertsguitar
    @robertsguitar 14 ปีที่แล้ว +1

    Fun fact: This prof started his masters leading to his Ph.D when he was 14
    :|

    • @proghostbusters1627
      @proghostbusters1627 4 ปีที่แล้ว

      And here am I watching this at 14. Man I feel I've fell behind already (I'm semi-joking)

  • @SevenRiderAirForce
    @SevenRiderAirForce 14 ปีที่แล้ว

    Math - this is how you do it.
    Oh, and I lol'd at 22:48 when they clapped for him.

  • @md.nasimreza3029
    @md.nasimreza3029 10 ปีที่แล้ว

    nice

  • @hellomate639
    @hellomate639 13 ปีที่แล้ว

    @inuyashalivesbaby
    Nah, just saying that my university isn't a great one (it's great by some standards, nobel prize winners have taught here), but it's easy to get into this one.

  • @ashokedas1552
    @ashokedas1552 8 ปีที่แล้ว

    good

  • @pufifa
    @pufifa 11 ปีที่แล้ว +2

    30:40 that thing won't stop staring at me :O

    • @saubaral
      @saubaral 4 ปีที่แล้ว +1

      thats not the graph we need, but the graph we deserve

  • @sarahdaud
    @sarahdaud 13 ปีที่แล้ว

    @inuyashalivesbaby haha i know what you mean! i study at LUMS univerity, Lahore, Pakistan and our science department is inspired by MIT.. we have moving boards here too its so much fun haha :D

  • @faizzzzan
    @faizzzzan 12 ปีที่แล้ว

    same

  • @inuyashalivesbaby
    @inuyashalivesbaby 13 ปีที่แล้ว

    @hellomate639 in a quite plainly condescending pompous way... That's all.

  • @hellomate639
    @hellomate639 13 ปีที่แล้ว

    @inuyashalivesbaby
    I'm not judging. Lol.
    I'm just saying quite plainly that those boards aren't a very impressive feature.

  • @alperener460
    @alperener460 9 ปีที่แล้ว +1

    is there one who know this guy's accent

    • @GorkemArar
      @GorkemArar 9 ปีที่แล้ว

      alperen çağrı er Fransiz

    • @zhangqinghui3546
      @zhangqinghui3546 9 ปีที่แล้ว +2

      Alperen Çağrı ER french....

  • @orangasli2943
    @orangasli2943 2 ปีที่แล้ว

    Finally we can understand
    "with respect" means
    "small changes of"
    For example let find the derivative of
    the function f(x)=x+y with respect to x..
    Means when x is moving slowly ..
    What is the gradient between z and x
    i.e
    z/x =?

  • @inuyashalivesbaby
    @inuyashalivesbaby 13 ปีที่แล้ว

    @hellomate639
    I made that comment two years ago. Can you imagine me saying that aloud in a MIT classroom?? lmao. That's why I don't go there...
    Believe it or not, I'm not that shallow. Don't judge my character based on that one comment. I'm teacher's assistant for a calculus lab at my university now. I have 23 students. lol.

  • @dongel1001
    @dongel1001 15 ปีที่แล้ว

    is he french? his accent is so funny

  • @UnjojoHalas
    @UnjojoHalas 13 ปีที่แล้ว

    lol. i like the way he says temperature. (hope i spelled it correctly)
    he's awesome!

  • @eligray
    @eligray 14 ปีที่แล้ว

    @katee808 Starting next month, I'll be paying the price for you =)

  • @Greg_Ulmer
    @Greg_Ulmer 10 ปีที่แล้ว +1

    coughing

  • @fermixx
    @fermixx 15 ปีที่แล้ว

    oh and by the way, that intro starts to piss me off after watching so many lectures !