Lec 19 | MIT 18.03 Differential Equations, Spring 2006

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  • Опубликовано: 10 дек 2024

Комментарии • 125

  • @chandus2496
    @chandus2496 9 лет назад +109

    This man is is probably the best math professor there is!!! With teaching like this, no wonder MIT is MIT.

    • @xyzoozo
      @xyzoozo 3 года назад

      @Peter S did u take h.gross lec? are they better?

  • @companymen42
    @companymen42 10 лет назад +37

    This dude is a riot! Thanks for deriving Laplace transforms for me, it's cool to see where it comes from.

  • @AbhijithVK
    @AbhijithVK 9 лет назад +31

    This is exactly why MIT is MIT. Have never got chance to understand laplace transforms in such a beautiful way from it's origins.

    • @AbhijithVK
      @AbhijithVK 9 лет назад +3

      :D no issues man.. if we are gonna write what we learned here in calicut university paper, they are gonna screw us big time! Personal experience :D

  • @maskman5802
    @maskman5802 8 дней назад +1

    MIT has been recording lectures and posting them since 2003 this is historic and amazing

  • @StratosFair
    @StratosFair Год назад +2

    Thank you mit for recording and sharing these wonderful lectures online for free

  • @padmamishra8434
    @padmamishra8434 9 лет назад +40

    Only if all professors could deliver a lecture as refined as this, Mathematical courses would be a lot more logical.

  • @Crasshopperrr
    @Crasshopperrr 10 лет назад +13

    He's very practised at sneaking in more calculations AFTER already giving them the gist of what's going on. "What the heck let's do this anyway". Clever.

  • @djtoddles8750
    @djtoddles8750 6 лет назад +8

    ~34:00 Calculating is hack! This lecture is a freakin work of art

  • @AhmadNasikun
    @AhmadNasikun 9 лет назад +4

    All this time I was just told the formula of Laplace Transform, without knowing how it comes to such form. Finally some great (yet weird on the same time) reveals how it's derived. Marvelous!!!

  • @georgesadler7830
    @georgesadler7830 3 года назад +2

    Professor Mattuck, thank for analyzing and explaining Laplace Transform it's Basic Formulas and it's relation to solving differential equations. Partial Fractions is another method that is really helpful for analyzing the Inverse Laplace Transform in differential equations.

  • @justjustgord
    @justjustgord 16 лет назад +2

    Absolutely superb.. If I heard this when I was 16 I would have understood it and had no problems.
    Explaining it by taking power series and gradually refining it is just beautifully simple - you could never forget it.
    great teacher - rating 10/5 !

  • @adrianvintila5077
    @adrianvintila5077 3 года назад +4

    Man.. MIT must be a good place to study. When we did Laplace at my University, half the lectures were taken up by us asking questions due to how unclear everything was.

    • @demr04
      @demr04 2 года назад

      If you don't study in the top ten university, most likelly that most of your understanding it's because of you alone. In my university it's almost all memorization.

  • @Rayquesto
    @Rayquesto 7 лет назад +15

    35:10 "You do the high school thing." That's how I would describe it.

  • @katunduchabala7266
    @katunduchabala7266 Год назад

    This lecture is a jump-start to the entire calculus body. It has given life to all the math😊. Thanks for sharing!

  • @MayankGoel447
    @MayankGoel447 11 месяцев назад

    This is the best explanation of Laplace transform I have seen till date

  • @deblaze666
    @deblaze666 11 лет назад +3

    thanks a million, you transform the confusing into the simple.

  • @ZopteY
    @ZopteY 11 лет назад

    WOOOOOOOOW you sir, are the kind of teacher that should teach everywhere

  • @Crasshopperrr
    @Crasshopperrr 10 лет назад +17

    45:00 "t^0 is just sitting there, defenceless"
    lol

    • @AhmadNasikun
      @AhmadNasikun 9 лет назад +1

      That statement of his really makes my day..

  • @SaadTaameOfficial
    @SaadTaameOfficial 10 лет назад +3

    This lecture made me love math even more.

  • @alanveiga452
    @alanveiga452 5 лет назад

    Thanks for making this lecture available. It was a lifesaver. My instructor teaches by using powerpoint presentations and that's not my style. He doesn't even bother proving anything. It's a nightmare..

  • @ZaynShaheen
    @ZaynShaheen 3 месяца назад +1

    3:33 " Look, you're supposed to be born knowing what that adds up to"

  • @YorangeJuice
    @YorangeJuice 2 года назад

    wow that explanation from the beginning to around 12:38 is just, amazing. thank you so much lol

  • @11pupona
    @11pupona 5 лет назад

    Thanks Mr. Mattuck. You give very good lectures. Cheers from spain.

  • @num3ric
    @num3ric 16 лет назад

    His presentation is so clear! If only my Real Analysis prof was like that...

  • @bboywaters
    @bboywaters 13 лет назад +1

    this guy is simply the best

  • @higgs_boson2231
    @higgs_boson2231 11 месяцев назад

    I've never seen a Laplace transform defined that way (and I've taken 2 courses which discussed them). Very intriguing.

  • @mertyigit4093
    @mertyigit4093 6 лет назад +1

    47 minutes of perfection...

  • @shakeralbakkar9810
    @shakeralbakkar9810 9 лет назад

    That was so great thanks prof
    You saved me in this exam period
    I need to watch all 32 vids

  • @Dsk7154
    @Dsk7154 6 лет назад

    He was awesome lecturer...he just explained it very simple

  • @TookMe20min2findThis
    @TookMe20min2findThis 12 лет назад +5

    I really envy those youngsters nowadays. They have RUclips, Wikipedia and the whole WEB!! and all sorts of gadgets to 'slowly' learn all that stuff. When we were learning this and couldn't understand something we were left only with some 'static' books and your lousy teacher. And If you didn't quite understand a key element like the Laplace transform you were left in the clouds for the rest of your life not quite knowing where this came from and just using blindly. Damn you bastards!! :)

  • @edwincuevas9965
    @edwincuevas9965 4 года назад

    This lecture is absolutely beautiful!!

  • @XguncheckX
    @XguncheckX 12 лет назад

    You sir, are a sir. Thank you for the wonderful cram session for my midterm.

  • @djtoddles8750
    @djtoddles8750 6 лет назад

    I love this guy for two reasons: 1. great explanations 2. he sounds like alan arkin and looks like will ferrell's "gus chiggins" character

  • @xyzoozo
    @xyzoozo 3 года назад

    Professor Mattuck is a wizard 🤍♥♥💖❤

  • @RandyLott
    @RandyLott 13 лет назад

    Using the Laplace transform is good if you are strong in Algebra. There is absolutely no Calculus involved after some basic setup. You could use Variation of Parameters or Undetermined Coefficients to find most solutions, but they are heavy with Calculus!

  • @footballover01
    @footballover01 14 лет назад

    Respect to you Professor, amazing, amazing lecturer

  • @hasinabrar3263
    @hasinabrar3263 5 лет назад

    what a legend this man is!

  • @anthonyrajabala
    @anthonyrajabala 14 лет назад

    This is a great lecture and Amazing !!! He is the best mathematician

  • @maazadnan117
    @maazadnan117 3 года назад

    My suggestion is if you don’t know about power series, watch last four lectures of 18.01 first then you will really enjoy this video.

  • @Stephematician
    @Stephematician 11 лет назад

    He applies the exponential shift formula to the Laplace transform of the function f(t) = 1.

  • @TheMrPranz
    @TheMrPranz 12 лет назад

    I know you posted a year ago, but I don't know why he said "if you're clever" because I think its quite simple. By using L'Hopitals n times in one step you're essentially differentiating n times, so you end up with (n(n-1)(n-2)..)*t^(n-n)/(s^n *e^(st)) which equals n!/(s^n (e^st)). :)
    I know its difficult to read maths in normal text, so just copy and paste the equations into wolfram or equivalent to see it in better form.

  • @namhoanghoai3813
    @namhoanghoai3813 9 лет назад +2

    this is just amazing

  • @MrErictan89
    @MrErictan89 13 лет назад

    I am doing process control, and i wish that mit would upload lectures on process control

  • @igamerxd8450
    @igamerxd8450 9 лет назад

    This is why i wanted to enter in MIT, dang it i live in europe, if not i would have done everything to be with a professor like him.

  • @abdelrahmangamalmahdy
    @abdelrahmangamalmahdy 11 лет назад +1

    yea , this is magic , this is math

  • @kyuliawan
    @kyuliawan 12 лет назад +1

    this dude is a BOSS

  • @HiEvanMY
    @HiEvanMY 11 лет назад

    Great professor. Thanks a lot. Excellent explanation

  • @fawzyhegab
    @fawzyhegab 8 лет назад +1

    It's a great lecture! very entertaining!

  • @duscen
    @duscen 14 лет назад +11

    Anyone know how to do the Le' Hospital of x^n / e^x in just one step?

    • @blablablerg
      @blablablerg 5 лет назад +4

      maybe using taylor expansion of e^x

    • @vishaldas9770
      @vishaldas9770 4 года назад +2

      @@blablablerg That's clever, if you use Taylor expansion of e^x, you don't even need to use L Hosp once bcuz Taylor expansion of e^x will have infinitely many terms of x^(whole numbers greater than n)..

    • @justpaulo
      @justpaulo 2 года назад +2

      11 years after... 😁
      I just think you pull the exponent "n" outside and make it common to e^st. In other words:
      lim t→∞ t^n / e^(st) = lim t→∞ [ t / e^(st/n) ]^n = [ lim t→∞ t / e^(st/n) ]^n .
      Using L'Hôpital's rule 1x then the lim t→∞ t / e^(st/n) = lim t→∞ [ (s/n) e^(st/n) ] ¯¹ = 0

    • @generalezaknenou
      @generalezaknenou 2 года назад

      @@justpaulo 1 month after you: thanks king 👑🔝

  • @tianmingguo8271
    @tianmingguo8271 6 лет назад

    Great math professor! Thank you so much!

  • @meatheadMD
    @meatheadMD 15 лет назад +2

    OMG. I understand calculus for once....and I'm in my third year of engineering.... O.O

  • @pierre45a
    @pierre45a 14 лет назад

    WOW from rote learning I thought I'd take a look online to see if there were concrete explanations for the Laplace transform. Blown away. Well done professor. How simple does he make it sound?!

  • @criskity
    @criskity 11 лет назад

    Wonderful explanation!!

  • @coolwinder
    @coolwinder 4 года назад

    33:15 Don't we have different conditions for s and a now, because a is imaginary component of exponent? That is condition for convergence of 1/( s + ia ) is s > 0, a > 0?

  • @heiheihei60
    @heiheihei60 7 лет назад +1

    Thank you so much!!!

  • @kshitij1703
    @kshitij1703 11 лет назад

    it was really good.....thanks for this video i really liked it

  • @coolwinder
    @coolwinder 4 года назад

    31:50 When we use complex exponent in f(t), how i*b doesn't impact the condition for s?

  • @DimuthuDissanayake
    @DimuthuDissanayake 11 лет назад

    wt a explanation , he s a genius

  • @coolwinder
    @coolwinder 4 года назад

    at 20:19 we say e^(-s) = 1, but now at 27:50 we have e^-(s-a), so when evaulating that step for lower condition s=0 we get e^a, not 1. so that whole integral becomes lim(R->inf) ( e^(-s) - e^a ) / ( -s + a) , right? So that at the end we dont get 1/s, what happened to e^a?

    • @coolwinder
      @coolwinder 4 года назад +1

      We say e^(-st) = 1 when t=0, not s=0! And because we have -(s-a)R instead of -sR, the condition for convergence changes to s-a > 0!

  • @grimshawr
    @grimshawr 15 лет назад +1

    I always wondered why Lapalace Transforms go from 0 to infinity instead of being a proper integral.

  • @rsplenum
    @rsplenum 14 лет назад

    Just simply Awesome

  • @dchap88
    @dchap88 13 лет назад

    "Now, if I've done my work correctly, youshould all be saying, 'Oh, is that all?' But, I know you aren't." -- You've done your work correctly. :-)

  • @justpaulo
    @justpaulo 2 года назад

    45:15
    just take the lim t→∞ [ t / e^(st/n) ]^n = [ lim t→∞ t / e^(st/n) ]^n .
    Using L'Hôpital's rule the lim t→∞ t / e^(st/n) = lim t→∞ [ (s/n) e^(st/n) ] ¯¹ = 0

  • @meatheadMD
    @meatheadMD 13 лет назад

    @1988dchapman
    Don't worry. I won't be designing any collapsing buildings or bridges. Made the career change and applied to MD last year :p

  • @boeithet1
    @boeithet1 11 лет назад

    I love how he explains it, but sometimes i cant read the blackboard very good. Are there higher quality videos?

  • @jimztar
    @jimztar 13 лет назад +2

    All lecturers should be forced to watch Arthur Mattuck's lectures.

  • @dthez4768
    @dthez4768 6 лет назад

    Lecture 18 was a guest lecture. Here is a link to a version from 2010 I think.
    ruclips.net/video/dadVWKS9lGM/видео.html

  • @Bloodsaberxy
    @Bloodsaberxy 15 лет назад

    so you rated him 2 huh...
    i agree though, great teacher and nicely done lecture

  • @imtiazreaz9325
    @imtiazreaz9325 7 лет назад +4

    where is lecture 18???

    • @mitocw
      @mitocw  7 лет назад +10

      Lecture 18 was a guest lecture, which we do not have the source. It's posted on TechTV: techtv.mit.edu/collections/math/videos/7437-1803-profs-miller-and-vandiver-31510-lecture See the course on MIT OpenCourseWare for more information and materials at ocw.mit.edu/18-03S06.

  • @calculosai1851
    @calculosai1851 11 лет назад

    Excellent! :D Thank you very much!

  • @DilipDU
    @DilipDU 9 лет назад +1

    where is lecture number 18 ? :)

  • @martinvall6087
    @martinvall6087 5 лет назад

    Topic this lecture: Laplace transforms in ODEs

  • @k.prabhu1225
    @k.prabhu1225 3 года назад

    Sir but s is a complex number but you have defined s=-log(x) (real) ??

  • @Crasshopperrr
    @Crasshopperrr 10 лет назад

    40:00 Forgot the exp(−t) next to the ⅓.

    • @Jerom_
      @Jerom_ 10 лет назад +5

      I don't think he did. Because he said 1/s is the laplace transform of 1.

  • @yishin
    @yishin 3 года назад

    awesome!

  • @Liaomiao
    @Liaomiao 13 лет назад

    Anyone know of a set of lectures/vids talking about power series and other series in general? I feel like i'm lacking a bit of knowledge in that area.

  • @reelsoulful
    @reelsoulful 8 лет назад +5

    Please upload this series in at least 360p

    • @justmohsend
      @justmohsend 7 лет назад

      www.edx.org/course/introduction-differential-equations-mitx-18-031x
      in their course on edx, some of the videos are uploaded in 720p. However, I think it is from another term.

  • @sihanchen1331
    @sihanchen1331 9 лет назад +2

    Where is Lecture 18???

    • @mitocw
      @mitocw  9 лет назад +10

      +Sihan Chen Sorry, lecture 18 is not available. According to the calendar, the topic was "Engineering applications" and covered damping ratios. For more information, see the course on MIT OpenCourseWare at ocw.mit.edu/18-03S06.

  • @Borthralla
    @Borthralla 7 лет назад

    BRAVO!!!

  • @TTminh-wh8me
    @TTminh-wh8me 3 года назад

    we dont have lecture 18 in the playlist ?

    • @mitocw
      @mitocw  3 года назад

      Lecture 18 is not available. See ocw.mit.edu/18-03S06 for more information and materials. Best wishes on your studies!

  • @stewieyan
    @stewieyan 6 лет назад

    isn't s a complex number? if s = -log(x), how is that a complex number?

  • @maryannahalajal2020
    @maryannahalajal2020 11 лет назад

    what does 30:45 to 31:00 mean? thanks..

  • @SSNewberry
    @SSNewberry 8 месяцев назад

    I was thinking "non-negative integers" and then he said it. Ichi-ban!

  • @Hack3r91
    @Hack3r91 14 лет назад

    I can't find Lec 18...

  • @TheMemorious
    @TheMemorious 14 лет назад

    Got to love Professor Mattuck, even when he tries to run you over in his bicycle.

  • @HotPepperLala
    @HotPepperLala 12 лет назад

    What happened to lecture 18...?

  • @sekleng
    @sekleng 13 лет назад

    4 guys got differentiated

  • @ITogoPogoB
    @ITogoPogoB 11 лет назад

    11:14 "raise this to the teeth power" lol

  • @AhmedKMoustafa2
    @AhmedKMoustafa2 8 лет назад

    it is written march 2003 in the beginning of the video, then why the title is spring 2006 ?? Not 2003

    • @mitocw
      @mitocw  8 лет назад +2

      +Ahmad K Mostafa The course was published on MIT OpenCourseWare in spring 2006.

    • @AhmedKMoustafa2
      @AhmedKMoustafa2 8 лет назад

      *****
      Got it .
      Thanks ^-^

  • @ukdmathematicsclassesbyabh1021
    @ukdmathematicsclassesbyabh1021 7 лет назад

    good morning

  • @abdulazizabdu8362
    @abdulazizabdu8362 8 лет назад

    Where is the Euler-Cauchy Equations?

    • @ericex12345
      @ericex12345 8 лет назад

      in the problem set of the book

  • @plutopulp
    @plutopulp 13 лет назад

    @Liaomiao The following isn't bad if ever: Power Series/Euler's Great Formula | MIT Highlights of Calculus

  • @Sidionian
    @Sidionian 11 лет назад +4

    May this great warrior's divine, old, shriveled up testicles be blessed and protected by the generous Lords of Chaos.
    (I just wanted to say something controversial).

  • @hishan.farfan
    @hishan.farfan 6 лет назад

    wow!

  • @tanmaypal6516
    @tanmaypal6516 5 лет назад

    Can any one say the name of this professor....plsss???

    • @mitocw
      @mitocw  5 лет назад +1

      Professor Arthur Mattuck

    • @tanmaypal6516
      @tanmaypal6516 5 лет назад

      @@mitocw thanks ...

  • @Liaomiao
    @Liaomiao 13 лет назад

    when he said at the end if you're clever you can use L'hopital's rule once did he mean you put a ln in front of both top and bottom and then use L'Hopitals?

  • @funkysagancat3295
    @funkysagancat3295 5 лет назад

    Where is the 18th???

    • @mitocw
      @mitocw  5 лет назад

      The video was of a guest lecture and not covered under our license. You can find the video here: ruclips.net/video/pRIEYR5JHQA/видео.html. Best wishes on your studies!

  • @dchap88
    @dchap88 13 лет назад

    @shinim3gami This comment scares me.

  • @LiquidOX2H2
    @LiquidOX2H2 14 лет назад

    65 guys who like this, 4 who DIDN'T understand :D

  • @MrWandalen
    @MrWandalen 7 лет назад

    Good content, but quality is terrible!!