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.
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!!!
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.
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 !
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.
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.
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..
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!! :)
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!
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.
@@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)..
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
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?!
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?
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?
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
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.
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.
+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.
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).
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?
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!
This man is is probably the best math professor there is!!! With teaching like this, no wonder MIT is MIT.
@Peter S did u take h.gross lec? are they better?
This dude is a riot! Thanks for deriving Laplace transforms for me, it's cool to see where it comes from.
This is exactly why MIT is MIT. Have never got chance to understand laplace transforms in such a beautiful way from it's origins.
: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
MIT has been recording lectures and posting them since 2003 this is historic and amazing
Thank you mit for recording and sharing these wonderful lectures online for free
Only if all professors could deliver a lecture as refined as this, Mathematical courses would be a lot more logical.
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.
~34:00 Calculating is hack! This lecture is a freakin work of art
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!!!
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.
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 !
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.
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.
35:10 "You do the high school thing." That's how I would describe it.
This lecture is a jump-start to the entire calculus body. It has given life to all the math😊. Thanks for sharing!
This is the best explanation of Laplace transform I have seen till date
thanks a million, you transform the confusing into the simple.
WOOOOOOOOW you sir, are the kind of teacher that should teach everywhere
45:00 "t^0 is just sitting there, defenceless"
lol
That statement of his really makes my day..
This lecture made me love math even more.
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..
3:33 " Look, you're supposed to be born knowing what that adds up to"
wow that explanation from the beginning to around 12:38 is just, amazing. thank you so much lol
Thanks Mr. Mattuck. You give very good lectures. Cheers from spain.
His presentation is so clear! If only my Real Analysis prof was like that...
this guy is simply the best
I've never seen a Laplace transform defined that way (and I've taken 2 courses which discussed them). Very intriguing.
47 minutes of perfection...
That was so great thanks prof
You saved me in this exam period
I need to watch all 32 vids
He was awesome lecturer...he just explained it very simple
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!! :)
This lecture is absolutely beautiful!!
You sir, are a sir. Thank you for the wonderful cram session for my midterm.
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
Professor Mattuck is a wizard 🤍♥♥💖❤
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!
Respect to you Professor, amazing, amazing lecturer
what a legend this man is!
This is a great lecture and Amazing !!! He is the best mathematician
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.
He applies the exponential shift formula to the Laplace transform of the function f(t) = 1.
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.
this is just amazing
I am doing process control, and i wish that mit would upload lectures on process control
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.
yea , this is magic , this is math
this dude is a BOSS
Great professor. Thanks a lot. Excellent explanation
It's a great lecture! very entertaining!
Anyone know how to do the Le' Hospital of x^n / e^x in just one step?
maybe using taylor expansion of e^x
@@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)..
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
@@justpaulo 1 month after you: thanks king 👑🔝
Great math professor! Thank you so much!
OMG. I understand calculus for once....and I'm in my third year of engineering.... O.O
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?!
Wonderful explanation!!
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?
Thank you so much!!!
it was really good.....thanks for this video i really liked it
31:50 When we use complex exponent in f(t), how i*b doesn't impact the condition for s?
wt a explanation , he s a genius
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?
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!
I always wondered why Lapalace Transforms go from 0 to infinity instead of being a proper integral.
Just simply Awesome
"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. :-)
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
@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
I love how he explains it, but sometimes i cant read the blackboard very good. Are there higher quality videos?
All lecturers should be forced to watch Arthur Mattuck's lectures.
Lecture 18 was a guest lecture. Here is a link to a version from 2010 I think.
ruclips.net/video/dadVWKS9lGM/видео.html
so you rated him 2 huh...
i agree though, great teacher and nicely done lecture
where is lecture 18???
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.
Excellent! :D Thank you very much!
where is lecture number 18 ? :)
Topic this lecture: Laplace transforms in ODEs
Sir but s is a complex number but you have defined s=-log(x) (real) ??
40:00 Forgot the exp(−t) next to the ⅓.
I don't think he did. Because he said 1/s is the laplace transform of 1.
awesome!
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.
Please upload this series in at least 360p
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.
Where is Lecture 18???
+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.
BRAVO!!!
we dont have lecture 18 in the playlist ?
Lecture 18 is not available. See ocw.mit.edu/18-03S06 for more information and materials. Best wishes on your studies!
isn't s a complex number? if s = -log(x), how is that a complex number?
what does 30:45 to 31:00 mean? thanks..
I was thinking "non-negative integers" and then he said it. Ichi-ban!
I can't find Lec 18...
Got to love Professor Mattuck, even when he tries to run you over in his bicycle.
What happened to lecture 18...?
4 guys got differentiated
11:14 "raise this to the teeth power" lol
it is written march 2003 in the beginning of the video, then why the title is spring 2006 ?? Not 2003
+Ahmad K Mostafa The course was published on MIT OpenCourseWare in spring 2006.
*****
Got it .
Thanks ^-^
good morning
Where is the Euler-Cauchy Equations?
in the problem set of the book
@Liaomiao The following isn't bad if ever: Power Series/Euler's Great Formula | MIT Highlights of Calculus
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).
wow!
Can any one say the name of this professor....plsss???
Professor Arthur Mattuck
@@mitocw thanks ...
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?
Where is the 18th???
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!
@shinim3gami This comment scares me.
65 guys who like this, 4 who DIDN'T understand :D
Good content, but quality is terrible!!