Professor Strang is awesome, but I found this video to be a bit rushed. He ignored many subtleties. For instance the series produces a periodic function, so the example at the end actually gives (... + δ(x+2pi) + δ(x) + δ(x-2pi) + ...) which is a periodic version of the Dirac delta spike. Another point is that (given f is periodic) we can integrate over any full cycle, it doesn’t have to be -pi to pi. It’s also worth mentioning that we could produce functions with any period T by replacing x with 2(pi)x/T, but this slightly changes the coefficient formula (1/pi in front becomes 2/T). Also it’s not hard to show the orthogonality (it comes down to a simple trig identity) instead of just assuming it. Still a good video just a little too brief. Much respect to professor Strang though.
not really you have professors with amazing skills pretty much everywhere in the world, but in the mit all the professors also some of the best researchers in the world, and the ones that reinvented so many fields
I'm still here MIT. Though i know i failed my jee journey, be it due to my lack of effort,laziness,other life things. I WAS and AM still here.I might've been intrigued in the past and stayed here for what, maybe a couple of seconds?, but i roughly know where am i headed.I promise i will be here again even if on and off but one day, one day i will gain all the possible knowledge.All the things i need to know to atleast try to understand this complx world.I will definately one day fix myself and offer my works if god bless im able to do. I might not have it today, not tomorrow or maybe the day after.But one day i will.I still have not lost hope. I think i have tired even god helping me.I may be skeptical of everyhing but i will be there.I know i still got this.
I've read a couple of explanations and read several videos, and I find something missing. I remember old Gilbert Strang and what he tought me about Calculus and Linear Algebra, get here, I see the board, and just by looking at it I get enlightened. Thank you for everything!
To me , fourier was marvlously msthematical genius of geniuses. With much awe as to how he conceived the idea of heat propagation that can be expressed in terms of sines and cosines. With reverence to his life and works, services. Thanks.
3 years ago when I first learnt Fourier series this had been the most confusing part in that semester. (my professor didn't spent much time on this because for some reason this was not going to be in the exams) I tried to work it out and with my own interpretations but failed. and since then I had been haunted by it, I come across Fourier from time to time in my study, I know how to apply the equations but never understand why these equations come to be like this, I never comprehended it. Thank you professor Strang for saving me again! Your 18.06 lectures also helped me a lot!
You nailed it elucidately , Prof. Strang. Now lam at peace with Fourier series.You have been precise , and hammered home the orthogonality point home, which is crucial to understanding of the Fourier series. REPLY
how exactly did he hammer the orthogonality point home? he never explained what the inner product represents graphically or logically as an integral and how that reflects on the functions we're looking at
A LOT OF WORDS FOR SOMETHING SIMPLE. Simple because functions like f(x) are just vectors! Thus, the a's, b's and c's are components and the cosines, sines and e's are basisvectors. That's why mr Strang claims that this is true: 6:06. Of course, when you dot a basisvector with a vector f(x) you get a component. When V = x . i + y . j + z . k, then: y = j . V. Just compare: 8:29.
I really hope at his age to be able at least to remember about ak and bk... I really love Fourier series but time will tell how all this will end up for me!
Thank you very much. But why we can find Fourier transform for delta function since delta function is not a periodic function. And why can we substitute delta(0) = 1. In the video, the prof say that delta(0) is infinite.
He doesn’t say the delta function at 0 is equal to 1, but its integral is. This is a property of the delta function, namely that its integral is equal to 1 whenever the extremes of integration include 0. Why this property holds is explained very nicely in ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-iii-fourier-series-and-laplace-transform/step-and-delta-functions-integrals-and-generalized-derivatives/ (pdf: Delta Functions: Unit Impulse -- ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-iii-fourier-series-and-laplace-transform/step-and-delta-functions-integrals-and-generalized-derivatives/MIT18_03SCF11_s24_3text.pdf) where delta is pictured as the limit of box functions of area 1 (11:08 picture of the delta function: ruclips.net/video/vA9dfINW4Rg/видео.html)
Reason why MIT is at the top is because teachers can teach.
And students are willing to learn
@Mr. Gang Banger True, but, in addition, Strang is a terrific teacher. I am an engineering teacher myself and I want to be like him when I grow up ;)
Professor Strang is awesome, but I found this video to be a bit rushed. He ignored many subtleties. For instance the series produces a periodic function, so the example at the end actually gives (... + δ(x+2pi) + δ(x) + δ(x-2pi) + ...) which is a periodic version of the Dirac delta spike. Another point is that (given f is periodic) we can integrate over any full cycle, it doesn’t have to be -pi to pi. It’s also worth mentioning that we could produce functions with any period T by replacing x with 2(pi)x/T, but this slightly changes the coefficient formula (1/pi in front becomes 2/T). Also it’s not hard to show the orthogonality (it comes down to a simple trig identity) instead of just assuming it. Still a good video just a little too brief. Much respect to professor Strang though.
ruclips.net/video/JF6skf4eaD4/видео.html
not really you have professors with amazing skills pretty much everywhere in the world, but in the mit all the professors also some of the best researchers in the world, and the ones that reinvented so many fields
"Ao has a little bit different formula. The π changes to 2π. I'm sorry about that."
Lol, legend. I love Prof Strang.
Dr. Gilbert Strang is legendary -- absolutely love his lectures!
After searching for countless articles on fourier series , this one really helps , many thanks professor !
ruclips.net/video/JF6skf4eaD4/видео.html
I feel more relieved for my midterm tomorrow now. Thank you loads, Professor. You're super awesome!
I don't think he could have presented this introduction to Fourier Transforms any better! Spectacular job, professor!
Thank you for the open courseware so we can learn from MIT around the world. Cheers. :)
after one year of searching finally i found a good stuff about Fourier series
wiche helped me to get evry thing
Thanks
By far the best explanation on RUclips. Thank you!
Absolute mad lad. Cheers Professor Gil from down under! Loved your book on Linear Algebra.
This is an amazing opportunity to go back to the roots. Thank you for making this possible
Yes...... "Roots"
ruclips.net/video/JF6skf4eaD4/видео.html
Really a awesome and comprehensible lecture on the basic concept of Fourier series.
Prof Gilbert Strang .. got me through Lin Alg all the way to graduating as a math major with honors. Wish I could take a real class at MIT
I'm still here MIT. Though i know i failed my jee journey, be it due to my lack of effort,laziness,other life things. I WAS and AM still here.I might've been intrigued in the past and stayed here for what, maybe a couple of seconds?, but i roughly know where am i headed.I promise i will be here again even if on and off but one day, one day i will gain all the possible knowledge.All the things i need to know to atleast try to understand this complx world.I will definately one day fix myself and offer my works if god bless im able to do. I might not have it today, not tomorrow or maybe the day after.But one day i will.I still have not lost hope. I think i have tired even god helping me.I may be skeptical of everyhing but i will be there.I know i still got this.
I've read a couple of explanations and read several videos, and I find something missing. I remember old Gilbert Strang and what he tought me about Calculus and Linear Algebra, get here, I see the board, and just by looking at it I get enlightened. Thank you for everything!
My professor literally was like “yeah I’m not a great lecturer, MIT puts all their stuff online though you should check it out” 😐
Watch most other any video on Fourier Transforms and you'll see what a gem the teaching of Prof. Strang is.
God tier course, Gilbert Strang
is the best teacher I have seen.
A brilliant gem of a lecture. Thanks Prof.
I bow my head and salute to your teaching Sir. :)
Awesome Professor.
I tried to look for other lectures about this subject, but nobody's better than Prof. Strang.
Thanks for making this possible, MIT.
To me , fourier was marvlously msthematical genius of geniuses. With much awe as to how he conceived the idea of heat propagation that can be expressed in terms of sines and cosines. With reverence to his life and works, services. Thanks.
Whoah came from Mattuck's lecture on it and this is much clearer. So quick and easy to understand
one of the best lectures I have ever seen
It blows my mind how any function can be represented as harmonics, truly something to know :)
Thank you so much. I’ll be eternally grateful.
Thank you Prof Strang for the wonderful explanations.
This lecture helps me understand Fourier Series from start to finish.
This is gold
Pure gold
Diamond
He started this lecture where he left in laplace equation video, amazing series of lectures to vizualize each and every steps.
Thank you Mr. Strang, very well explained.
This professor is just AMAZING .... hats off.
I'm crying. It's so beautiful.
This is the best teacher I have seen in my entire life😮
like a boss. That was a very useful lecture. I got more out of that than other bits on the topic.
i love this guy and his explanation
Just brilliant tuition thanks!
Strang is an awesome an professor makes the difficult subjects comprehensible
Nicely explained and in a very simple way
teaching was so clear .
thank you professor
Really good and great opportunity for the students
this one kool professor. thanks for the fourier stuff.
My professor "teached" us all the fourie and basic signals in 5 lessons... a true legend
I have achieved enlightenment watching this video.
Professor strang, you freaking legend.
this has been very helpful. thank you.
Excelente, claro y preciso
3 years ago when I first learnt Fourier series this had been the most confusing part in that semester.
(my professor didn't spent much time on this because for some reason this was not going to be in the exams)
I tried to work it out and with my own interpretations but failed.
and since then I had been haunted by it, I come across Fourier from time to time in my study, I know how to apply the equations but never understand why these equations come to be like this, I never comprehended it.
Thank you professor Strang for saving me again! Your 18.06 lectures also helped me a lot!
God bless any institution that sets out to teach for the betterment of humanity, not selling sealed papers.
wished I had this professor when I was in school
Wow...Best video on Fourier series..
Wow. My whole semester in 10 minutes. Genius
We all just witnessed MASTER at work!
This is the probably the best class I ever watched(I already know the topic, I am just refreshing my memory)
But damn, I wanna take class from him.
best platform to learn and concept clearence thanks
This video literally made my jaw drop
This shows why MIT is good one!
You made this so much easier than my professor did today.....
Excellent Teacher! Thanks a lot!
You nailed it elucidately , Prof. Strang. Now lam at peace with Fourier series.You have been precise , and hammered home the orthogonality point home, which is crucial to understanding of the Fourier series.
REPLY
how exactly did he hammer the orthogonality point home? he never explained what the inner product represents graphically or logically as an integral and how that reflects on the functions we're looking at
Thank you from Algeria
What all else couldn't do in hours he did in minutes. But he is Gilbert Strang then.
I want to take a class like this!! JUsT WOWW!
This guy is incredible
amazing, thank you!
His spirit and methodology
That was awesome!!
His body might seems like old but his spirit and knowledge is high 👍
Old people are the ones with knowledge...
How I calculate the fourier function from a given curve (the only data is the curve)
nice video! keep up the good work guys!!!
A LOT OF WORDS FOR SOMETHING SIMPLE. Simple because functions like f(x) are just vectors! Thus, the a's, b's and c's are components and the cosines, sines and e's are basisvectors. That's why mr Strang claims that this is true: 6:06. Of course, when you dot a basisvector with a vector f(x) you get a component. When V = x . i + y . j + z . k, then: y = j . V. Just compare: 8:29.
Excellent lecture
Wooo! Prof. Strang is great! Even a dumbass like me finally understood the Fourier series!
Thank you
Thank you very much sir
What if you don’t want the domain of ‘x’ to be limited to -pi < x < pi?
thanks Sir Gilbert Strang
Awesome video!
I really hope at his age to be able at least to remember about ak and bk... I really love Fourier series but time will tell how all this will end up for me!
Wonderful!
Ok I got Fourier series. Now on to Fiveier
Adamsınız profesörümm
Great lecture
I wish we had professors half as good over at ASU.
is the Dirac delta function satisfies Dirichlet's condition? I think this function does not show periodicity,
Excellent !
How is this man so easy to understand?
Never be better
this man is more of a god i realized this when i listened to his lectures on linear algebra
Great teacher
This is a very complicated way to explain a very simple idea.
awesome video
Man, he is good!
0 dislikes thats awesome. Thats the power of a great video. Keep up the good work Sir.
Sohams Day
There's 2 now :(
Now there are 12!
Update: 14 dislikes now! But it wasn't me
20 now
27!
Excellent breif one
Magnificent 💙
thanks
Thanks
Thank you very much. But why we can find Fourier transform for delta function since delta function is not a periodic function. And why can we substitute delta(0) = 1. In the video, the prof say that delta(0) is infinite.
He doesn’t say the delta function at 0 is equal to 1, but its integral is. This is a property of the delta function, namely that its integral is equal to 1 whenever the extremes of integration include 0. Why this property holds is explained very nicely in ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-iii-fourier-series-and-laplace-transform/step-and-delta-functions-integrals-and-generalized-derivatives/ (pdf: Delta Functions: Unit Impulse -- ocw.mit.edu/courses/mathematics/18-03sc-differential-equations-fall-2011/unit-iii-fourier-series-and-laplace-transform/step-and-delta-functions-integrals-and-generalized-derivatives/MIT18_03SCF11_s24_3text.pdf) where delta is pictured as the limit of box functions of area 1
(11:08 picture of the delta function: ruclips.net/video/vA9dfINW4Rg/видео.html)
This is heaven