Fourier Series

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MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015
View the complete course: ocw.mit.edu/RES-18-009F15
Instructor: Gilbert Strang
A Fourier series separates a periodic function into a combination (infinite) of all cosine and since basis functions.
License: Creative Commons BY-NC-SA
More information at ocw.mit.edu/terms
More courses at ocw.mit.edu

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5 май 2016

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Комментарии : 232

@smashshred3249 6 лет назад

Reason why MIT is at the top is because teachers can teach.

@muneebasghar8042 4 года назад

And students are willing to learn

@anselmoufc 3 года назад

@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 ;)

@nathanaelcase2783 3 года назад

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.

@vibinjacob4610 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-JF6skf4eaD4.html

@emanuelriquelmemontoya3819 3 года назад

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

@umikohiromi6015 6 лет назад

"Ao has a little bit different formula. The π changes to 2π. I'm sorry about that." Lol, legend. I love Prof Strang.

@SK-ww5zf Год назад

Dr. Gilbert Strang is legendary -- absolutely love his lectures!

@shivaniits 6 лет назад

After searching for countless articles on fourier series , this one really helps , many thanks professor !

@vibinjacob4610 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-JF6skf4eaD4.html

@johningeerlandsen4279 Год назад

Thank you for the open courseware so we can learn from MIT around the world. Cheers. :)

@pisrutphummirat5594 6 лет назад

I feel more relieved for my midterm tomorrow now. Thank you loads, Professor. You're super awesome!

@OswaldChisala 7 лет назад

I don't think he could have presented this introduction to Fourier Transforms any better! Spectacular job, professor!

@safkanderik7217 8 лет назад

after one year of searching finally i found a good stuff about Fourier series wiche helped me to get evry thing Thanks

@avadoty774 7 месяцев назад

My professor literally was like “yeah I’m not a great lecturer, MIT puts all their stuff online though you should check it out” 😐

@caseyli5580 6 лет назад

By far the best explanation on RU-vid. Thank you!

@ErnestoIser 8 лет назад

This is an amazing opportunity to go back to the roots. Thank you for making this possible

@maxwellsequation4887 3 года назад

Yes...... "Roots"

@vibinjacob4610 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-JF6skf4eaD4.html

@shafqat1138 4 года назад

Absolute mad lad. Cheers Professor Gil from down under! Loved your book on Linear Algebra.

@Rakabhush_DoubleZeroEight 5 месяцев назад

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.

@afluffyhamster9709 8 лет назад

This is gold

@ErikPukinskis 7 лет назад

Pure gold

@BENGAL-PALM-COMPANY 3 года назад

Diamond

@imranq9241 4 года назад

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

@helwing01 3 года назад

I tried to look for other lectures about this subject, but nobody's better than Prof. Strang.

@devindrasingh3536 4 года назад

Really a awesome and comprehensible lecture on the basic concept of Fourier series.

@estebanlopez1701 4 года назад

Thanks for making this possible, MIT.

@englishinenglish3473 Год назад

It blows my mind how any function can be represented as harmonics, truly something to know :)

@aoiroadelacvg7489 5 лет назад

God tier course, Gilbert Strang is the best teacher I have seen.

@kotreshmarali1203 7 лет назад

I bow my head and salute to your teaching Sir. :) Awesome Professor.

@cpadude123 4 года назад

Watch most other any video on Fourier Transforms and you'll see what a gem the teaching of Prof. Strang is.

@vas5182 Год назад

A brilliant gem of a lecture. Thanks Prof.

@aleksandarjovanovic9080 7 лет назад

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!

@georgesadler7830 2 года назад

This lecture helps me understand Fourier Series from start to finish.

@santiagoarce5672 4 года назад

Whoah came from Mattuck's lecture on it and this is much clearer. So quick and easy to understand

@rktiwa 4 месяца назад

What all else couldn't do in hours he did in minutes. But he is Gilbert Strang then.

@amit92000 4 года назад

His body might seems like old but his spirit and knowledge is high 👍

@viciadoemhalo3 2 года назад

Old people are the ones with knowledge...

@Matchless_gift 4 года назад

He started this lecture where he left in laplace equation video, amazing series of lectures to vizualize each and every steps.

@sukumarde8972 2 года назад

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.

@brazhell 7 лет назад

Thank you Mr. Strang, very well explained.

@quantummath 6 лет назад

This professor is just AMAZING .... hats off.

@s4ulyaniv35 4 года назад

Thank you so much. I’ll be eternally grateful.

@_HJ_K 3 года назад

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!

@kedu4allknowledge_and_educ255 Год назад

Thank you Prof Strang for the wonderful explanations.

@heddeebongmasango 2 месяца назад

This is the best teacher I have seen in my entire life😮

@maxemc2716 4 года назад

I'm crying. It's so beautiful.

@declanwk1 6 лет назад

one of the best lectures I have ever seen

@tek1234 5 лет назад

My professor "teached" us all the fourie and basic signals in 5 lessons... a true legend

@jonhouck7604 3 года назад

Strang is an awesome an professor makes the difficult subjects comprehensible

@The112Windows 6 лет назад

I have achieved enlightenment watching this video.

@julesleb 4 года назад

Professor strang, you freaking legend.

@pipertripp 3 года назад

like a boss. That was a very useful lecture. I got more out of that than other bits on the topic.

@jamieeccleston2988 5 лет назад

God bless any institution that sets out to teach for the betterment of humanity, not selling sealed papers.

@shubhamghosal9336 2 года назад

We all just witnessed MASTER at work!

@trickamathematica4019 7 лет назад

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

@anadawaween 6 лет назад

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

@Abdulrazak-pe7ps 6 лет назад

Really good and great opportunity for the students

@qzorn4440 7 лет назад

this one kool professor. thanks for the fourier stuff.

@dreamscometrue5013 2 года назад

Wow. My whole semester in 10 minutes. Genius

@wontpower 5 лет назад

This video literally made my jaw drop

@negargh4208 7 лет назад

teaching was so clear . thank you professor

@philidor9657 5 лет назад

You made this so much easier than my professor did today.....

@ebenfalls9929 2 года назад

i love this guy and his explanation

@aliqobadian-kalhor9485 6 лет назад

wished I had this professor when I was in school

@nileshtiwari6851 4 года назад

Nicely explained and in a very simple way

@funkyiceman 7 лет назад

Just brilliant tuition thanks!

@siamak1246 2 года назад

This shows why MIT is good one!

@jacobvandijk6525 3 года назад

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.

@erencolak7387 4 года назад

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.

@michaelmolter8828 2 года назад

What if you don’t want the domain of ‘x’ to be limited to -pi < x < pi?

@snehamathivanan7679 4 года назад

Wow...Best video on Fourier series..

@MatteoIervasi96 6 лет назад

Wooo! Prof. Strang is great! Even a dumbass like me finally understood the Fourier series! Thank you

@ghazanfarkhan4986 Год назад

best platform to learn and concept clearence thanks

@jenishmonpara 3 года назад

His spirit and methodology

@bobthornton8282 6 лет назад

This guy is incredible

@creativegoods7737 7 лет назад

Thank you from Algeria

@RyanAmplification 6 месяцев назад

Ok I got Fourier series. Now on to Fiveier

@sachinpradeep6968 4 года назад

I want to take a class like this!! JUsT WOWW!

@enfermo64 7 лет назад

Excelente, claro y preciso

@nedbowlas913 4 года назад

this has been very helpful. thank you.

@rohanmandloi7561 Год назад

That was awesome!!

@kituli1438 3 года назад

Excellent Teacher! Thanks a lot!

@ataa510 6 лет назад

thanks Sir Gilbert Strang

@user-kd1gf4xu8k 4 месяца назад

Excellent lecture

@WaveIO 3 года назад

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!

@lockercoin3693 8 лет назад

nice video! keep up the good work guys!!!

@sohamsdays 7 лет назад

0 dislikes thats awesome. Thats the power of a great video. Keep up the good work Sir.

@lucasm4299 7 лет назад

Sohams Day There's 2 now :(

@lukeusperez8585 7 лет назад

Now there are 12!

@---hz3sy 6 лет назад

Update: 14 dislikes now! But it wasn't me

@talsokolinsky6611 6 лет назад

20 now

@danilorosich 6 лет назад

27!

@shavuklia7731 7 лет назад

amazing, thank you!

@TheWalterHWhite Год назад

I use to attend MIT, but not as a student. I was a janitor, but I had a penchant for non-linear equations and Fourier systems. One of the professors, a noble Fields recipient, would put equations for students to solve on a board outside the classroom.

@newton464 Месяц назад

Wonderful!

@ozzyfromspace 4 года назад

How is this man so easy to understand?

@NaveenKumar-yu6eo 6 лет назад

this man is more of a god i realized this when i listened to his lectures on linear algebra

@ahaulss93 6 лет назад

I wish we had professors half as good over at ASU.

@azer1838 7 лет назад

How I calculate the fourier function from a given curve (the only data is the curve)

@siddharajsinhvaghela5924 7 лет назад

Thank you very much sir

@ShubhamSoni-kz9eu 4 года назад

is the Dirac delta function satisfies Dirichlet's condition? I think this function does not show periodicity,

@abiolaadeye2961 4 года назад

Awesome video!

@mehmetcetinkaya2700 Год назад

Adamsınız profesörümm

@taewoonglee4894 7 лет назад

Never be better

@AlexAlex-fo9gt 2 года назад

11:00-11:25 As written in description for this video Fourier series is used for periodic functions. Is the Delta-function periodic function?

@believe8463 2 года назад

Any function can be made periodic if you allow it to be defined on some interval [a,b]

@covidhoax7646 Год назад

This is a very complicated way to explain a very simple idea.

@c.danielpremkumar8495 5 лет назад

Excellent !

@user-yy6ij4qs5o 4 года назад

Great lecture

@blzKrg 3 года назад

Man, he is good!

@jonhouck7604 3 года назад

Correct me if I'm wrong but isn't the integral from 1/2pi *( integral -pi to pi of 1 dx ) = 1/2*pi *(pi-(-pi)) = 1?? Maybe I'm having a brain fart...

@husseinalsultan 3 года назад

Excellent breif one

@gangadharpeyyala9187 4 года назад

Did he teach the origin of Fourier series like why anybody want to represent any function in terms of sine and cosine functions.. If he did so, pls tell..