Fourier Series

Рет қаралды 471,861

8 жыл бұрын

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

Пікірлер: 232

@smashshred3249 6 жыл бұрын

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

@muneebasghar8042 4 жыл бұрын

And students are willing to learn

@anselmoufc 3 жыл бұрын

@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 жыл бұрын

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 жыл бұрын

kzfaq.info/get/bejne/gKxmps6XmcvFdGg.html

@emanuelriquelmemontoya3819 3 жыл бұрын

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 жыл бұрын

"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 Жыл бұрын

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

@shivaniits 6 жыл бұрын

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

@vibinjacob4610 3 жыл бұрын

kzfaq.info/get/bejne/gKxmps6XmcvFdGg.html

@johningeerlandsen4279 Жыл бұрын

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

@afluffyhamster9709 8 жыл бұрын

This is gold

@ErikPukinskis 7 жыл бұрын

Pure gold

@BENGAL-PALM-COMPANY 3 жыл бұрын

Diamond

@pisrutphummirat5594 6 жыл бұрын

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

@OswaldChisala 7 жыл бұрын

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

@shafqat1138 4 жыл бұрын

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

@caseyli5580 5 жыл бұрын

By far the best explanation on KZfaq. Thank you!

@ErnestoIser 8 жыл бұрын

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

@maxwellsequation4887 3 жыл бұрын

Yes...... "Roots"

@vibinjacob4610 3 жыл бұрын

kzfaq.info/get/bejne/gKxmps6XmcvFdGg.html

@safkanderik7217 8 жыл бұрын

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

@devindrasingh3536 4 жыл бұрын

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

@estebanlopez1701 4 жыл бұрын

Thanks for making this possible, MIT.

@vas5182 Жыл бұрын

A brilliant gem of a lecture. Thanks Prof.

@kotreshmarali1203 7 жыл бұрын

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

@aoiroadelacvg7489 5 жыл бұрын

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

@imranq9241 4 жыл бұрын

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 жыл бұрын

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

@cpadude123 4 жыл бұрын

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

@brazhell 7 жыл бұрын

Thank you Mr. Strang, very well explained.

@kedu4allknowledge_and_educ255 Жыл бұрын

Thank you Prof Strang for the wonderful explanations.

@georgesadler7830 2 жыл бұрын

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

@declanwk1 6 жыл бұрын

one of the best lectures I have ever seen

@quantummath 6 жыл бұрын

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

@s4ulyaniv35 4 жыл бұрын

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

@santiagoarce5672 4 жыл бұрын

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

@englishinenglish3473 Жыл бұрын

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

@maxemc2716 4 жыл бұрын

I'm crying. It's so beautiful.

@aleksandarjovanovic9080 7 жыл бұрын

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!

@Matchless_gift 4 жыл бұрын

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

@sukumarde8972 2 жыл бұрын

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.

@jonhouck7604 3 жыл бұрын

Strang is an awesome an professor makes the difficult subjects comprehensible

@negargh4208 7 жыл бұрын

teaching was so clear . thank you professor

@Abdulrazak-pe7ps 6 жыл бұрын

Really good and great opportunity for the students

@funkyiceman 7 жыл бұрын

Just brilliant tuition thanks!

@pipertripp 3 жыл бұрын

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

@heddeebongmasango Ай бұрын

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

@qzorn4440 7 жыл бұрын

this one kool professor. thanks for the fourier stuff.

@The112Windows 6 жыл бұрын

I have achieved enlightenment watching this video.

@julesleb 4 жыл бұрын

Professor strang, you freaking legend.

@amit92000 4 жыл бұрын

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

@viciadoemhalo3 2 жыл бұрын

Old people are the ones with knowledge...

@nileshtiwari6851 4 жыл бұрын

Nicely explained and in a very simple way

@shubhamghosal9336 2 жыл бұрын

We all just witnessed MASTER at work!

@tek1234 5 жыл бұрын

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

@avadoty774 6 ай бұрын

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

@ebenfalls9929 2 жыл бұрын

i love this guy and his explanation

@dreamscometrue5013 2 жыл бұрын

Wow. My whole semester in 10 minutes. Genius

@trickamathematica4019 7 жыл бұрын

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 жыл бұрын

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

@snehamathivanan7679 4 жыл бұрын

Wow...Best video on Fourier series..

@jamieeccleston2988 4 жыл бұрын

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

@wontpower 5 жыл бұрын

This video literally made my jaw drop

@aliqobadian-kalhor9485 6 жыл бұрын

wished I had this professor when I was in school

@Rakabhush_DoubleZeroEight 5 ай бұрын

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.

@enfermo64 7 жыл бұрын

Excelente, claro y preciso

@philidor9657 5 жыл бұрын

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

@erencolak7387 4 жыл бұрын

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.

@rohanmandloi7561 Жыл бұрын

That was awesome!!

@nedbowlas913 4 жыл бұрын

this has been very helpful. thank you.

@siamak1246 2 жыл бұрын

This shows why MIT is good one!

@ghazanfarkhan4986 Жыл бұрын

best platform to learn and concept clearence thanks

@creativegoods7737 7 жыл бұрын

Thank you from Algeria

@kituli1438 3 жыл бұрын

Excellent Teacher! Thanks a lot!

@lockercoin3693 8 жыл бұрын

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

@bobthornton8282 6 жыл бұрын

This guy is incredible

@user-kd1gf4xu8k 4 ай бұрын

Excellent lecture

@abiolaadeye2961 4 жыл бұрын

Awesome video!

@ataa510 6 жыл бұрын

thanks Sir Gilbert Strang

@mehmetcetinkaya2700 Жыл бұрын

Adamsınız profesörümm

@sachinpradeep6968 4 жыл бұрын

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

@_HJ_K 3 жыл бұрын

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!

@jacobvandijk6525 3 жыл бұрын

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.

@shavuklia7731 7 жыл бұрын

amazing, thank you!

@jenishmonpara 3 жыл бұрын

His spirit and methodology

@user-yy6ij4qs5o 4 жыл бұрын

Great lecture

@RyanAmplification 6 ай бұрын

Ok I got Fourier series. Now on to Fiveier

@siddharajsinhvaghela5924 7 жыл бұрын

Thank you very much sir

@rktiwa 3 ай бұрын

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

@MatteoIervasi96 6 жыл бұрын

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

@andrewniven4350 5 жыл бұрын

Great teacher

@kaushikkvasan5607 5 жыл бұрын

awesome video

@taewoonglee4894 7 жыл бұрын

Never be better

@sohamsdays 7 жыл бұрын

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

@lucasm4299 7 жыл бұрын

Sohams Day There's 2 now :(

@lukeusperez8585 7 жыл бұрын

Now there are 12!

@---hz3sy 6 жыл бұрын

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

@talsokolinsky6611 6 жыл бұрын

20 now

@danilorosich 6 жыл бұрын

27!

@michaelmolter8828 2 жыл бұрын

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

@c.danielpremkumar8495 5 жыл бұрын

Excellent !

@ozzyfromspace 4 жыл бұрын

How is this man so easy to understand?

@newton464 15 күн бұрын

Wonderful!

@WaveIO 3 жыл бұрын

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!