Fourier Series

[@smashshred3249]

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

[@muneebasghar8042]

And students are willing to learn

[@anselmoufc]

@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]

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]

kzbin.info/www/bejne/gHeZpJ6cacqUepY

[@emanuelriquelmemontoya3819]

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

[@juniorcyans2988]

Good teachers make the materials easy to understand, so that students can learn. The problem is that many teachers teach poorly and that's why I'm here learning from YT videos. Thank MIT teachers!

[@theodoremolloy9007]

LOved this! Im studing electrical engineering and really needed this! I got low second five times, and I am on my second retake of my second year. Im also on acedemic probation at oxford brooks! this single-handedly SAVED MY DEGREE!!! thanks again! :)

[@Hannah-ew3ri]

I’m your professor and I hate you

[@SK-ww5zf]

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

[@gerrygus]

the man explained both linear algebra and Fourier in 15 minutes, while school failed to teach me in three classes. Astonishing mastery!

[@umikohiromi6015]

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

[@shivaniits]

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

[@vibinjacob4610]

kzbin.info/www/bejne/gHeZpJ6cacqUepY

[@ErnestoIser]

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

[@maxwellsequation4887]

Yes...... "Roots"

[@vibinjacob4610]

kzbin.info/www/bejne/gHeZpJ6cacqUepY

[@OswaldChisala]

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

[@pisrutphummirat5594]

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

[@Erlandsen-tech-private]

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

[@Rakabhush_DoubleZeroEight]

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.

[@TragicGFuel]

Chup lazy lodu

[@JamesBind-ek5yy]

Hello bro just here to remind you after 8 months that you’re not alone, keep going no matter what and let’s go beyond the limit of our natural perception and understanding.

[@safkanderik7217]

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

[@avadoty774]

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

[@imranq9241]

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

[@caseyli5580]

By far the best explanation on KZbin. Thank you!

[@shafqat1138]

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

[@englishinenglish3473]

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

[@afluffyhamster9709]

This is gold

[@ErikPukinskis]

Pure gold

[@HARDY-PALM-LIFE]

Diamond

[@jamieeccleston2988]

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

[@heddeebongmasango]

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

[@helwing01]

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

[@aleksandarjovanovic9080]

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!

[@_HJ_K]

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!

[@devindrasingh3536]

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

[@sukumarde8972]

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.

[@aoiroadelacvg7489]

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

[@tek1234]

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

[@sohamsdays]

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

[@lucasm4299]

Sohams Day There's 2 now :(

[@lukeusperez8585]

Now there are 12!

[@talsokolinsky6611]

20 now

[@danilorosich]

27!

[@divyanshmani4397]

These assholes!

[@kotreshmarali1203]

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

[@estebanlopez1701]

Thanks for making this possible, MIT.

[@The112Windows]

I have achieved enlightenment watching this video.

[@vas5182]

A brilliant gem of a lecture. Thanks Prof.

[@cpadude123]

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

[@rafaelsouza4575]

I ran it in Python to test the Fourier series from the delta function, and incredibly, the series just plotted the delta function like a charm. Unbelievable!

[@MohamedAhmed-le8mv]

I would like to see your code. hh not that I can't find it or write it on my own. but I would like to see it

[@Matchless_gift]

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

[@georgesadler7830]

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

[@trickamathematica4019]

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]

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

[@jacobvandijk6525]

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.

[@santiagoarce5672]

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

[@rktiwa]

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

[@quantummath]

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

[@philidor9657]

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

[@declanwk1]

one of the best lectures I have ever seen

[@amit92000]

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

[@viciadoemhalo3]

Old people are the ones with knowledge...

[@dreamscometrue5013]

Wow. My whole semester in 10 minutes. Genius

[@wontpower]

This video literally made my jaw drop

[@shubhamghosal9336]

We all just witnessed MASTER at work!

[@MatteoIervasi96]

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

[@s4ulyaniv35]

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

[@TheWalterHWhite]

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.

[@jonhouck7604]

Strang is an awesome an professor makes the difficult subjects comprehensible

[@NaveenKumar-yu6eo]

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

[@siamak1246]

This shows why MIT is good one!

[@aliqobadian-kalhor9485]

wished I had this professor when I was in school

[@maxemc2716]

I'm crying. It's so beautiful.

[@julesleb]

Professor strang, you freaking legend.

[@WaveIO]

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!

[@Abdulrazak-pe7ps]

Really good and great opportunity for the students

[@brazhell]

Thank you Mr. Strang, very well explained.

[@ozzyfromspace]

How is this man so easy to understand?

[@pipertripp]

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

[@mikewaxx]

This is quite informative IF you already have pretty good knowledge of fourier series

[@FergusScotchman]

That's exactly what I was thinking.... everyone who already took applied math with Fourier Transforms thinks this is great. If you don't know anything about Fourier Transforms, you have no idea what the heck he is doing or why. That's why I always hated textbooks from Caltech and MIT. They were great if you wanted to go back and re-learn materials, but terrible at explaining basic concepts to someone who has no exposure. I mean who starts a lecture by saying I'm not sure where to start with Fourier Transforms, but what we are trying to get is a function with a coefficient for sine and a coefficient for a cosine value? My first question is WTF would you want that?

[@nealzerzz792]

@@FergusScotchmani mean thats what youre lookin for when doing harmonic analysis But i agree this isnt much of an introduction to the concept

[@ebenfalls9929]

i love this guy and his explanation

[@kedu4allknowledge_and_educ255]

Thank you Prof Strang for the wonderful explanations.

[@ghazanfarkhan4986]

best platform to learn and concept clearence thanks

[@qzorn4440]

this one kool professor. thanks for the fourier stuff.

[@snehamathivanan7679]

Wow...Best video on Fourier series..

[@RyanAmplification]

Ok I got Fourier series. Now on to Fiveier

[@erencolak7387]

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.

[@Christopher-e7o]

X,2×+5=8[n3]

[@josiahbaker7811]

This guy's version of hell is 30 hands raised up, all asking if he can write in + C

[@philippebegin562]

Very clear explanations! Thank you!

[@negargh4208]

teaching was so clear . thank you professor

[@pythagorasaurusrex9853]

Good video! I think I discovered a little tiny mistake on the first board at the beginning of the video. Sir, you write Sum(...cos)+Sum(...sin)=sum(...e^i(...)). As the complex form gives complex numbers for each term to sum up, the left side only contains real numbers. I think you forgot the "i" in front for the sin-summation. :)

[@DBG01]

This is mistake in original theory itself, some how imaginary number "i" was introduced in the derivation, so as to meet the equality.

[@obzen12]

can't b_n contain i as well

[@JFrost-rf8ix]

Anyone please explain the part from 3:40 - 4:00 a bit clearly .... Pls explain how the lower and higher values of k will change the frequency more visually??/

[@Novak2611]

you can plot for example the graph of sin(2x), sin(5x), sin(9x) using for example:www.desmos.com/calculator you will see that the higher k the more it oscillates

[@g1ntok147]

Sinwt

[@creativegoods7737]

Thank you from Algeria

[@nileshtiwari6851]

Nicely explained and in a very simple way

[@funkyiceman]

Just brilliant tuition thanks!

[@ekhliousful]

@7:25 when the professor said"this times this when i integrate gives zero"why is that i mean the orthogonality gives zero when talking this function how to relate between the two cases of vectors and functions? and from where the cos (kx) came ?& what is it or its nature ?

[@jacobvandijk6525]

Just read my reaction.

[@ekhliousful]

@@jacobvandijk6525 where is that?

[@jacobvandijk6525]

@@ekhliousful Here it is: 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.

[@ekhliousful]

@@jacobvandijk6525 thanks for your time i really appreciate it

[@jacobvandijk6525]

@@ekhliousful You're welcome, Ahmed.

[@josefinasolilabambidesousa8297]

Muito obrigado pela belíssima explicação.👏👏🇦🇴🇦🇴🇦🇴🇦🇴

[@sachinpradeep6968]

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

[@michaelmolter8828]

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

[@davidjohnson-my6sr]

at around 14 mins, why isnt a0 equal to 0 for delta function? we split the integral up from -pi to 0, 0 to 0, 0 to pi, so wont the integral evaluate to 0 + 0 + 0? ir doesnt matter that the function is one for only x=0

[@ChrisGeiersbach]

I was confused by this too. The en.wikipedia.org/wiki/Dirac_delta_function is "a function that is equal to zero everywhere except for zero and whose integral over the entire real line is equal to one".

[@pineapplegodguy]

it's because the delta function's definition is the derivative of the step function. thus the integral of the delta is the step, and since the step equals 1 at pi and 0 at -pi, the integral of the delta in that interval is 1-0=1

[@jenishmonpara]

His spirit and methodology

[@rohanmandloi7561]

That was awesome!!

[@ahaulss93]

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

[@bobthornton8282]

This guy is incredible

[@hashimkhan9719]

Everything's clear to me except for one point. Coskx cancelling all the SinNx terms make sense. But how come coskx knocks out all other cosnx terms except the one with n=k? After all, its a dot product.

[@toantruong9533]

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.

[@giovannaroda3177]

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: kzbin.info/www/bejne/rHKclZl_g7xniMk)

[@jonhouck7604]

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...

[@nedbowlas913]

this has been very helpful. thank you.

[@ni3cat]

Professor says, it is going to take 2 sessions to explain Fourier series but video itself is 16 minutes.

[@MuhmmadShahAlam-i9k]

Excellent lecture

[@AlexAlex-fo9gt]

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]

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

[@kituli1438]

Excellent Teacher! Thanks a lot!

[@leophysics]

This is heaven

[@taewoonglee4894]

Never be better

[@ataa510]

thanks Sir Gilbert Strang

[@SpicyTurkey83]

goodness does it make a difference when the professor's actually SPEAK English.

[@abiolaadeye2961]

Awesome video!