Fourier Series Part 1

Joseph Fourier developed a method for modeling any function with a combination of sine and cosine functions. You can graph this with your calculator easily and watch the modeling in action. Make sure you're in radian mode and let c=1:
f(x) = 4/(pi)*sin(x) + 4/(3pi)*sin(3x) + 4/(5pi)*sin(5x) + 4/(7pi)*sin(7x) + 4/(9pi)*sin(9x) + 4/(11pi)*sin(11x)
Http://www.wolframalph... is also an excellent resource for graphing this function. Click here for convenience: www.wolframalp...

[@saulremi314]

I had a friend in grad school who needed Fourier Series and so I made these videos for him.

[@ShravanSwamy]

thankyou to that friend, also to you for making the videos ;)

[@HawkFest]

I'd like us to be friends then 😁... In exchange would you like to learn Assembler programming using arithmetic bit-shift techniques for some mathematical operators like exponential functions in base 2? Skiing? Playing drums? The best salad dressing in the world?... Joke aside, it's very generous of you, thank you!

[@brianty6676]

You're a good friend.

[@KeshariPiyush24]

@@HawkFest I am interested in learning how binary calculations are done for some complex tasks like calculating square root of 2.....can you please make a video on it?

[@romylubag4290]

@@HawkFest b9b k9

[@IntisarJabir]

best explanation for people like us who are in engineering when we shouldn't be

[@letsoalomogaumabolo1638]

😭😭😭

[@jeremijosol9360]

THIS IS 9 YEARS AGO AND I FIND THIS VERY HELPFUL! I LOVE HOW THE WAY YOU TEACHES AND MADE ME LEARN IN JUST 8 MINUTES😍 THANK YOUUU

[@duncancarr7822]

Wow. This is a great bunch of tutorials. I watched 3 hours of Stanford lectures on this and pretty much didn't learn anything. It was horrible. I wasn't anticipating success. I was gobsmacked at how beautifully you explained all this. I learned so much. Thank you!

[@AlphaPontiff]

Thanks Duncan!

[@imln]

Oooooo😮😮

[@laylaknopfler5989]

Lucky friend

[@mukwati]

Just got recommended this from SMARTER EVERYDAY with Dustin. I have learnt from these videos and I had to open them and give them all a like because i never really did 10 years ago. Thanks you.

[@JSA2019]

I wish the guy who (tried) to teach me this stuff at college was as good as you.

[@saulremi314]

+JSA2019 :)

[@stonebrother3751]

at least he tried

[@vector6077]

can relate.

[@redgefleming1535]

U cant complain if u dont pay him

[@leif1075]

What college did you go to?

[@NiallRogers]

I don't understand why he isn't receiving my tuition money. Much more effective in 30 mins than the three lectures at school.

[@AnuRMusicVideos]

I tried to read about this in my textbook and had no idea what they were trying to do. This is so much easier, thank you!!

[@sulekhasreenivas1946]

During my college days I was actually broken down during this topic. Because most of the students and teacher just following the equation to just find the answer. But I was always worrying about what's the meaning of this thing.I thought it was my inefficiency to understand this like other.Today I understand both maths and myself. Thank you brother.

[@VitorJTekkRodrigues]

How come you made me understand this so easily when I tortured myself reading about it for hours without any progress?

[@saulremi314]

+Vitor Rodrigues :)

[@okaypam]

+Big Bang Physics Can you please talk about fourier transform and laplace transform! PLEASE! you made it so easy to understand! it is ok if it takes you 4 videos hahah but pleaseee

[@morgansampi5336]

+Vitor Rodrigues RIGHT? my god.. hey, i'm guesing you already did your exam. Was this enough? if i watched the four parts of his videos " fourier series" are those considered as a whole chapter done?

[@morgansampi5336]

+Vitor Rodrigues RIGHT? my god.. hey, i'm guesing you already did your exam. Was this enough? if i watched the four parts of his videos " fourier series" are those considered as a whole chapter done?

[@hamadosman8073]

Yea I guess

[@MexterO123]

Excellent Tutorial, I learned more here than 3 days of engineering lecture. :/

[@EKGaming]

6 years down the line here I am with the same situation.

[@ChrisBennett17]

Easily the best explanation i've seen yet on youtube

[@saulremi314]

Chris Bennett Excellent!

[@S3ANPukekoh3]

wow, you explained what my DE lecturer couldn't explain over a 2 hour lecture

[@BeldwinMinor]

Thanks so much! I've been trying to use the Fourier functions for a project without really understanding what I'm doing. This helped things make A LOT more sense.

[@jaijoshi950]

You don't know what have you done.. You have Taught and made this complex mathematical equation easy for a biologist like me ..... Great work thanks for posting such a beautiful and super explanatory video.. : )

[@saulremi314]

Any time, glad to help

[@W-ibrahim_Basha]

"Shokran Jazeelan" that's in English Thank you so much :) Now I understand what is Fourier series and that's because of you great teacher. I take off my hat to you :) Sudan University

[@yassiraladdin5886]

It's very cool to see a sudanese student here!!!

[@DivyanshBatham]

Now that's called an A-Class Explanation, just loved it! Instantly shared it to my friends for better understanding of the CONCEPT. Thanks A LOT :D

[@alaajerbi8002]

Thank you very much Sir! You really made things clearer and much fun than the boring lectures at my university! Thank you!

[@block672008]

You saved me a great deal of paving my way through intricacies of pseudo scientific gabble uttered by people who overrated their capabilities and decided to become PhDs and so on and stay at the university to teach forgetting that apart from a title it takes this little tiny bit of skill to pass complicated knowlede to somebody unfamiliar with a particular notion, law etc.. Run for the presidential seat you got my voice!!! Many thanks!!!!

[@saulremi314]

Excellent!

[@jaiyeolaoluseye5749]

years has past and you make it look so easy

[@TheEpicAndrew]

THIS IS FOURIER! Thanks king Leonidas for this awesome tutorial

[@afzals568]

1st time fourier made sense to me. I have my main exam in 4 days but i have your back now. Thank you so much means alot.

[@ESHIELDS]

currently taking networks and systems, trying to finish my electrical engineering degree; hard when your teachers cant explain the material like this. you're a lifesaver!

[@masudchowdhuryrana599]

Dear Sir, I`m a final year(EEE) engineering student with major in electronics and, for some reason, I`ve always struggled with signal related courses. Having done 3 different courses(barely passed!) regarding signals and system under 4 different teachers, I was expected to know a fair amount about Fourier Analysis. Yet had no clue, whatsoever, about Fourier Analysis until today!!! Thank you so much for being such a great teacher. Please keep teaching Sir. Stay blessed, stay well.

[@saulremi314]

Thanks Masud!

[@masudchowdhuryrana599]

The pleasure is all mine Sir. Have a lovely day.

[@porkypine1888]

brilliantly concise videos! I think a mixture of your videos and MathDoctorBob's is the best solution!

[@salmaalfawal6155]

The whole video I was thinking of taking a screenshot, what you did is the best idea ever , you really think of the learner, totally subscribed

[@asadrasheed5625]

Thanks alot. This lecture accumulated my broken concepts into one completed understandable place.

[@confidential303]

This is also what i wanted to do, teaching Fourier transform, you have done a hell of a job!! Thumbs up for you!

[@pierreboulbin8753]

I'm french student, I understand you better than my french teacher ! Thks a lot ! ;)

[@philipjohn1338]

Bro, you have amazing videos. I cannot believe you don't have millions of supporters.

[@lalitupadhyay3460]

I am very glad, for your teaching trigonometry in deep, because with out knowing the base root of theory, no one can learn properly. What are sine, cos, and tan and there reciprocal / complementary, cosine, cosec, cot.may also be explained.

[@luckyspears4227]

well I could not believed how I was able to get the concept in 8:44 minutes. Thank you very much! !

[@unclearnuclear]

Only because he didn't mention it, probably for brevity (though he does explain things great otherwise), there is a phenomenon where, at each jump discontinuity between steps, the Fourier series will behave a little oddly. To describe it graphically with the step function at the beginning of the video, it jumps up slightly before plummeting down to a lower step, and then dips before stabilizing, again dipping before shooting back up to the upper step, over-reaching a little, and stabilizing yet again on that step. The dipping and over-reaching become smaller and smaller when more and more terms are used in the series. This is called the Gibbs phenomenon, and it doesn't go away - which is why there are sometimes small bursts just as a radio is turned on.

[@daveredfield5947]

I Study Engineery and i Love Mathematics, thanks for Upload this Video! Greetings From El Salvador! C.A

[@davidwilkie9551]

Infinity is the actual origin of the x, y, and z axies because they represent the intersection of circles or cycles of infinite period or radius. So "reachable" is more apt for the perturbation or interference represented in the trig functions because they are "difference" terms relative to the connection at the origin. If this video wasn't such a good presentation, it would not be possible to comment, so this is good teaching and learning. IMO

[@majorrgeek]

the best teachers of maths are those that make it simple - maths is simple

[@willm6598]

thank you so much, I was about to just skip these questions on the exam because no one starts from the beginning and explains first what we are even doing, now I understand what I am actually writing down on the piece of paper and what it all actually means

[@indrashispowali]

I liked the way you solved the problem. Very Conceptual 👍

[@jameslke1241]

I really appreciate the clear screenshot ☺️

[@asmabibi1236]

omg 9 years passed and it still help me so much

[@alexisgrenier6592]

This just save me so much time for my tomorrow's quizz. Thanks for these 5 videos, it helped a lot!!

[@aumacarolyn477]

thank you..i didn't even knw there were tutorials online..you just made my learning experience much easier

[@futur96]

u have no idea how i just understood whats going on!!! like seriously i had no clue till u came along thank you!!!!!!!!!!!

[@saulremi314]

Excellent!

[@curtpiazza1688]

Great presentation! 😊

[@akramh2785]

watching this video got me like ''my teacher had no idea what he was talkiing about''

[@atheneus]

Exactly!

[@ItsPouring]

Oh my Gosh!! Math Heaven - I see the White Light! _EVERYTHING_ so clearly and cleanly explained...Perfect! Thank you math god!🤓 ✨🙏✨

[@DatSuKid]

Very clear presentation. I salute you for aiding in helping our world grow and learn.

[@AnhadGill]

Despite the little gap between the white charts bothering me throughout, I get everything. Thank you!

[@CienciaTube]

Fourier series works just for periodic function, Fourier transform works for non periodic functions as you take the T --> infinite

[@MohammadTawaha]

god bless you "جزاك الله كل خير"

[@saulremi314]

Thanks!

[@millsykooksy4863]

Lol 😀

[@hlq16]

+Big Bang Physics That means may God give you good in return in Arabic, just in case you were wondering what the Arabic script meant

[@lounisnei7229]

+Hasan Luqman Qazi yep reward not return maybe

[@PeterGennery]

Great video, I'm learning Fourier analysis and I've used your video as a recap from my lecture notes. Thanks a bunch.

[@paul1964uk]

An ingenious method for revealing information!

[@Leo-ry3zr]

Great video and presentation. I also really liked the white background format and how some of the information is already pre-written. Keep up the good work.

[@adamyavarshney9034]

best explanation of Fourier series 😊

[@rifqiasrilnurrachman9310]

damn bro, thank you so much for helping a lot of physics grad student in this shitty pandemic

[@SwarajChakraborty-qt9jf]

Amazing approach of teaching Fourier series. I would love to collaborate with you someday if possible.

[@J0F0A0]

Big Bang Physics, I must commend you! This is an excellent lecture and example. It really helped, thank you. Regards BEng Mechanical Engineering Student

[@mohammedkhan4990]

Excellent presentations and visuals. You are extremely effective at teaching!!! Thank you.

[@saulremi314]

Thanks

[@saulremi314]

Thanks. Spread the word.

[@darkexcalibur87]

Fianlly! A video that makes sense!

[@ufewl]

yea cos iti says sod all that is not fooking obvious!!

[@prakharkumar7368]

Great work sir. After going through many lecture and book finally found satisfactory result

[@liamkellyguitar]

I should be giving my £9000 a year to you, thanks!

[@morgansampi5336]

+Liam Kelly i'll gladly accept them, anytime!

[@lounisnei7229]

+Liam Kelly we study that for free in algeria universities :3 but free and we get from the internet everything when we know that u guys pay in the univ and how much we can't beleive the price hehe but GL guys without the internet u guys will defeat us but now there is the internet and taht cool teachers soo :3 draaw haha ^^

[@tsheyhailu1748]

Bo

[@haroonj4298]

Well your style of teaching is just beautiful, i also want to learn discrete cosine transformation the goal is to understand mjpeg technique.

[@mamadetaslimtorabally7363]

Man! That's awesome. Thanks a lot. Hey dude, you look like Arthur Betterbiev.

[@neptun2810]

3:31 At last, the piece of Information I have been looking for, after about a million texts and Videos. I haven't found these 3 one liners in all of German internet, first English video I find about the Fourier series and there it is.

[@sriharint]

One word - SAVIOUR. Thanks a lot!

[@samuelosei-somuah3072]

Great approach to explaining Fourier

[@AlanMedina314]

I really like the background and approach on to Part 2.

[@sunilreddy146]

A simpler way to explain about Ao is to just calculate the area in any one of it's period. In the given function, it's 0. Also to know and do things or solve the Ao, An & Bn, half wave symmetric and other properties come in real handy.

[@saulremi314]

Another way to do it is just to look at the midline of the graph. This graph isn't shifted up or down so obviously Ao is 0. If the graph were shifted up, just find the height of the midline and that's Ao.

[@GH123XL]

I have 2 questions: (1). Why do we have to approximate? Why cannot we calculate it exactly? (2). Suppose we never have approximation theory, what couldn't we do what we can do now? Thank you very much Sir.

[@bwaaah9201]

i study last minute then got stuck thank you so much

[@Mlagma04]

bestdamntutoring is right. Really any function can be modeled by Fourier series. Inherently nonperiodic funtions can be forced to be "periodic."

[@mcwolfus8824]

We had to do this for electronics years ago. Good explanation.

[@rahmatullahmaruf2539]

I have never seen such awesome tutorial. Thanks sir

[@yassine321]

Yeah fourrier is another historical genius

[@CrushOfSiel]

Wow my friend. Excellent video. So easy to understand :D. Subscribed just now.

[@srajanvarshney8126]

Dude you cleared the concept.Thumbs up to you.

[@andrewc3937]

Good job, just check the sinusoids, the sine and cosine graphs are interchanged.

[@longhorn4500]

Maybe I don't understand something, but I think that the thing that we are trying to model by sine is not a function. I thought that function has to give us the only number for any input, but in this case we have such inputs where function gives us infinitely many different outputs.

[@lounisnei7229]

guys remember when u see 1/ n^2 it's anyway convergence by riemann also it's= Pi^2 / 6 u'll get it after do derichlet will verified and also u'll do the equal of penseval after ofc do f( eff) ² they put it in exams alot if am not mistaken

[@dursunn]

I'm trying to apply the Fourier series to a time series with a daily cycle. There are daily sales on the X axis and daily temperature values on the Y axis. I want to forecast sales by temperature. Since I don't know the F(x) function, I can't integrate and find the coefficients. Can you help me?

[@kido1649]

Bro is carrying people in math for 12 years!😮

[@coolayer]

Excellent! My life is easy now.

[@thiebes]

Isn't the period L? So around 7:00 when you are talking about a0, the coefficient on the right hand side should be 1/4pi right?

[@GreaterDeity]

2L

[@christoffere425]

This means that for a fourier series square wave we should use the cos terms instead of sin right? Since a square is always even.

[@james3440]

Why do you need to model a function, if you have the function? Your using exactly what you want to model in the modeling of it?

[@marknguyen7699]

I have question: a periodic function is: y(t)= 2At (volts) for 0

[@AppProgrammer]

Very good explanation. Very clear and structured! Keep it up

[@tharushikaliyanage2147]

You are a best teacher 😍 thank u 🙏

[@AlchemistOfNirnroot]

A little confused on my part. But if N ---> infinity, then does the approximation become exact? I'm eluding to the f(x) 'equation'.

[@ernestorestrepo40]

fantastic explanation..... finally grasped the basics of this !! thanks again

[@kpieceemmry3387]

Please prof you didn’t explain what brought about that graph and how it is related to Fourier series You started by saying some1 postulated that formula I am a bit confuse about the big secrete an application behind Fourier series

[@josuecarnivoro]

all engineers (and students), pay your respects to Joseph Fourier.

[@hasnainrana201]

Good sir excellent work

[@pratiktosulthonihidayat2459]

short and brief tutorial. Well done !

[@monsoon02np1]

This is your excellent tutorial.

[@chinesefella94]

Excellent explanation. Brilliant.

[@morgansampi5336]

+Jeremy Tan Jia Ming AW thanks! you're brilliant boy

[@6900xx]

When you said : Part 2 is coming, I was like: Wooooaaaa Show it to me.

[@isaacboateng8250]

How to determine the value of L of the periodic function f(t)=4t 0

[@saulremi314]

Otherwise is the function equal to zero?

[@olubiyiife371]

Express f(x) = x2 for 0

[@morgansampi5336]

+Olubiyi Ife okay wait

[@himadrianjoy9782]

good picture quality .......................................best for 10+2 level in indian students