Computing the Fourier Series of EVEN or ODD Functions **full example**

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  • Опубликовано: 1 дек 2024

Комментарии • 80

  • @ricardoraymond9037
    @ricardoraymond9037 3 года назад +24

    Noting the wide range of maths topics you cover, you got to be the a know- all maths prof.
    AMAZING. I am only an Accountant curious about Fourier series, and you have made it simple to grasp with the dot product analogy.
    Cheers Prof.

  • @lukecaetano8405
    @lukecaetano8405 3 года назад +26

    Thank God I found this man and was saved from the misery of my horrific teacher not explaining why the Sine in Bn goes to zero. grrr

    • @DrTrefor
      @DrTrefor  3 года назад +10

      That's so frustrating!

  • @KarthiDreamr2
    @KarthiDreamr2 7 месяцев назад +1

    Thank you 🙏 for providing a deeper explanation 📚 of concepts instead of merely applying formulas directly, as some math instructors do on RUclips 🎥.

  • @NothingMaster
    @NothingMaster 3 года назад +51

    This is called the hand waving method for finding the solution.
    I love how you get super excited about solving these simple equations. Your enthusiasm is contagious.

  • @makutascarlet3238
    @makutascarlet3238 2 года назад +4

    I wish I came upon this video a lot sooner. I finally understand why I should care about the evenness and oddness of the function: computation becomes a lot simpler, and for my purposes, it can make code run faster. Thank you Dr. Bazett

  • @VictorAlfarochannel
    @VictorAlfarochannel 3 года назад +9

    Sir, you truly are a great teacher. I aced my first test in Vector calculus, didn’t do so great on the next two. However, I watched all of your videos in the Vector calculus playlist and I aced it! You are amazing sir.

    • @DrTrefor
      @DrTrefor  3 года назад +2

      That’s awesome, thanks for sharing!

  • @xxshogunflames
    @xxshogunflames 3 года назад +18

    Fourier sequences have been coming up in my probability and data analysis courses. Awesome vid!

    • @DrTrefor
      @DrTrefor  3 года назад +5

      Great timing, thanks!

    • @SuperDeadparrot
      @SuperDeadparrot Год назад

      I was surprised when they popped up in my image analysis courses.

  • @th3wlis
    @th3wlis Год назад +2

    I am a first year physics student and your videos on Fourier series save my life thank youuu

  • @jebo56
    @jebo56 Год назад +4

    I'm on my third course of basically only using this guys playlists... How did people pass anything 100 yrs ago?

  • @danielprager4723
    @danielprager4723 Год назад +11

    Another great video, thank you! The summation at 9:00 for the sine terms should be n = 1 to infinity, rather than n = 0.

  • @tristanblikman
    @tristanblikman Месяц назад +1

    this was so easy to follow and understand. Now there's no chance i'll mess it up on my exam tomorrow :D

  • @pellumbmaraj6934
    @pellumbmaraj6934 2 года назад +7

    I think that you need to have it from 1 to infinity, because at n = 0, we will have division by 0, which is undefined.

    • @212ntruesdale
      @212ntruesdale Год назад +2

      Noticed that, too. I’m still going to give him all the points possible! 😂

  • @eliotfan0118
    @eliotfan0118 3 года назад +12

    Dear Dr. Bazett,
    Thank you for your informative video. I have a few questions however.
    1. Is there a particular reason you did not substitute L for 2 at the end?
    2. How do you, in general, find the value of L?
    Thank you sir

    • @DrTrefor
      @DrTrefor  3 года назад +7

      This doesn't matter so much. As in, the original function will have a periodicity of L, so it will come from the original problem, and you can either substitute in the specific value L=2 or not, doesn't much matter.

  • @avocadolover257
    @avocadolover257 7 месяцев назад

    thank you for your clear and fun explanation. i aspire to be a math professor

  • @NatureLibrary
    @NatureLibrary 3 года назад +1

    Thank you sir...
    Love from India 🇮🇳

  • @michaelzumpano7318
    @michaelzumpano7318 Год назад

    That was great! You’re an awesome teacher.

  • @peggi3561
    @peggi3561 2 года назад +1

    Great explanation.👍
    but one thing. I think summation should go from 1 to infinity. not from 0 to infinity. You can also put n=0 in that b(n) and check that it gives undefined.

  • @wakeawake2950
    @wakeawake2950 3 года назад +7

    The first term of this Fourier series at 9:15 is divided by 0, I'm confused plzz explain 🙏🙏,bty awesome video thnk u professor

    • @DrTrefor
      @DrTrefor  3 года назад +13

      Oh good catch. That sum should start at 1 not 0.

    • @wakeawake2950
      @wakeawake2950 3 года назад +4

      @@DrTrefor thnk u 4 ur reply sir 🙏🙏

  • @WinterFlare
    @WinterFlare 24 дня назад

    Bro is the goat 🙏

  • @ahmedAlmahdi2000
    @ahmedAlmahdi2000 9 месяцев назад +1

    Thank you Dr. 👏💯

  • @Ali_Alhakeem
    @Ali_Alhakeem 2 года назад +2

    Really helpful ! thanks alot

  • @haoqinggenius4335
    @haoqinggenius4335 Год назад +5

    why isnt L = 4? he's intergrating from -2 to 2. why would L be 2?

    • @aineemartin5764
      @aineemartin5764 11 месяцев назад +7

      You integrate from -L to L

    • @Josuke217
      @Josuke217 11 месяцев назад +2

      The general formula is f(x)= ao/2 + an cos (2πnx/b-a) + bn sin(2πnx/b-a) . an and bn summation terms from n=1 to infinity.
      [L,-L] = [-2,2]
      b-a = 4
      So what's written in the video is correct, 2πnx/4 is written directly as πnx/2

    • @hasanmammadov7518
      @hasanmammadov7518 10 месяцев назад +2

      Cause your period is equal to 4. And L= Period/2

  • @ibrahimsoliman1842
    @ibrahimsoliman1842 3 года назад +1

    Great effort. My appreciation thanks

  • @physicsmathsworld2033
    @physicsmathsworld2033 3 года назад +1

    Beautiful lectures ❤

  • @melm4251
    @melm4251 Год назад

    i'm currently failing my series and transforms class but maybe, just maybe i can do it with your help! i've watched this video atleast 10 times today and just finished working out a problem that would have been impossible for me this morning

  • @alanizquierdo6783
    @alanizquierdo6783 2 года назад

    thank you for the lesson and smile!

  • @dovidglass5445
    @dovidglass5445 3 года назад +4

    Thanks again for this awesome series! Right at the end it should be 2 instead of L right?

    • @DrTrefor
      @DrTrefor  3 года назад +6

      Ah yes great catch. Quoting the general formal and forgot to sub in the specific value of L

    • @dovidglass5445
      @dovidglass5445 3 года назад +1

      @@DrTrefor No problem, your videos are so well done, my pleasure :)

  • @hellasceasar4398
    @hellasceasar4398 Месяц назад

    i have a similiar problem like this one but f(t) is not given how would i find out what f(t) is from the graph?

  • @_tasneem7378
    @_tasneem7378 2 года назад +1

    Many thanks sir.

  • @AbakwaPikin-vq8hz
    @AbakwaPikin-vq8hz 9 месяцев назад

    Thank you❤❤❤
    I think cos((pi)^n) = (-1)^n
    Instead of (-1)^(n+1)

  • @sounakroy1933
    @sounakroy1933 2 года назад +1

    Hello Professor. I am stuck. You introduced 3 formulas in the video.
    I tried to solve { (integral 0 to 2pi) cosnt * cosmt dt }
    I ended up with...
    1/2 * [(sin 2pi(m+n))/(m+n)+(sin2pi(m-n))/(m-n)]
    You see there are 2 terms.
    The term on the right contain m-n in the denominator. If i put m=n it will be undefined. Where did i go wrong?

  • @stevematson4808
    @stevematson4808 2 года назад +1

    Question. If i have a graph made of plot points recorded during an experaments but i do not have the formula to describe that curve- can I use the Fourier series to sort of make a usable formula to then find the dirivitive or integral?

    • @allanjmcpherson
      @allanjmcpherson 2 года назад +1

      You wouldn't be able to use the Fourier series in that way. What you could do is to use a discrete approximation to the derivative or the integral using your existing date points. There is also such a thing as the discrete Fourier transform (DFT) but it's more useful for gaining information about the frequency content of the signal.

  • @suhailawm
    @suhailawm 3 года назад +1

    Thanks professor

  • @osman2k
    @osman2k 4 месяца назад

    thank you, sir!!

  • @catherinesimpson3811
    @catherinesimpson3811 Год назад

    Literally brilliant! Quick question! How do you know to write n=1 in the initial formula but to change it to n=0 in the final formula? Sorry if it’s obvious I’m just unsure!

  • @ekalavyain1131
    @ekalavyain1131 3 года назад +2

    Sir can you do special functions and tensors?

    • @donegal79
      @donegal79 3 года назад +2

      JUST SAY THANKS FOR WHAT YOU HAVE WATCHED. i FIND THAT GENERALLY HELPS, BEFORE YOU ASK FOR SOME ADDITIONAL FREE HELP.

  • @vishwpatel8992
    @vishwpatel8992 2 года назад

    From where u got the basic ideas like we r approximating periodic function by sine and cosine in Fourier tra.

  • @yousifalmayyahi4462
    @yousifalmayyahi4462 3 года назад +1

    I would like to know the Z-Transform things.

  • @Afghanman25
    @Afghanman25 Год назад

    Thanks for the video dr! just one small question, at 6:05 why doesnt the function cancel out since its being integrated from 0 to 2 (0 to pi when you take into account the stretching factor)?
    don't odd and even functions both cancel out from 0 to pi?

    • @harmonicspice2536
      @harmonicspice2536 Год назад

      you have to look at the sign function graph, and you will see that this is positive area only , no negative areas.
      if you look at the sine wave graph between 0 to 2 it will look like a flipped prabula shifted to the right and it will be touching the x-axis and to passing through it

  • @alfredbanda1693
    @alfredbanda1693 Год назад

    I think a 0 coefficient should be 1/4 instead of 1/2 since L = 2 correct me if am wrong

  • @muditfatehpur7452
    @muditfatehpur7452 14 дней назад

    8:17 here shouldn't there be => [ cos(n*pi) - 1 ] . please clarify

  • @GammaStyleGaming
    @GammaStyleGaming 2 года назад +1

    "In this video-you" every time lol

    • @DrTrefor
      @DrTrefor  2 года назад +1

      um lmao what is this:D

  • @thehalf-dane4907
    @thehalf-dane4907 2 года назад

    maybe a more beginner to math here, but I didn't quite catch how the substitusions you did at the end worked, if anyone could help me that would be great.

  • @beau-payage
    @beau-payage 3 года назад

    Consider the function f(t)=t. if we set t=1, L=1, then left hand side = f(1)=1, but right hand side = sum 0 = 0. What is wrong with it?

    • @allanjmcpherson
      @allanjmcpherson 2 года назад

      There is a discontinuity at t = 2, and the Fourier series only converges to the function where it is smooth. At discontinuities, the Fourier series converges to the midpoint. In this case, it's the midpoint between -2 and 2, which is zero. I recommend his video on the big idea of the Fourier series to see why.

  • @freebird889
    @freebird889 Год назад

    Why did L=2? Why does your Transformation formula look different than mine?

  • @puremaths2444
    @puremaths2444 3 года назад +1

    Hello sir I found that some books uses a sub /2 and others use a sub 0 only kindly clarify for me

    • @DrTrefor
      @DrTrefor  3 года назад +2

      It’s just a convention, either is fine.

  • @elle948
    @elle948 3 года назад

    Professor, you are a godsend! Thank you so much, your videos are amazing!!! SO glad to have found your channel :"")
    Looking forward to future videos!!!

  • @MrUnknowz
    @MrUnknowz Год назад

    Hi Dr Bazzet , just wondering how did (n*pi*t)/L came about

  • @theimmux3034
    @theimmux3034 2 года назад

    9:14 the first term includes sin0/0

  • @harshikagunawardhana7685
    @harshikagunawardhana7685 3 года назад +2

    Thank you.

  • @asoosman
    @asoosman 3 года назад

    How to teaching
    What is the tablet or type to teaching online?

  • @Ashley-de3tu
    @Ashley-de3tu Год назад +1

    At 5:55 what he did ?? Can anyone tell ?? Plz reply anyone
    (I am weak at maths but his teaching is making me fall in love with this subject)

    • @petarpejic1468
      @petarpejic1468 Год назад

      An "integration by parts" its the riverse of the product rule of derivation, as far as i understand.

  • @robertoberidojr.435
    @robertoberidojr.435 3 года назад +1

    Beautiful

  • @continnum_radhe-radhe
    @continnum_radhe-radhe 2 года назад +1

    🔥🔥🔥

  • @tsehayenegash8394
    @tsehayenegash8394 Год назад

    I have 15 years temperature data. I want to remove seasonality variation from the time series data, so how can I get the constan term ao, the amplitude and the phase change by using these given temperature data? thank you

  • @ironsideeve2955
    @ironsideeve2955 3 года назад +1

    Zero people disliked this because it's odd

  • @II-th7bn
    @II-th7bn 3 года назад

    Please tell background of topic also .and speak slow english

    • @chathuravimanga
      @chathuravimanga Год назад +3

      Try slowing down the playing speed. His speed is pretty much perfect for an average student fluent in English.

  • @abdealrazakmekebret6385
    @abdealrazakmekebret6385 5 месяцев назад

    n go from zero 😅