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How To Find The Fourier Series Of Even And Odd Functions

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In Mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series.
In This Video, You'll Learn
1. How to Sketch a graph
2. How to Determine Even and Odd Functions
3. How To Solve for Fourier Series Coefficients
4. How To Integrate Fourier series
5. How to Solve Questions on Fourier series
6. How To Find the Fourier Series of f(x)=1-x
7. How To Find The Fourier Series of f(x)=1+x
8. How to compute and derive a series or formula for π²/8
9. How To Find a Series for pie squared over 8
#engineeringmathematics
#avitechmaths
#avitechnologies
#fourierseries
#fourier
#evenfunction
#oddfunction
#ema382
#advancedcalculus
#calculus

Опубликовано:

5 сен 2024

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Комментарии : 122

@amarachinjumobi4971 Год назад

I'm female too... and I am definitely going to share this videos with others having problems with Fourier series... because it's the best I have come across so far😊

@AVITECHNOLOGIES Год назад

Thank you. You are welcome to my channel once again 😊. Currently, female subscribers on my channel are less than 25% 😂 I hope the number goes up soon.

@smartdean8910 3 месяца назад

Thanks so much 🙏 all this for free. Best fourier series ever.

@AVITECHNOLOGIES 3 месяца назад

You're welcome

@atunbitoluwanimi6208 Год назад

Best video I've seen on fourier series! Let me check others. You teach so well and by the way I'm a female.

@AVITECHNOLOGIES Год назад

I'm so happy right now, welcome to my community. Here's my playlist on Fourier Series: ru-vid.com/group/PLyIQ6tJ1a5bajJUe52S3qzli2PwZgcjw8 Thank you very much.

@samiradan6901 9 месяцев назад

You know, we want to kick out our math teacher from the Uni, and please come and be our teacher. You explained much better than him. Thanks a lot, bro

@AVITECHNOLOGIES 9 месяцев назад

Send an email to avitechsinach@gmail.com Classes can be online or physical. You're welcome 😊

@samiradan6901 9 месяцев назад

@@AVITECHNOLOGIES please don't delete this channel. Your next channel will be fully supported by us

@enweremfavour5315 8 месяцев назад

You made my back to back A in Engineering Maths possible. Even though you didn't teach me part one but I had A in Engineering Maths II because of you. Thank you very much, I'm eternally grateful to you sir.

@AVITECHNOLOGIES 8 месяцев назад

I am so happy to hear This. You're welcome 😊

@scottgabriel6184 9 месяцев назад

You're God sent! You make Fourier series easy for me now! 🎉

@AVITECHNOLOGIES 9 месяцев назад

You're welcome 😊

@sabdullahtu-techandunboxin8131 4 месяца назад

idk what to say , it the first video in my life watching complete for studying , your method is so awesome keeing engaged and all previous concepts used are also cleared in each step like integration by part which i kept forgetting but u told me a way i can remember it always . you are real teacher , u need to be teaching in my uni , love your sir , your concepts and teachings are unmatchable coz a real teacher is unbeatable and i'd want to say you my real teacher

@AVITECHNOLOGIES 4 месяца назад

Thank you very much for the compliments, I'm so happy that I could help. You're welcome to my channel, please, make yourself comfortable.

@collinswanjala-ds4jw 6 месяцев назад

Thank you so much , have totally understood unlike when I went to class

@AVITECHNOLOGIES 6 месяцев назад

You're welcome.

@nta699 11 месяцев назад

It's a joy watching you go through your explanations! Keep it up!!

@TomisinAjeneye 3 месяца назад

Incredible Video, Love from UK 🇬🇧

@senohannington4982 11 месяцев назад

Woa thanks Soo much brother for the brilliant lecture I have understood even and odd functions well than before 🙏🙏🙏 Blessings follow you

@SofiaAntoniaBalog Месяц назад

Thank you so much. So incredibly helpful :)

@AVITECHNOLOGIES Месяц назад

You're welcome

@yaldaalhabib3490 Год назад

This helped me a lot! The most useful vid on the topic

@sutheen 29 дней назад

I'm preparing My test 1 on 17 August sir. You will be saving me. I'm from Malawi. Would you do us another video on solving PDEs using Laplace equation, Separation of variables. Some on heat equation,wave equation ❤❤

@AVITECHNOLOGIES 29 дней назад

@@sutheen I am so sorry, since RU-vid took off my monetisation, I've stopped making videos.

@songweteddy6563 3 месяца назад

You are really a genius. 🙏🙏🙏 Kindly Share the link for complex analysis and PDEs aswel

@AVITECHNOLOGIES 3 месяца назад

I am very sorry, I don't have any videos on them.

@rakiyamohammedkabiradamu8118 Год назад

Great. This is Fourier series made easy. Fantastic. Thanks.

@AVITECHNOLOGIES Год назад

You're welcome 😊

@muralikumargurusamy5504 4 месяца назад

You are good at teaching, very understandable

@AVITECHNOLOGIES 4 месяца назад

Thank you.

@liya1042 Год назад

We are watching 🤲

@user-lm7cr3mo9n Год назад

In fact I like this your tutorial you are one of the best.

@AVITECHNOLOGIES Год назад

Thank you very much 😊

@michaelekele7574 Год назад

🎉 best video ever, you just made my day 😍😘 Fourier series made easy....

@chennifi3130 9 месяцев назад

Sooo underated. Thank you for the beautiful explanation 😊

@AVITECHNOLOGIES 9 месяцев назад

You're welcome.

@user-jg1pz2fy1x 8 месяцев назад

good job continue to make other videos

@AVITECHNOLOGIES 8 месяцев назад

Okay, Thanks

@gatkuothbidong 5 месяцев назад

❤❤❤ thank you teacher, the way teach is very clear. I'm watching your video from Ethiopia. M sugh u.

@AVITECHNOLOGIES 5 месяцев назад

You're welcome 😊

@Carbonated.Milk. Год назад

thank you for the helpful video!

@AVITECHNOLOGIES Год назад

I'm glad that I could Help. Cheers

@williamsekani754 9 месяцев назад

your explanations are just superb 😀

@AVITECHNOLOGIES 9 месяцев назад

Thanks

@user-xg8ur2uw7m 8 месяцев назад

Sir I want to hug you ❤❤❤ superb Sir 🙇‍♂️, you don't know what great thing you did tomorrow is my end semester exam 😂 love you sir

@AVITECHNOLOGIES 8 месяцев назад

I Love All of My Viewers. You matter so much to me. I'm so glad that my videos could help. I wish you success, Cheers😊

@verifieddanny543 10 месяцев назад

This video is soooo detailed

@farrisroyzz6942 Месяц назад

thanks a lot its help me

@AVITECHNOLOGIES Месяц назад

You're welcome

@elijahayara8553 5 месяцев назад

Thank you boss for your dedication to making us pass Thank you

@AVITECHNOLOGIES 5 месяцев назад

You are welcome Sir 😊

@preciahpatricianyambe2445 9 месяцев назад

Very helpful videos🎉❤

@AVITECHNOLOGIES 9 месяцев назад

You're welcome.

@user-hy9uc8ii6p 6 месяцев назад

Super explanation sir.

@AVITECHNOLOGIES 6 месяцев назад

Thank you😊

@ericacuman7885 3 месяца назад

Nice one sir❤

@AVITECHNOLOGIES 3 месяца назад

You're welcome

@samuelkamtande7579 11 месяцев назад

Very good explanation ❤

@user-bl9ql6ki9h 9 месяцев назад

you are the best papa

@tahakabbara2408 9 месяцев назад

top professor 👏

@okohdebra2219 Год назад

Best video ever❤❤

@prorajesh103 Год назад

thank you brother..you helped alot

@AVITECHNOLOGIES Год назад

You're welcome 😊

@muhammadaimanaffendimohdas8191 Месяц назад

Thanks

@AVITECHNOLOGIES Месяц назад

You're welcome

@raphetmweemba7091 10 месяцев назад

You're powerful 💪❤️❤️

@AVITECHNOLOGIES 10 месяцев назад

Thank you. 😊

@gloriakiptum1781 6 месяцев назад

Thanks sir

@AVITECHNOLOGIES 6 месяцев назад

You're welcome 😊

@siphokunene8612 5 месяцев назад

Wow!

@zakhelexulu3394 Год назад

It`s clear.

@osunrinadebukola6082 3 месяца назад

We are watching ooooo😂😂😂😂 I am a female too . Welldone boss.

@AVITECHNOLOGIES 3 месяца назад

Wow, that's great. You're welcome.

@PromiseAnthony-ds8ol 4 месяца назад

Sir, please do you tutor privately

@AVITECHNOLOGIES 4 месяца назад

Yes, I do.

@apaubright5540 Год назад

Thank you🎉

@AVITECHNOLOGIES Год назад

You are welcome 😊

@emmanuelonyedika4160 Год назад

When finding a⁰ why did you use only the bottom as f(x)?

@jirex430 Год назад

Thank you 💕

@AVITECHNOLOGIES Год назад

You're welcome. The pleasure is Mine.

@lambertjunior272 9 месяцев назад

Gracias avi 👏👏👏

@AVITECHNOLOGIES 9 месяцев назад

Thanks Lambert 😊

@AVITECHNOLOGIES 9 месяцев назад

Thanks Lambert 😊

@hellenmulatya3589 6 месяцев назад

A girl here😂❤You are a saviour

@AVITECHNOLOGIES 6 месяцев назад

😅 I guess I've saved more lives than doctors 😂😂😂😂

@ericoduroboateng5269 Месяц назад

it is always impotant to draw the graph to see if is even or odd

@AVITECHNOLOGIES Месяц назад

Yes

@ruifernandes5888 10 месяцев назад

since your period for determination goes from -pi to pi -> 2pi why is it that you used pi in the formulas for the period? The final values, i believe, should be halved because of this. For example If you pick your determined value for a0 and do that: (2+pi)/2, you have the average value of the function, that is what that coefficient represent.

@AVITECHNOLOGIES 10 месяцев назад

I don't understand.

@nkegneJoannita-wh5bc 3 месяца назад

a question please we are intergrating for a single period right which start from negative pie to positive pie but you solving only for half period y is that so 🙏🙏🙏

@AVITECHNOLOGIES 3 месяца назад

It is explained in the video. The function is an Even function, so the integral from -π to π is the same as taking double of the integral from 0 to π.

@reeschubili897 Месяц назад

Why are we having 2/π for a note, instead of 1/2π? Kindly enlighten me. Thank you.

@AVITECHNOLOGIES Месяц назад

All textbooks follow same formula, however, one can decide where to place constants. First of all, the function is an even function, so I won't be using same formula. Watch this video First. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-BSEN9GhdDRE.html Then watch this other video for even and odd functions: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4bFNAthJOLA.html

@technicalsanjeev8630 2 месяца назад

Sir why did write 2/pie in case of even function instead of only 1/pie integrate 0 to pie--> f(x).dx

@AVITECHNOLOGIES 2 месяца назад

Watch this video about even and odd functions. ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4bFNAthJOLA.html

@justinetheewordgiver1197 10 месяцев назад

I'm a male too but gonna subscribe

@AVITECHNOLOGIES 10 месяцев назад

You're welcome.

@siambeecrowd3859 3 месяца назад

Sir,if we take x=+-π then what will be the value of f(x) when we deduce the series

@AVITECHNOLOGIES 3 месяца назад

The value of f(x) can either be 1+π or 1-π. Taking a midpoint, that would 1.

@jbztech Год назад

He said share this to your female coursemates 😂😂😂😂😂 Okay sir.

@AVITECHNOLOGIES Год назад

Yes o 😂😂😂😂

@edwinmutua9184 7 месяцев назад

Hey...ive got a screenshot having a question paper in which there is a fourier question...kindly help me...am from kenya and i have learnt alot in your vedios

@AVITECHNOLOGIES 7 месяцев назад

Send an email to avitechsinach@gmail.com

@tomasito_2021 Год назад

Great video. Just what I needed to get through Fourier series. I've got a question however: At 23:04, since u chose n=1, shouldn't that also apply to the denominator at that point as well since after all, it's the same n which would consequently affect your working at 26:05? I'd appreciate if u can clarify this for me.

@AVITECHNOLOGIES Год назад

I've watched the video at the timestamps, but I don't seem to comprehend your question.

@tomasito_2021 Год назад

@@AVITECHNOLOGIES What I meant to say was that, where u had 2/πn^2 ((-1)^n -1), and u assumed that n was odd (in this case 1), why didn’t you get -4/π , since it was the same n at the denominator?

@AVITECHNOLOGIES Год назад

Ohhh, now I get, in Fourier series, we try to get a general formula in terms of n, but we also try to eliminate locations were n is the power of 1 or negative 1. {(-1)^n -1}, This bracket is going to have a constant value for ANY odd value of n. But at the denominator is going to present different values. I would make a short video to explain this, if you don't still understand.

@oladeleomoyemi6917 Год назад

I too gbadun your video guy... You fit teach PDE too?

@AVITECHNOLOGIES Год назад

Yes, I fit, but I don't know when I'll be able to make it. I already have a long list of videos to make. I will surely make videos on it, but I don't know when. Thanks Boss.

@fridahmusaula 2 месяца назад

Am here

@AVITECHNOLOGIES 2 месяца назад

You're welcome

@bellobalikisadedoyin168 10 месяцев назад

Am a female ❤thanks for this

@AVITECHNOLOGIES 10 месяцев назад

You're welcome.

@emmanuelonyedika4160 Год назад

Why was the upper f(x) neglected when finding a⁰

@AVITECHNOLOGIES Год назад

The function is an even function, so you can modify the Formula for a0 and pick any 1 of the function value. If you check properly, I integrated from zero to pie, that's why I used the other f(x) value. To fully understand Even and odd functions, click this link: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4bFNAthJOLA.html

@BlessingAkogwu-pp5uk Год назад

Please help me answer this exam question: " show that an even function can have no sine term in it's Fourier expansion"

@AVITECHNOLOGIES Год назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-4bFNAthJOLA.html That's my Video on Even & Odd Functions. For an even function, the Fourier coefficient Bn is equal to zero because the integral of odd functions over symmetric intervals is ZERO. Click the link above To Understand how to prove it. I trust that video will answer your question. Thanks

@moiz8989 Месяц назад

2/pi ? isnt it supposed to be 1/2*pi?

@AVITECHNOLOGIES Месяц назад

No.

@amarachinjumobi4971 Год назад

I'm female too... and I am definitely going to share this videos with others having problems with Fourier series... because it's the best I have come across so far😊

@AVITECHNOLOGIES Год назад

Thank you very much🤗