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

[@lukecaetano8405]

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]

That's so frustrating!

[@NothingMaster]

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.

[@DrTrefor]

Haha indeed!

[@ricardoraymond9037]

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.

[@KarthiDreamr2]

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

[@makutascarlet3238]

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

[@th3wlis]

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

[@xxshogunflames]

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

[@DrTrefor]

Great timing, thanks!

[@SuperDeadparrot]

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

[@VictorAlfarochannel]

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]

That’s awesome, thanks for sharing!

[@danielprager4723]

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

[@jebo56]

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

[@eliotfan0118]

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]

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.

[@tristanblikman]

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

[@avocadolover257]

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

[@NatureLibrary]

Thank you sir... Love from India 🇮🇳

[@ahmedAlmahdi2000]

Thank you Dr. 👏💯

[@michaelzumpano7318]

That was great! You’re an awesome teacher.

[@wakeawake2950]

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]

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

[@wakeawake2950]

@@DrTrefor thnk u 4 ur reply sir 🙏🙏

[@melm4251]

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

[@WinterFlare]

Bro is the goat 🙏

[@haoqinggenius4335]

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

[@aineemartin5764]

You integrate from -L to L

[@Josuke217]

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]

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

[@peggi3561]

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.

[@physicsmathsworld2033]

Beautiful lectures ❤

[@_tasneem7378]

Many thanks sir.

[@pellumbmaraj6934]

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]

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

[@ibrahimsoliman1842]

Great effort. My appreciation thanks

[@dovidglass5445]

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

[@DrTrefor]

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

[@dovidglass5445]

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

[@Ali_Alhakeem]

Really helpful ! thanks alot

[@muditfatehpur7452]

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

[@alanizquierdo6783]

thank you for the lesson and smile!

[@Afghanman25]

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]

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

[@Ashley-de3tu]

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]

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

[@AbakwaPikin-vq8hz]

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

[@osman2k]

thank you, sir!!

[@catherinesimpson3811]

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]

Sir can you do special functions and tensors?

[@donegal79]

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

[@sounakroy1933]

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?

[@suhailawm]

Thanks professor

[@hellasceasar4398]

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?

[@vishwpatel8992]

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

[@yousifalmayyahi4462]

I would like to know the Z-Transform things.

[@stevematson4808]

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]

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.

[@freebird889]

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

[@GammaStyleGaming]

"In this video-you" every time lol

[@DrTrefor]

um lmao what is this:D

[@thehalf-dane4907]

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.

[@squareroot1697]

Tabular method for IBP

[@puremaths2444]

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

[@DrTrefor]

It’s just a convention, either is fine.

[@harshikagunawardhana7685]

Thank you.

[@MrUnknowz]

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

[@theimmux3034]

9:14 the first term includes sin0/0

[@asoosman]

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

[@beau-payage]

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]

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.

[@alfredbanda1693]

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

[@robertoberidojr.435]

Beautiful

[@continnum_radhe-radhe]

🔥🔥🔥

[@elle948]

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!!!

[@ironsideeve2955]

Zero people disliked this because it's odd

[@tsehayenegash8394]

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

[@abdealrazakmekebret6385]

n go from zero 😅

[@II-th7bn]

Please tell background of topic also .and speak slow english

[@chathuravimanga]

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