Computing the Fourier Series of EVEN or ODD Functions **full example**
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- Опубликовано: 6 окт 2024
- In this video we do a full example of computing out a Fourier Series for the case of a sawtooth wave. We get to exploit the fact that this is an odd function where f(-x)=-f(x)) as we can simplify considerably our computations of the Fourier Coefficients if the function is either even or odd.
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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.
Haha indeed!
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.
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
That's so frustrating!
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
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.
That’s awesome, thanks for sharing!
Thank you 🙏 for providing a deeper explanation 📚 of concepts instead of merely applying formulas directly, as some math instructors do on RUclips 🎥.
Fourier sequences have been coming up in my probability and data analysis courses. Awesome vid!
Great timing, thanks!
I was surprised when they popped up in my image analysis courses.
Another great video, thank you! The summation at 9:00 for the sine terms should be n = 1 to infinity, rather than n = 0.
thank you for your clear and fun explanation. i aspire to be a math professor
I'm on my third course of basically only using this guys playlists... How did people pass anything 100 yrs ago?
Thank you sir...
Love from India 🇮🇳
Thank you Dr. 👏💯
Many thanks sir.
Really helpful ! thanks alot
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
Great effort. My appreciation thanks
Beautiful lectures ❤
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
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.
That was great! You’re an awesome teacher.
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.
Noticed that, too. I’m still going to give him all the points possible! 😂
thank you, sir!!
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.
thank you for the lesson and smile!
Thanks professor
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
Oh good catch. That sum should start at 1 not 0.
@@DrTrefor thnk u 4 ur reply sir 🙏🙏
Thank you❤❤❤
I think cos((pi)^n) = (-1)^n
Instead of (-1)^(n+1)
Thanks again for this awesome series! Right at the end it should be 2 instead of L right?
Ah yes great catch. Quoting the general formal and forgot to sub in the specific value of L
@@DrTrefor No problem, your videos are so well done, my pleasure :)
Thank you.
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!
I am a first year physics student and your videos on Fourier series save my life thank youuu
Beautiful
why isnt L = 4? he's intergrating from -2 to 2. why would L be 2?
You integrate from -L to L
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
Cause your period is equal to 4. And L= Period/2
Sir can you do special functions and tensors?
JUST SAY THANKS FOR WHAT YOU HAVE WATCHED. i FIND THAT GENERALLY HELPS, BEFORE YOU ASK FOR SOME ADDITIONAL FREE HELP.
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.
"In this video-you" every time lol
um lmao what is this:D
🔥🔥🔥
I think a 0 coefficient should be 1/4 instead of 1/2 since L = 2 correct me if am wrong
From where u got the basic ideas like we r approximating periodic function by sine and cosine in Fourier tra.
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?
I would like to know the Z-Transform things.
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)
An "integration by parts" its the riverse of the product rule of derivation, as far as i understand.
Why did L=2? Why does your Transformation formula look different than mine?
9:14 the first term includes sin0/0
Hi Dr Bazzet , just wondering how did (n*pi*t)/L came about
How to teaching
What is the tablet or type to teaching online?
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?
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
Hello sir I found that some books uses a sub /2 and others use a sub 0 only kindly clarify for me
It’s just a convention, either is fine.
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?
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.
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?
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.
Zero people disliked this because it's odd
n go from zero 😅
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
Please tell background of topic also .and speak slow english
Try slowing down the playing speed. His speed is pretty much perfect for an average student fluent in English.
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!!!