Fourier Series: How To Determine Fourier Series | Example 1
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- čas přidán 22. 08. 2024
- Fourier series is a sum that represents a periodic function as a sum of sine and cosine waves.
1. Introduction To Fourier Series
2. Integration of Periodic Function
3. Integration of Functions over a single period
4. How to Solve For Fourier series
5. How To Determine Fourier series
6. How to Pass Engineering Mathematics
7. How To integrate Fourier Series
8. How To solve for Integrals of Periodic Functions
9. How to Solve for the Fourier Series Coefficients
10. Fourier series coefficient calculation
You can learn more by clicking Any of These Links;
Fourier Series & Periodic Function: • Fourier Series & Perio...
EMA382 | Engineering Mathematics IV For Uniben 300 Level Students: • EMA382 | Engineering M...
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In one of the steps of in the integration on the board you're missing 1/n and a negative number multiplied by a negative number is positive number.
Check the comments section first, if I haven't answered this. If I haven't, please, indicate the time at which I made such mistake. Thanks
@@AVITECHNOLOGIES 19:05 ...... - 1/n2pi is not affected by constant 1/n
Thank you sir for your good explanation
From somalia i have an exam tomorrow.
You're welcome.
I wish you success in your Exams.
God bless you finally a teacher who can teach so well
Amen 🙏
Well Explained
Thanks
very powerful
You make these simple very nice 👍
Ur explaination is well understandable
Keep it up👏👏
Thank you.
This was really helpful.....thank you sir
You're welcome 😊
Nicely done.
Very clear explanation
Thanks.
Very helpful 👏🏾😊
Great brother keep up
Thanks
Bro if i may ask ... Is it that when ur asked to determine the fourier series of a function..., it's actual meaning is for you to find the value of the fourier coefficients which are a not, a subscript n and b subscript n
The Fourier coefficients are used to get the Fourier series. The Fourier series is a summation of an infinite amount of sines and cosine. You cannot get the Fourier series without solving for the Fourier coefficients (a0,an,bn).
After getting the values of the Fourier coefficients, you then have to put these coefficients into the Fourier series formula, which is ;
f(x)=a0/2+sum_(n=1) to ^ (n=infinity) of (anCosnx+bnSinnx).
The final answer of f(x) after substituting a0,an and bn is the Fourier Series of the Function.
This is so helpful. Pls why are we not solving for odd and even functions of an and Bn ?
Follow the videos on this playlist to understand when you can determine if a function is even or odd.
In this case, the interval for the function is not over a symmetric interval, hence we can't determine even or odd.
Thank you sir the class. But why did you calculate cos2pi n as 1 instead of n at 22:51
Cos(2πn) has a special value of 1.
Thank you so much for the reply 😊 Does it apply to sin 2pi n too?
How did you deal away with the -1/n (for bn part) that comes after the intergral sign? There is -1/n infront of Cosnxdx too
Indicate the Time stamp please.
The -1/n where did it went to ?? For the (Vdu )
@@AVITECHNOLOGIES 19:34
@@ebobaidoo9573I factorized it. If you start at 19:07, you'll notice I said -1/n is a constant, hence we can factorize it. I wrote it outside the bracket. Formerly, it was only 1/2π that was outside the bracket, but after factorization, it became -1/2πn.
@@aliyuabdulrazak3216I factorized it. If you start at 19:07, you'll notice I said -1/n is a constant, hence we can factorize it. I wrote it outside the bracket. Formerly, it was only 1/2π that was outside the bracket, but after factorization, it became -1/2πn.
ON POINT
Secondly bro, when u were solving for a subscript n in the question, u got to a certain point in which u said sin 2π =0.., no disputes so meaning after substituting both the upper boundary limit and lower boundary limit the whole of that side is meant to be 0. So isn't the 0 meant to multiply the 1/2π outside to also make it 0 cos u didn't multiply u kept it and continued ur solution
Sin2π=0. That's a special value.
1/2π outside was a factor that is multiplying a bracket involving 2 terms. Only one of the terms became zero, you have to also solve the other term, which was the integral of cosnx from 0 to 2π.
You need to be done with simplifying all terms in the bracket before multiplying by 1/2π.
Good evening sir. The video is very helpful. But I have an observation when solving for bn.
When we solved for An, the nth term in the answer before multiplying by O was square of n.
But for the bn, we only obtained a single n.
I was able to observe this after the integration by part.
I hope you'll be able to get my point with how I explained.
I don't Understand your question.
Add the time stamps.
@@AVITECHNOLOGIES It's now clear sir. After going over it again.
Thanks very much for attending to me.
Umm what a simplified version
I have a question sir, please given a question that wasn't stated whether even or odd but after plotting the graph I discovered the function. Would it be right for me to solve with the given function of the graph I drew or solve for but, since it wasn't stated in the question?
Thank you
Good morning. If After drawing a graph, you find out that it's even or odd, you can solve with the shorter integrals. But make sure that the interval is Symmetrical, that is [ - L, L ] or [ - π, π ].
When you determine the function is Odd, Solve for Bn. Also, If you determine the function is Even, Find A0 & An.
@@AVITECHNOLOGIES Thank you sir. Very helpful
20:32 is that not supposed to be 1/2πn² not 1/2πn
Good morning sir
Good morning
Is it 1/pi because my period is 2pi right?
like twos divide to make one over
I don't seem to understand your question, but I'm sure this video will answer your question.
czcams.com/video/BSEN9GhdDRE/video.html
Thanks
Sir please like integration of sinnx=0 why didn't you use that when integrating but rather normal integration
Are you assuming the integration of sinnx is equal to zero? This is wrong. The limit matters, please, use normal integration always and input your limits to the result of the integrals to be sure.
If your question wasn't answered, please, indicate the time in the video that you don't understand.
bn getting at 19:57 1/n is missing
It's not missing.
why a0 is 1/pi? in formula.
is it 1/ 2pi, since the period is 2pi?
formula for a0 is 1/T?
It all depends on what you use to define it. Everything will become balanced when you look for the Fourier series expansion.
czcams.com/video/BSEN9GhdDRE/video.html
@@AVITECHNOLOGIES Thank you!!
In one of your videos on Fourier series you changed on of your values of an to (-1)^n instead of n ….but here you didn’t change it …why is that please ?
I don't know the video you're talking about, but it might interest you to know that cosnπ is equal to (-1)^n. So if I am solving a problem and encounter it, I'll simply change cosnπ to (-1)^n.
However, the value of cos2nπ is equal to 1. So, these substitutions are made when solving problems. It wasn't necessary, that's why I didn't use it.
Oh so cosn2pie can’t be (1)^n?