I've done a lot of work on Fourier analysis, and it still remains one of my favorite areas in mathematics. The Fourier transform of the quadratic exponential..i.e. (e^(x^2)) is fascinating .....thank you for posting. ...
You don't understand how much this helps. I'm a computer science major, who recently decided to double major with physics as well, so I jumped in and took two courses, Intro to physics and PHY 307 which is advanced mathematics for physicists, and it kicked my ass. Thanks yo this video I'll catch up hopefully soon, thank you very much!
Thanks so much! I'm in intermediate engineering analysis at UF and you've already saved me in the first week when other resources didn't seem very helpful.
Dr. Tisdell, thank you very much for sharing your knowledge with us. I've been watching a lot of your lectures on youtube. I can't afford for school right now, but with your generosity i'm now in school... Again thanks.
Thanks , you have a very elegant way of explaining it. Thanks so much for uploading this. People like you make the internet a toy of the gods and worthwhile. Thanks again so much.
at the start on his formula sheet you can see that fourier series is a function with general period 2L where L is to be found. Now equate 2L to the period in the example which is 2*pi. and divide both sides by 2 to get L=pi. If your struggling to find the period look on the graph where it starts to repeat from -pi to pi which is a span of 2pi.
HI - that's me. It is probably not this particularly class, but I included something like this just to put a "face" to the voice with the aim of humanising the presentation a little. There are some claims that this can lead to better learning outcomes.
thanks Dr Chris...I like Fourier series now coz i understand but it was my enemy in class six weeks ago..thanks alot..exams next week...I will watch more and more of your lectures..thanks again...
Yoshi, think of it in terms of functions as opposed to numbers. Better yet, think of it as positives and negatives. You know, pos * neg = neg etc? Start simple with y=x (odd function) times y=x^2 (even function). This equals x^3, which is an odd function. Try graphing sin(t)*cos(t). This is even times an odd and look at the result. The resultant function is clearly odd (symmetric about the origin). Hope this helps!
Hi - this is a deliberate educational strategy of mine. I have provided hundreds of solutions on TH-cam but I am reluctant to do so with the questions in my ebook.. The questions in my ebook are designed to challenge, inspire and even frustrate learners at times. This is all part of a holistic educational process to make you learn. Thanks for the feedback!
Great to see that you have turned "an enemy" into "a friend". J. Fourier would be proud! Hope you also take a look at my new ebook. The free download link is in the description.
this 10 minute clip taught me more than all 6 lectures on the subject combined :D oh, and with all due respect - don't turn on the subtitles... they are hillarious xD
Hello, I have to say that these are the clearest explanations yet of Fourier that I have seen. I have come unstuck at the end problem though. I keep getting the a_n coefficent as (2/(n*pi))*Sin(npi) = 0, but now they all = 0? Thanks
This can be proved by using basic algebra. If f is odd [so f(x) = - f(-x)] and if g is even [so g(x) = g(-x)] then the product H(x):= f(x)g(x) = -f(-x)g(-x) = -H(x) so the product is an even function. Note the distinction between ODD and EVEN functions and ODD and EVEN numbers.
My pleasure. If you found this helpful then you also might like my new ebook. It has many more examples and is free to download - the link is in the description.
How come the final answer you are summing up from k=1 to inf? If you look at the initial fourier formula it goes from -inf to inf? Should it not be k=-inf to inf? Is it because during integration we have multiplied by two as it's an even function so the -inf to 0 is taken care of? Thanks
Hi - thanks for the comments. In the theory of Fourier series, the value of L is usually HALF the period of f. In this example we have f with period 2\pi, so L=\pi.
The aim is to formulate an expression for b_n. Depending on what n is, the value of b_n may take on various values. In some examples, if n is even then the value of b_n can be simplified; while if n is odd then the value of b_n can be simplified.
Hello Chris, need to say your lectures on FS are great = simple and clear. Didn't you consider to look at this "problems" from a different point of view? I mean something like reconstruction of a time domain signal from inputs given by e.g. PSD in a frequency domain.
Brilliant, this along with 'Scanimate - Intro to Fourier Series' really shows what the fourier series is all about. Unfortunately time doesn't permit me to look for a mathematical proof.
I've not seen that kind of definition before in regards to Fourier series and believe my way of defining L is the most simple. You might like to ask about his definition.
Amazing Explanation Dr. Tisdell . I would like to know if you have a video explaining Complex Fourier Series. Please guide me if you have lecture notes or explanations on complex Fourier series.
@commelions Why would a $t^2$ appear? We are not integrating $t$, we are integrating $\cos nt$. If you're new to integration then Fourier series are quite a challenge. They usually appear in a third university course in calculus, whereas integration of something like $\cos nt$ appears in a first course in calculus.
So, just for clarity the practice question at the end of this video the answer is 1; is that correct? I am trying to get my head around this as I was meant to know it last year! Thank you very much for this video though, I found it very beneficial.
Think of it as more like addition. This is because it is similar to adding exponentials, ie x^^3 times x^^5 is x^^8. To understand this better, study Euler's equation e^^ix = cos x + i sin x. :)
@lugiachan Consider the even values of n, so n = 2,4,6 etc Can you see why cos (n pi) = 1? Consider the odd value of n, so n = 1,3,5 etc. Can you see why cos (n pi) = -1. Put these cases together and the result follows.
@mchei let me reply myself.... i found that : The product of two even functions is an even function. The product of two odd functions is an even function. The product of an even function and an odd function is an odd function. and The integral of an odd function from −A to +A is zero The integral of an even function from −A to +A is twice the integral from 0 to +A
Thanks for your feedback. If you found this video helpful then you also might like my new ebook. It has many more examples and is free to download - the link is in the description.
what would be wrong in setting up "=If( f(x) >= 0 ; Fourier(x) = ( high value) ; Fourier(x) = ( low value) )" ? It looks like the same outcome, just takes less work.
@csGolddragon No, what I've said is correct. If h(x) = f(x)g(x) with f odd and g even then h is odd (ie, h(x) = -h(-x) for all x). You can prove this (or just confirm it with on wikipedia).
How did you use Maple to come up with that plot? I have a project right now and have the F.S. of our function but can only get the plot to show one "cycle" of the periodic function.
can someone explain the bit at 7:40 where he's talking about doubling the integral. Why did we write 2 in the numerator outside and how does doubling the integral -pi to pi make it go from 0 to pi?
Regarding the answer to the practice question at the end, the function seems to be neither odd nor even. Also the final answer has all three components a0, a1 and b1.
I have a question! If we take a harmonic wave added to another harmonic wave, and then want's to calculate with them. Lets say that we have f(x)=3sin(3*pi*x)+4sin(4*pi*x), this will result in f(x)={6,8381 0
I wish my math professors were as good as you. In my college, professors assume that everything should be intuitive so they rush through a topic and test us in depth, on it. :(
@golnar Yes, if you want to "simplify" the sum. It would also be OK to leave it without changing to 2k-1 (or 2k if you are summing over the even terms). It depends on your preference.
thanks a lot, but can you please explain how do we we rite 2k-1 instead of n, i dont understand it, for exampl eif n=3 then (2*-1) is 5 which is not true
@ELT626SSN Some texts prefer to have a_0/2 in the Fourier series (rather than just "a_0"). In that case there is no "2" in the (integral) definition of a_0.
@lminors Correct - the function isn't even (I didn't claim that it was). Think of shifting the curve down 1/2 a unit to produce an odd function and calculate the FS for that. Then simply add 1/2 to your answer. Over and out.
Alright alright I have an exam in an hour and a half and I must this really helped a lot but I'm still confused with that thing you did at the end with the cos... how did you turn that into (-1)^n ? will it always be like that ? is there a different transformation for sin ? please help
@NevermindVzla Yes, it will always be like that (can you see why?). There is also one for sin, but I'll leave it to you to determine it. Good luck with your exam!
How would you find a0 if the function was even? I'm getting caught up on weather or not I need to integrate the left and right sides of the y-axis separately.
I have only just learnt this myself but I think what it means is that: Because the series is periodic it will repeat it self, as the minimum and maximum of cosine is -1 and 1 then if the n is positive it will be at a maximum and if the n is negative then it will be at a minimum. -1^1=-1 -1^2=+1 -1^3=-1 -1^4=+1 So it is just repeating for pi. ^1 = -pi ^2 = +pi ^3 = -pi ^4 = +4. Wow I described that awfully.
![[Part 1] ทารกน้อยถูกทิ้ง👶 หญิงชราเก็บขวดขายเลี้ยงดูเขาจนโต #โลกการละคร](http://i.ytimg.com/vi/nPTDvFCExks/mqdefault.jpg)
I've done a lot of work on Fourier analysis, and it still remains one of my favorite areas in mathematics. The Fourier transform of the quadratic exponential..i.e. (e^(x^2)) is fascinating .....thank you for posting. ...
You have no idea how much this helped. I've been in PDE's for a month now and my teacher hasn't been able to explain this so simply!!
You just saved my semester sir
You don't understand how much this helps. I'm a computer science major, who recently decided to double major with physics as well, so I jumped in and took two courses, Intro to physics and PHY 307 which is advanced mathematics for physicists, and it kicked my ass. Thanks yo this video I'll catch up hopefully soon, thank you very much!
u've just simplified this for me. i've got an exam in two weeks and i'm more confident of aceing it now.thanks.
Why is there a little window left in the bottom of the screen with a man imparting a class?
To distract us from the otherwise brilliantly demonstrated problem, I guess... :-/
That's me, it doesn't match up with the main picture. if it really bothers you then try covering me up with a post-it note, or just your thumb.
Dr Chris Tisdell lol
was scrolling in the comments for an explanation to that little dude in the corner
The way u teach is easy to understand and ur voice nice to listen! Thanks from Kazakhstan! Keep it up!
Thanks so much! I'm in intermediate engineering analysis at UF and you've already saved me in the first week when other resources didn't seem very helpful.
Dr. Tisdell, thank you very much for sharing your knowledge with us. I've been watching a lot of your lectures on youtube. I can't afford for school right now, but with your generosity i'm now in school... Again thanks.
I know people don't say this a lot on education videos, but I think I am going to have to break the replay button for this one...
Thanks , you have a very elegant way of explaining it. Thanks so much for uploading this. People like you make the internet a toy of the gods and worthwhile.
Thanks again so much.
i know you here this a lot!!! but seriously THANK YOU :)
really nice of you to go out of your way to help people
You make a great online math tutorial. One of the best I have seen. Thank You! Keep the PDE stuff coming!
You, my good sir, are amazing. Your effort is much appreciated. Knowledge is power!
at the start on his formula sheet you can see that fourier series is a function with general period 2L where L is to be found. Now equate 2L to the period in the example which is 2*pi. and divide both sides by 2 to get L=pi. If your struggling to find the period look on the graph where it starts to repeat from -pi to pi which is a span of 2pi.
HI - that's me. It is probably not this particularly class, but I included something like this just to put a "face" to the voice with the aim of humanising the presentation a little. There are some claims that this can lead to better learning outcomes.
thanks Dr Chris...I like Fourier series now coz i understand but it was my enemy in class six weeks ago..thanks alot..exams next week...I will watch more and more of your lectures..thanks again...
This video is the only reason I got any of my homework done. Thank you so much!
Yoshi, think of it in terms of functions as opposed to numbers. Better yet, think of it as positives and negatives. You know, pos * neg = neg etc? Start simple with y=x (odd function) times y=x^2 (even function). This equals x^3, which is an odd function. Try graphing sin(t)*cos(t). This is even times an odd and look at the result. The resultant function is clearly odd (symmetric about the origin). Hope this helps!
Very helpful tutorial. Only one question, when integrating at 8:50 I believe the integral should be -(1/n)cos(nt) because of the chain rule. :)
Hi - this is a deliberate educational strategy of mine. I have provided hundreds of solutions on TH-cam but I am reluctant to do so with the questions in my ebook.. The questions in my ebook are designed to challenge, inspire and even frustrate learners at times. This is all part of a holistic educational process to make you learn. Thanks for the feedback!
Great to see that you have turned "an enemy" into "a friend". J. Fourier would be proud! Hope you also take a look at my new ebook. The free download link is in the description.
But it says 404
In most examples it is the function that you begin with. In this video it is f(t) (of course, neglecting points of discontinuity etc).
Using this for my Mechanical Vibrations class... Very thorough and informative. Thank you.
thank you sir ...i study in 1 years master Electrical Engineering, and i hope that ..benefit from your extensive experience
bilal
And it's very nice of you to post your feedback - thanks!
this 10 minute clip taught me more than all 6 lectures on the subject combined :D
oh, and with all due respect - don't turn on the subtitles... they are hillarious xD
2 gün sonra diff sınavı var sayende 10 dkda fourier öğrendim sıfırdan sen nası 1 kralsın what kind of king you are?
thank u very much sir , u have saved my life your lectures are awesome and easy to follow
thanks alot sir... this helped in my exams.. respect from india..
Hello, I have to say that these are the clearest explanations yet of Fourier that I have seen. I have come unstuck at the end problem though. I keep getting the a_n coefficent as (2/(n*pi))*Sin(npi) = 0, but now they all = 0? Thanks
A magnificent, little lecture! Very helpful! Thank you, Sir!
My pleasure and good luck with Fourier series. Hope the free ebook is also of some use.
You are amazing. I was about to give up on this if it had not been for this fantastic video. Thank you.
Thanks a lot, very useful video for a frenchie who wanted to work for the holidays :)
This can be proved by using basic algebra. If f is odd [so f(x) = - f(-x)] and if g is even [so g(x) = g(-x)] then the product H(x):= f(x)g(x) = -f(-x)g(-x) = -H(x) so the product is an even function. Note the distinction between ODD and EVEN functions and ODD and EVEN numbers.
Thank you so much, Dr. Tisdell, for sharing your expertise here in youtube. :)
My pleasure. If you found this helpful then you also might like my new ebook. It has many more examples and is free to download - the link is in the description.
How come the final answer you are summing up from k=1 to inf?
If you look at the initial fourier formula it goes from -inf to inf?
Should it not be k=-inf to inf?
Is it because during integration we have multiplied by two as it's an even function so the -inf to 0 is taken care of?
Thanks
Hi - thanks for the comments. In the theory of Fourier series, the value of L is usually HALF the period of f. In this example we have f with period 2\pi, so L=\pi.
The aim is to formulate an expression for b_n. Depending on what n is, the value of b_n may take on various values. In some examples, if n is even then the value of b_n can be simplified; while if n is odd then the value of b_n can be simplified.
Absolutely excellent video. Thank you so much for making this.
Hello Chris, need to say your lectures on FS are great = simple and clear. Didn't you consider to look at this "problems" from a different point of view? I mean something like reconstruction of a time domain signal from inputs given by e.g. PSD in a frequency domain.
Brilliant, this along with 'Scanimate - Intro to Fourier Series' really shows what the fourier series is all about. Unfortunately time doesn't permit me to look for a mathematical proof.
I've not seen that kind of definition before in regards to Fourier series and believe my way of defining L is the most simple. You might like to ask about his definition.
Sir how one can thank you for your help you are an expert 😀 👍 🙂
Thank you for this ^^. That even/odd method is very interesting ^^. You learn something new every day.
Amazing Explanation Dr. Tisdell . I would like to know if you have a video explaining Complex Fourier Series. Please guide me if you have lecture notes or explanations on complex Fourier series.
@commelions Why would a $t^2$ appear? We are not integrating $t$, we are integrating
$\cos nt$. If you're new to integration then Fourier series are quite a challenge. They usually appear in a third university course in calculus, whereas integration of something like $\cos nt$ appears in a first course in calculus.
Your videos are very helpful, and your voice is very nice to listen to. :) Thanks!
You explained it in plain English! Thank you
My pleasure. Glad you found it useful.
So, just for clarity the practice question at the end of this video the answer is 1; is that correct? I am trying to get my head around this as I was meant to know it last year!
Thank you very much for this video though, I found it very beneficial.
GameWith Dave Hi - the answer(s) are in the free ebook in the description.
Fourier series are only defined for periodic functions (with piecewise continuity etc), since the series involve periodic functions (sin and/or cos).
woah, i never understood what my lecturers meant by "f(x) in this case is odd" or "f(x) is even." Thank you for explaining what they mean by that! :D
Hi, what do you mean but "upperlimit" and "lowerlimit"?
what class do you typically learn fourier series in? differential equations or an engineering class?
Think of it as more like addition. This is because it is similar to adding exponentials, ie x^^3 times x^^5 is x^^8. To understand this better, study Euler's equation e^^ix = cos x + i sin x. :)
@lugiachan Consider the even values of n, so n = 2,4,6 etc Can you see why cos (n pi) = 1? Consider the odd value of n, so n = 1,3,5 etc. Can you see why cos (n pi) = -1. Put these cases together and the result follows.
thanks these videos are very helpful, can you please do videos on the Fourier transform
Thank you for uploading this video, I sincerely appreciate it . It helps me alot .
Well done - you answered your own question.
Thank you for this great, and easy to understand lesson. It is much appreciated.
@mchei
let me reply myself....
i found that :
The product of two even functions is an even function.
The product of two odd functions is an even function.
The product of an even function and an odd function is an odd function.
and
The integral of an odd function from −A to +A is zero
The integral of an even function from −A to +A is twice the integral from 0 to +A
Yes, Sf(t) is the Fourier series of f(t). If f(t) = t then which interval is it defined on?
Thanks for your feedback. If you found this video helpful then you also might like my new ebook. It has many more examples and is free to download - the link is in the description.
what would be wrong in setting up "=If( f(x) >= 0 ; Fourier(x) = ( high value) ; Fourier(x) = ( low value) )" ?
It looks like the same outcome, just takes less work.
10 years later, did you withdraw the ebook? Nothing on the link provided.
Because in his main fourier series equation, it is just a(0), if you look at the one you've been given it's likely to be a(0) / 2
@csGolddragon No, what I've said is correct. If h(x) = f(x)g(x) with f odd and g even then h is odd (ie, h(x) = -h(-x) for all x). You can prove this (or just confirm it with on wikipedia).
Thanks, this was so helpful! Any chance you could do one on complex fourier series? :)
How did you use Maple to come up with that plot? I have a project right now and have the F.S. of our function but can only get the plot to show one "cycle" of the periodic function.
can someone explain the bit at 7:40 where he's talking about doubling the integral. Why did we write 2 in the numerator outside and how does doubling the integral -pi to pi make it go from 0 to pi?
Regarding the answer to the practice question at the end, the function seems to be neither odd nor even.
Also the final answer has all three components a0, a1 and b1.
Please, I want the book in pdf version
Hi Chris, thank you for this tutorial, it was super helpful!! One thing that confused me was the period -why isn't it L=2π?
Hi, if we are only interested in odd values of n, then 2k-1 is always odd (for k=1,2,3,4,..) so we can replace n with 2k-1 and we sum k=1,2,3,4 etc.
you're a saviour, many thanks
I mean if we have cases when f(x)=something for 0
Very good video. Please what exactly is "n" in fourier series formula and why is (cos n*pi) equal to (-1)^n ?
+Jimmy Santadeo
n is a number whether 1,2,3,4,...
while cosn*pi =-1 because of pi=180 degree....if n equal to 1, 3 is odd so (-1)^1 stay with -1
Thank you very much! :)
@DrChrisTisdell I figured it out, thanks !
My exam was postponed for today, any last minute advices Dr ?
Yes, that is a great suggestion. I do have some videos on Fourier Transform and convolution, but I also plan to do it for Laplace transforms.
I have a question! If we take a harmonic wave added to another harmonic wave, and then want's to calculate with them. Lets say that we have f(x)=3sin(3*pi*x)+4sin(4*pi*x), this will result in f(x)={6,8381 0
Thank much Dr. Chriss for your free lectures. It very useful, easy to understand! . You saved me a lot of time and money! . Thank you sir!.
Thanks a lot for this video Dr. Tisdell!
My pleasure. Hope the free ebook is also of some help to you. The link is in the description.
From the definition of f we have f(x) = f(x + 2\pi) so the period must be 2\pi. The L value in your Fourier series is HALF the period of f.
I wish my math professors were as good as you. In my college, professors assume that everything should be intuitive so they rush through a topic and test us in depth, on it. :(
@lugiachan Because n = 2k-1 is always an odd number (whenever k is an integer) and we are only interested in summing over the odd values of n.
@golnar Yes, if you want to "simplify" the sum. It would also be OK to leave it without changing to 2k-1 (or 2k if you are summing over the even terms). It depends on your preference.
thanks a lot, but can you please explain how do we we rite 2k-1 instead of n, i dont understand it, for exampl eif n=3 then (2*-1) is 5 which is not true
Hi - I would say both! It just depends on what kind of degree you are pursuing.
@ELT626SSN Some texts prefer to have a_0/2 in the Fourier series (rather than just "a_0"). In that case there is no "2" in the (integral) definition of a_0.
@lminors Correct - the function isn't even (I didn't claim that it was). Think of shifting the curve down 1/2 a unit to produce an odd function and calculate the FS for that. Then simply add 1/2 to your answer. Over and out.
Alright alright I have an exam in an hour and a half and I must this really helped a lot but I'm still confused with that thing you did at the end with the cos... how did you turn that into (-1)^n ? will it always be like that ? is there a different transformation for sin ? please help
Very helpful thank you very much. Good explanation.
@NevermindVzla Yes, it will always be like that (can you see why?). There is also one for sin, but I'll leave it to you to determine it. Good luck with your exam!
Many thanks for the feedback.
How would you find a0 if the function was even? I'm getting caught up on weather or not I need to integrate the left and right sides of the y-axis separately.
Also, can you always limit the range to positive L by multiplying the function by 2, or is this just a property of even functions?
I have only just learnt this myself but I think what it means is that:
Because the series is periodic it will repeat it self, as the minimum and maximum of cosine is -1 and 1 then if the n is positive it will be at a maximum and if the n is negative then it will be at a minimum.
-1^1=-1
-1^2=+1
-1^3=-1
-1^4=+1
So it is just repeating for pi.
^1 = -pi
^2 = +pi
^3 = -pi
^4 = +4.
Wow I described that awfully.
Hi doctor chris， is the Fourier series elongated twice by period？