Not only are you a great mathematican, but your way of explaining and your pedagogical skills are truely remarkable. Not many good mathematicans possess these qualities.
What a beautiful and simple explanation to this concept. I feel so lucky to be able to watch this as I am taking a Signals and Systems class, and we were just given the formula with no derivation. I am amazed. Thank you!
Finally a concise way that explains the transition from the trigonometric to the exponential depiction of FS. Thanks, in particular for the clear explaination of how to connect the two sums together!
This was one of the best and most satisfying math videos I have ever watched. You'r presentation, explaination and also you'r handwriting skills are top notch. Thank you!
My word....this gentleman explained CFS in 15 bloody minutes ppl! My old lecturer needed a whole 3hr session....smh Had to subscribe, especially when he used the word 'beautiful.' Because Mathematics is indeed beautiful!
Professor MathTheBeautiful, thank you for a beautiful explanation and derivation of the Complex Fourier Series in Partial Differential Equations. In Signal and Systems Theory and Communication Systems, Fourier Series Coefficients are given with no derivations. This is an error free video/lecture on TH-cam TV.
The problem with Mathematics is that there are so many bad teachers, the good ones are very few and when we find a good one one, he is an absolute treasure. This is why I became a Math teacher, I wanted to be one of the good ones. I strongly feel that we should do away with many of those horrible teachers and replace them with the internet and people like him. He is is absolutely brilliant and God bless him.
I think that gathering together c_n and c_-n under one sum was not explained. If I remember correctly, its due to cos & sine being even and odd functions, resulting in a_-n = a_n and b_-n = -b_n, so they can be also gathered with exp.
Another big advantage is that they look just polynomials. Just let x=exp(i*alpha)… Power series as the professor said but stressing the fact that now we have complex polynomials.
Under the scope of *linear algebra* , Fourier in [a,b] makes total sense, as a linear system of (uncountably) infinite equations and (countably) infinite, column, orthogonal, basis vectors in the form of e^iωx. Its just a fancy matrix, which can be solved with inner products on both sides for each vector then dividing by norm squared to calculate each complex scalar. Why do we use inner products? Cause Gauss, Jordan or Cramer's elimination obviously can't solve an infinite-dimensional system in finite time. Its pretty interesting if you think about it.
Although a_n is not defined for 0, but only for the natural numbers, but still I feel that a_0 should be denoted be something else like d_0 because it can create confusion, as if a_n is that equation , then if we put n=0, we get a_0=2*a_0.
This may still hold true if a_0 = 0; however, simply plugging in a_0 into the equation for a_n would hold no meaning as the infinite sum begins at 1. It is not defined for 0, and I would hope that any mathematician who doesn't see that fairly quickly should be inclined to look over sigma notation again. I can see where the confusion may arise, but I think if symbols confused someone, it's unlikely they made it this far into math lol.
Linking the "e's" to the polar ones on the unit circle = 1....is ok too....Never The Less...Your PRESENTATION on "C.F.S." CONNECTIONS IS SPEECHLESS .....ps....Great Job.....
Whatever periodic function that you are trying to generate. For example, a delta function (pulse), a step function (square wave), or a sawtooth wave. Lots of applications in electronics and heat transfer.
I know some people who are very unfamiliar with math (basically, they survived arithmetic and basic algebra but then got stuck somewhere and didn't want to continue any more after that), and even they agree that the complex series looks a lot more beautiful than the trigonometric mess, haha.
+Lemma Yeah, well actually they think both equations look kinda scary (I remember feeling that way myself about this kind of stuff before I got into complex exponentiation etc), but they certainly find the complex version more pleasant. =P But of course, that's quite understandable, since that equation is much shorter.
We define Cn=(An-iBn)/2 and C-n=(An+iBn)/2 that's Okey we suppose n=0 C0=(A0-iBn)/2 and C0=(A0+iBn)/2 so C0= A0/2 but you define C0=A0 how can is it possible
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You Sir, explain in minutes what my professor would do in hours
very impressive handwriting, most professors lack this basic skill, 12/10
Yes, those figure brackets!
Not only are you a great mathematican, but your way of explaining and your pedagogical skills are truely remarkable. Not many good mathematicans possess these qualities.
What a beautiful and simple explanation to this concept. I feel so lucky to be able to watch this as I am taking a Signals and Systems class, and we were just given the formula with no derivation. I am amazed. Thank you!
You did it. You finally broke it through to me how intuitive complex fourier series and transform is. Thank you so much
Finally a concise way that explains the transition from the trigonometric to the exponential depiction of FS. Thanks, in particular for the clear explaination of how to connect the two sums together!
this is letterally a golden 15 mins thank you
that 's really what I was looking for thanks for your clearly introduction
This was one of the best and most satisfying math videos I have ever watched.
You'r presentation, explaination and also you'r handwriting skills are top notch.
Thank you!
Incredible, just incredible... Thank you!
Thank you sir! This is the first time I've seen the Fourier Series explained so intuitively.
Glad it was helpful!
Great explanation! It's nice to see a prof that's passionate about what he is doing!
Thank you, that means a lot!
you are a sales rep for complex Fourier series! I wish to use it.
Really good explanation. Thank you !
My word....this gentleman explained CFS in 15 bloody minutes ppl!
My old lecturer needed a whole 3hr session....smh
Had to subscribe, especially when he used the word 'beautiful.'
Because Mathematics is indeed beautiful!
Wow this is impressive. I could only wish that the professors at my school could get the point across this well.
thank you for deep learning from south korea
Splendid lecture!
We need more lectures from you
I love this...
no word jus 🙏 really great sir...
As physics that studies applications starting from quantum mechanics, they are enthusiastic about this clear and convincing explanation
this was really good, thank you
Thank you so much Arnold from UNZA, Zambia.
Thanks. I'll be back.
Explained with such enthusiasm, thumbs up .
Thanks! I am very enthusiastic!!!!!!!! Yeah!
Thank you sooooooo much!
Professor MathTheBeautiful, thank you for a beautiful explanation and derivation of the Complex Fourier Series in Partial Differential Equations. In Signal and Systems Theory and Communication Systems, Fourier Series Coefficients are given with no derivations. This is an error free video/lecture on TH-cam TV.
Glad it was helpful!
The problem with Mathematics is that there are so many bad teachers, the good ones are very few and when we find a good one one, he is an absolute treasure. This is why I became a Math teacher, I wanted to be one of the good ones. I strongly feel that we should do away with many of those horrible teachers and replace them with the internet and people like him. He is is absolutely brilliant and God bless him.
Thank you, that means a lot!
Fantastic teacher, God bless you... I had so many bad professors, unbelievable.
Thank you. Sometimes it takes a bit of luck to connect with the professor.
Most beautiful explanation love from India❤️
wow................. beautiful explaining..................
Goddamn, I'm sold! I'll take two complex Fourier series, please.
i concurs
I think that gathering together c_n and c_-n under one sum was not explained. If I remember correctly, its due to cos & sine being even and odd functions, resulting in a_-n = a_n and b_-n = -b_n, so they can be also gathered with exp.
Exactly the question I had!
Thank you
God bless you
It motivates me to study and love maths after this video. Thank you Sir
That's my goal so thank you for letting me know!
Another big advantage is that they look just polynomials. Just let x=exp(i*alpha)… Power series as the professor said but stressing the fact that now we have complex polynomials.
Assuming that F is 2pi periodic and piecewise differentiable on [-pi,pi].
12:13 *You're breathtaking*
god bless you sir. thanks from algeria
Thank you! My greetings to Algeria. Hoping to visit one day.
you are welcom sir any day
That's it!!
Under the scope of *linear algebra* , Fourier in [a,b] makes total sense, as a linear system of (uncountably) infinite equations and (countably) infinite, column, orthogonal, basis vectors in the form of e^iωx.
Its just a fancy matrix, which can be solved with inner products on both sides for each vector then dividing by norm squared to calculate each complex scalar. Why do we use inner products? Cause Gauss, Jordan or Cramer's elimination obviously can't solve an infinite-dimensional system in finite time.
Its pretty interesting if you think about it.
i love youuuuuu
Although a_n is not defined for 0, but only for the natural numbers, but still I feel that a_0 should be denoted be something else like d_0 because it can create confusion, as if a_n is that equation , then if we put n=0, we get a_0=2*a_0.
This may still hold true if a_0 = 0; however, simply plugging in a_0 into the equation for a_n would hold no meaning as the infinite sum begins at 1. It is not defined for 0, and I would hope that any mathematician who doesn't see that fairly quickly should be inclined to look over sigma notation again. I can see where the confusion may arise, but I think if symbols confused someone, it's unlikely they made it this far into math lol.
what is the value between -1 to 1? Why is can be combined for Cn?
cz c0 is defined as a0
@@NingNeilXie Thanks
Do you have to prove separately that this works for complex functions as well?
Not so much prove separately, but to make sure that everything holds up.
Unclear, unreadable only English is perfectly 🥰 💞 that is better than hindian teachers
sir;
You were right; I am ready for a Cuban-seed cigar and a glass of bourbon after that.
wow that ending bummed me out though its like why do i need to know this if the computational algorithm is half as fast smh
If the input function is a complex function (which is not uncommon in computing!), computers have to use the complex version anyway.
that's amazing daddy
where does this guy teach?
Drexel University in Philadelphia
Oh he said Drexel later in the video.
Linking the "e's" to the polar ones on the unit circle = 1....is ok too....Never The Less...Your PRESENTATION on "C.F.S." CONNECTIONS IS
SPEECHLESS .....ps....Great Job.....
Whats f(x) ?
11:06 this video is a proof of how functions on bounded intervals are similar to the complex fourier series
Whatever periodic function that you are trying to generate. For example, a delta function (pulse), a step function (square wave), or a sawtooth wave. Lots of applications in electronics and heat transfer.
I like the new haircut, or rather the lack thereof.
Sounds like they used two microphones and combined them, so u get a chorus/echo effect. Slightly distracting.
I know some people who are very unfamiliar with math (basically, they survived arithmetic and basic algebra but then got stuck somewhere and didn't want to continue any more after that), and even they agree that the complex series looks a lot more beautiful than the trigonometric mess, haha.
So it's unanimous!
+Lemma
Yeah, well actually they think both equations look kinda scary (I remember feeling that way myself about this kind of stuff before I got into complex exponentiation etc), but they certainly find the complex version more pleasant. =P
But of course, that's quite understandable, since that equation is much shorter.
OH! SHIT! That's what one of my students would have said. I had banished him to the back of the class but one day he decided to pay attention....
We define Cn=(An-iBn)/2 and C-n=(An+iBn)/2 that's Okey we suppose n=0 C0=(A0-iBn)/2 and C0=(A0+iBn)/2 so C0= A0/2 but you define C0=A0 how can is it possible
🧩🎼🦋🪷🌈🛸🧜🏽♀️💎🧞♀️
Hey you look like Grothendieck
I bet you this guy is an engineer, typical balding patterns and glasses. This sadly is my destiny too....
no shampoo
Some chick dig bald guys "like woah".
th-cam.com/video/vOxWfRrb2Sk/w-d-xo.html
What's so sad about it?
Good but anyone can do this or copy it from a book, solve examples, it's impossible to learn math with theory.
you are verbose, beauty you tied to simplicity and then again listed simplicity. Choose one they are not mutually exclusive per your explanation...
this one talks too much