Fourier Series. An Intuitive Explanation.

• Fourier Series. An Int...
00:00 Why Fourier series?
01:08 The concept of Fourier series
03:05 Fourier coefficients
06:15 Fourier basis
09:38 Example: Sawtooth function
More: en.fufaev.org/fourier-series

[@fufaev-alexander]

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[@randomz5890]

Such a clear explanation of very opaque mathematics. Great video!

[@fufaev-alexander]

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[@helmutalexanderrubiowilson6835]

You are underrated!!! Fantastic channel

[@AJ-et3vf]

Great video as usual! Thank you!

[@fufaev-alexander]

Thank you!

[@sergiolucas38]

Amazing video, thank you :)

[@fufaev-alexander]

Thank you!
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[@nvnrmchl]

Do metal organic frameworks next! It’s an emerging field

[@fufaev-alexander]

That sounds interesting, but I don't know anything about it!
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[@arpg3910]

Excellent video, as always. About the delta dirac's completeness relation expression, where did it come from tho? And how should one interpret that formula?

[@fufaev-alexander]

Check out my lesson:
en.universaldenker.org/lessons/1375
under the title "Property #2: Fourier basis is complete"
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[@teikono]

Lovely explanation 👍

[@fufaev-alexander]

Thank you 🙂

[@chrstfer2452]

What makes that a "much better" notation than sigma, just because it's not a greek letter? One downside is that ive no idea how i'd quickly enter that in latex without defining a macro for it. Also, it makes other series-type operations *more* complicated to typeset (for instance, the union of indexed sets operator seems to me would just become the same operator but with a box around it).
If you want to stop using sigma, einstein notation is better imo, this new boxed plus thing is like solving a nonproblem

[@chrstfer2452]

And then you use it as an integral synonym too? Idk man, i think i just disagree

[@fredthechamp3475]

I agree with you on his use of the "sigma" notation. He makes such a weird assertion.

[@youtubepooppismo5284]

I guess because you can put any commutative binary operator inside, without having Sigma, Pi, Union, Intersection, Iterated logical AND and OR (whatever they're called) and others that i've never seen

[@davethesid8960]

And it looks a lot like direct sum notation, only it's a box not a circle.

[@thisisrr1]

Great stuff

[@fufaev-alexander]

Thank you!!

[@raven5165]

I think you can also approxiamate function definately by Taylor series too if it is infinitely differentiable and converges

[@fufaev-alexander]

yes, you are right! Unfortunately, not every function is "well behaved". :D
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[@xfcisco]

Best maths channel no cap

[@fufaev-alexander]

Oh thank you xfcisco!

[@rktiwa]

This is different way of explaining it. I hope if I watch it a couple of times may be I get it. So far I haven't been able to understand how it works through other videos dealing with this. Let me tell you though you are a class in yourself.

[@schebbi]

Find das video sogar besser als das 3blue1Brown video zum thema, viel weniger abstrakt!

[@fufaev-alexander]

Danke dir!
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[@AlvaroALorite]

1:26 where did that New notation for summation come from?

[@fufaev-alexander]

Let's put it this way: this is my personal, thought-out notation. Maybe it will become accepted at some point. 😁😄
I like this notation, because you can write other operations into the square, too, not only plus sign (for summation)

[@AlvaroALorite]

@@fufaev-alexander i like it to!

[@fufaev-alexander]

@@AlvaroALorite thank you 😇

[@biswajit681]

Next video on vector space

[@fufaev-alexander]

Mmm, can you be more specific?

[@biswajit681]

@@fufaev-alexander Vector Space Linear Algebra

[@AriKath]

i didn't really understand