FA 1 | Fourier series introduction
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- Опубликовано: 6 окт 2024
- An introduction to Fourier analysis.
FA playlist: • Fourier Analysis
PDE playlist: www.youtube.com...
Part 1 topics:
-- idea of Taylor series
-- idea of Fourier series (2:30)
-- an example, Fourier series for x (4:33)
-- guiding questions for studying Fourier series (7:24)
The answer to FFT
cosine is an even function
the function in the previous slide is odd function
even*odd = odd and the integral of odd is zero
Other than that , thank you so much for making this so simple to understand
This is a good video. Thank you man. PDE teacher this semester has a super heavy accent haha
Because cos(x) doesn't intersect the origin
My guess is that it's because x is an odd function while cos is even.
i love your explanations ^^
because the coefficients (a) of cos(x) are 0
Great job!
Cos(x) 'even' valued while y = x is 'odd'..
Thanks
Brilliant!
Thanx,,thats a nice explanation :)
How do you create those graphical representation? Please share as they provide very good understanding.
He does it using Mathematica
Wow. Thanks!
how did fourier discover this?
it's got something to do with the fact that 1,cos, sin,... is a basis for a certain function space (more general than continuous functions). what more, it's an orthogonal basis (it's as good as the (1,0,0), (0,1,0), (0,0,1) basis for R^3). so the motivation is to express every function from that space via this basis. and the fourier coefficients are like coefficients of vectors with respect to a basis. loosely speaking. it doesn't really answer why or how tho lol.
That gets me a little closer to the explanation I've long been searching
@@fitofight8540 Probably a moment of genius. Some of the world's mathematical inventions have nothing to do with math or science at all. Ex. There's a system of power called the three phase system that revolutionized electronic power distribution. The genius that came up with it thought of the idea from staring at the sun. Yes, staring at the sun and afterwards, he noticed when he closed there eyes, there appeared to be three dots that were rotating in a circle and he became obsessed with those 3 dots in a circle. Somewhere in his brain, those three dots connected to his knowledge of power/electronics and his mind worked out a new electronic power distribution system.
If he hadn't stared at the sun and became obsessed with those 3 dots.... would he have ever discovered three phase power? Have other people seen those dots from staring at the sun and closing their eyes and thought nothing about it? It seems like random chance and just the right circumstances generated this discovery. Newton claims to have thought of the idea of gravity when an apple fell on his head and that revolutionized physics (although Leibnitz was coming up win his own form of calculus).
Oshanii's answer is good enough but you might be interested to know his motivation was also to solve PDEs (The heat equation in particular). When it comes to many discoveries, the rigour actually comes much later. I am pretty sure Fourier's university colleagues were very skeptical of his ideas. Calculus has MANY examples of hand waviness that is justified later and beautifully turns out to agree with our motivation.