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vpde_lecture20 [2020/03/19 12:41] trinh |
vpde_lecture20 [2020/03/19 15:49] trinh [Fourier series for even and odd- extensions] |
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| === Odd- and even extensions of $f(x) = x^2$ === | === Odd- and even extensions of $f(x) = x^2$ === | ||
| - | We'll draw the odd and even periodic extension of $f(x) | + | We'll draw the odd and even periodic extension of $f(x) = x^2$ originally |
| - | + | ||
| - | === Fourier series of $f(x) = e^x$ === | + | |
| - | + | ||
| - | We'll then do two examples. One will be the Fourier series for full $2\pi$-periodic extension of $e^x$ defined on $[0, 2\pi]$. The other will be the even extension of $e^x$ defined on $[0, \pi]$. | + | |