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| -rw-r--r-- | Problem Set 2.page | 10 |
1 files changed, 5 insertions, 5 deletions
diff --git a/Problem Set 2.page b/Problem Set 2.page index 2637ab2..beafd04 100644 --- a/Problem Set 2.page +++ b/Problem Set 2.page @@ -23,18 +23,18 @@ Cook up other examples and post them on the wiki! 1. Compute the Fourier Series of the following functions. Do both the exponential and sin/cos expansions. - a. $f(x) = \sin^3(3x)\cos^2(4x)$ + a. f$f(x) = \sin^3(3x)\cos^2(4x)$ - $g(x) = x(x-2\pi)$ (Hint: Use integration by parts) 2. Show that -$\int_0^{2\pi} \sin^4(x) dx = \frac{3 \pi}{4}$ +$$\int_0^{2\pi} \sin^4(x) dx = \frac{3 \pi}{4}$$ (Hint: write out the exponential fourier expansion of $\sin^4(x)$.) 3. Compute the exponential Fourier coefficients of $\sin^2(x)$: -$a_n = \frac{1}{\sqrt 2\pi} \int_0^{2\pi} \sin^2(x) e^{-inx} dx$ -and use this to show that -$\int_0^{2\pi} |\sin^2(x)|^2 dx = \sum |a_n|^2.$ +$$a_n = \frac{1}{\sqrt 2\pi} \int_0^{2\pi} \sin^2(x) e^{-inx} dx$$ +and use this to verify that +$$\int_0^{2\pi} |\sin^2(x)|^2 dx = \sum |a_n|^2.$$ # Solutions |