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Lecture 35, 11/18/2022. This page is for Section 1 only.
ACMS 20550: Applied Mathematics Method I
Instructor: Bei Hu, b1hu@nd.edu, Hurley 174A
Chapter 7: Fourier Series and Transform
- Complex format
$f(x) \sim \sum_{n=-\infty}^{+\infty} c_n e^{inx}$, where
$c_n = \frac1{2\pi} \int_{-\pi}^\pi f(x) dx$
- Other intervals. Fourier Series: $-l< x< l$
$\begin{array}{rcl} f(x) & \sim & \frac12 a_0 + a_1 \cos \frac{\pi x}l + a_2 \cos \frac{2\pi x}l + a_3 \cos \frac{3\pi x}l + \cdots \\
&& \mm + b_1 \sin \frac{\pi x}l + b_2 \sin \frac{2\pi x}l + b_3 \sin \frac{3\pi x}l + \cdots \end{array}$
$\mm\mm $
$a_n = \frac1l\int_{-l}^l f(x) \cos \frac{n\pi x}l dx $
$\mm\mm $ $b_n = \frac1l\int_{-l}^l f(x) \sin \frac{n\pi x}l dx $