Solution of IDZ Ryabushko 12.3 - Option 22

Section: Chapter 12. Series
Topic: Fourier series of periodic functions
Description: Expansion of periodic functions into Fourier series on the interval [-π,π] and on an arbitrary interval. Expansion in cosines and sines for even and odd extensions. Application of Fourier series for summing numerical series.

Tasks:
1. Expand the periodic function f(x) with period ω = 2π, defined on the interval [–π; π], into a Fourier series.
2. Expand the function f(x) defined on the interval (0; π) into a Fourier series, continuing (extending) it in an even and odd way. Plot graphs for each extension.
3. Expand the periodic function f(x) with period ω = 2l into a Fourier series on the given interval.
4. Expand a function defined graphically into a Fourier series.
5. Using the Fourier series expansion of the function f(x) on the given interval, find the sum of the given numerical series.

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