Practical Session 7: Fourier Series

This practical session provides 10 problems for mastering Fourier series. Students compute coefficients for periodic functions, handle even and odd symmetries, and write series in summation notation. Problems cover square waves, polynomials, and rectified sine waves. Half-range expansions (cosine and sine series) are practiced on the interval from zero to pi. Additional problems apply Fourier series to evaluate infinite series using Dirichlet's theorem and Parseval's identity, including deriving the Leibniz formula for pi and summing reciprocal squares. The session concludes with homework problems and a summary of key formulas. Each problem includes a complete step-by-step solution, making it suitable for classroom use or self-study.