fourier series
Most of the phenomena studied in the domain of engineering and science are periodic in nature> For instance, current and voltage in an alternating current circuit. These periodic functions could be analyzed into their constituent components (fundamentals and harmonics) by a process called Fourier analysis. Periodic functions occur frequently in the problems studied during engineering education. Their representation in terms of simple periodic functions such as sine and cosine, which leads to Fourier series(FS). Fourier series is a very powerful tool in connection with various problems involving partial differential equations. The Fourier series representation of analytic functions is derived from Laurent expansions. The elementary complex analysis is used to derive additional fundamental results in the harmonic analysis including the representation of C∞ periodic functions by Fourier series, the representation of rapidly decreasing functions by Fourier integrals, and Sh