Fourier Series

Fourier Series(Q179467)

Some functions are hard to work with, for example, discontinuous and fractal functions. On the other hand, some functions have wonderful properties for example sin, cos, and the linear function. In the Fourier series, we can use functions with wonderful properties to approximate functions that are hard to work with, for example, we use sin and cos to approximate fractal functions. Moreover, we can also approximate the functions by adding up functions together and the Fourier series will tell us what coefficient to use in our combination. However, you can only approximate a function on an interval.

Fourier Series equation $f(\omega )=\int f(x)e^{-i\omega x}dx$

Eulers formula $e^{ix}=\cos {\omega x}+i\sin {\omega x},$