Hi Rushi,

The Fourier series are one of the most important series in real world applications. you can use it in several area like

I can say about these applications.

Signal Processing. It may be the best application of Fourier analysis.

Approximation Theory. We use Fourier series to write a function as a trigonometric polynomial.

Control Theory. The Fourier series of functions in the differential equation often gives some prediction about the behavior of the solution of differential equation. They are useful to find out the dynamics of the solution.

Partial Differential equation. We use it to solve higher order partial differential equations by the method of separation of variables.