# Project 11: Fourier Series

## Description:

A Fourier series is a way of representing a periodic function as a sum of sine and cosine functions.

In our project, we are going to pick a function and compute it's fourier coefficients analytically

## Algorithm and Discussion

In this experiment

Suppose f is a periodic function with a period T = 0.131. Then the Fourier series representation of f is a trigonometric series (that is, it is an infinite series consists of sine and cosine terms of the form.

The coefficient gotten is: $a = n * \frac{\pi}{L}$

## Implementation and Code

When $$y = sin(x) + \frac{sin(3x)}{3}$$

When $$y = sin(x) + \frac{sin(3x)}{3} + \frac{sin(5x)}{5}+ \frac{sin(7x)}{7}$$

We can keep adding to increase the function, it adds more waves.

### Next: check your answer both graphically and numerically using simpson's rule.

# Conclusion

In this experiment, with period T = 0.131. The Fourier series representation of f is a trigonometric series (that is, it is an infinite series consists of sine and cosine terms of the form. After compting its fourier coefficients analytically. We got the coefficient to be $0.040158442751923665$ which is reasonable.