Fourier analysis

Description

One possible direction of this project might be to understand these key points:

1. What is a Fourier series?

• What is a Fourier transform?
• Main properties of the Fourier transform. You have to understand what is behind the sentence:
  “The Fourier transform is a linear, unitary, invertible operation”

1. Understand the convolution theorem.

Finally one would like to study in detail a concrete application. Here you can choose whatever you like. A good example is the study of the heat equation: Joseph Fourier realized that heat transfer is more easily describe by using what we now call Fourier Series. There are many others: signal processing, image procesing, solving diferential equations, …

The Wikipedia page on Fourier Analysis is a great point to start to learn about these 4 points.