# Fourier Series. Analysis and construction

## Do you want to improve your understanding and knowledge of Fourier series?

Fourier series is a mathematical technique used to represent periodic functions as an infinite sum of sine and cosine functions. They were developed by the French mathematician Joseph Fourier in the 19th century as a tool for studying heat conduction in solids.

The basic idea behind Fourier series is that any periodic function can be decomposed into a series of sinusoids of different frequencies and amplitudes. This means that if we know the frequencies and amplitudes of the sinusoids that make up a periodic function, we can represent that function as a sum of those sinusoids. The representation of a function in terms of Fourier series allows us to analyze its behavior at different frequencies and is used in areas such as engineering, physics and telecommunications.

The decomposition of a function in terms of Fourier series is performed by calculating integrals. There are different techniques to perform this decomposition, among them are the Fourier Fourier series, the complex Fourier series and the trigonometric Fourier series.

Fourier series have a wide variety of applications in areas such as signal processing, partial differential equation solving and mechanical vibration analysis. They are also an important tool in communication theory, since they allow the representation of signals in terms of frequencies.

Below are several simulations and other educational resources, which can also serve as very illustrative examples. In addition, a selection of books and courses is included to help you broaden your knowledge of this subject.

## Waveform making

Learn how to make waves of all shapes by adding sines or cosines. Create waves in space and time and measure their wavelengths and periods See how changing the amplitudes of different harmonics changes the waves. Compare the different mathematical expressions of waves.

## Graphical construction of Fourier series

This simulation shows how to construct a Fourier series graphically. It checks the different results by changing the parameters of the series.

## Fourier series analysis

This simulation allows us to see several examples of functions that can be constructed by means of Fourier series development.
###### Mathematics  Maths Essentials  MathTrackX: Polynomials, Functions and Graphs

###### Cálculus  Calculus Applied!  Multivariable Calculus 2: Integrals