The Fourier series is named in honor of Jean-Baptiste Joseph Fourier (1768–1830), who made important contributions to the study of trigonometric series, after preliminary investigations by …

Sep 26, 2025 · A Fourier series is a way to represent a periodic function as a sum of sine and cosine functions, or equivalently, as a sum of complex exponentials, each with different …

That is the idea of a Fourier series. By adding infinite sine (and or cosine) waves we can make other functions, even if they are a bit weird. You might like to have a little play with: And it is …

Dec 3, 2025 · A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and …

Nov 16, 2022 · In this section we define the Fourier Series, i.e. representing a function with a series in the form Sum ( A_n cos (n pi x / L) ) from n=0 to n=infinity + Sum ( B_n sin (n pi x / L) …

Nov 14, 2025 · Fourier series, in mathematics, an infinite series used to solve special types of differential equations. It consists of an infinite sum of sines and cosines, and because it is …

Jan 9, 2025 · Q1: What is a Fourier series? Answer: The infinite trigonometric series given by f (x) = a 0 + ∑ n=1 [ a n cos (nx) + b n sin (nx) ] (if it exists) is called the Fourier series expansion of …

A Fourier Series is a mathematical representation of a periodic function as an infinite sum of sine and cosine functions (or equivalently, complex exponentials).

We introduce general periodic functions and learn how to express them as Fourier series, which are sums of sines and cosines.

In the first decade of the 19th century, Jean Baptiste Joseph Fourier invented a technique using sums of trigonometric functions--called ``Fourier Series''--to solve the differential equations of …