# Tag Archives: periodic functions

## Math2111: Chapter 1: Fourier series. Section 4: Examples and general periodic functions

In this blog entry you can find lecture notes for Math2111, several variable calculus. See also the table of contents for this course. This blog entry printed to pdf is available here.

In this part we calculate the Fourier series for some given functions $f:[-\pi, \pi] \to \mathbb{R}$. We also define Fourier series for functions $f:[a, b] \to \mathbb{R}.$

Examples of Fourier series

Example (sawtooth wave function) Find the Fourier series of the function

$\displaystyle f(x) = x \quad \mbox{for } -\pi < x < \pi,$

$\displaystyle f(x) = f(x+2\pi) \quad \mbox{for } x \in \mathbb{R}.$

Further we define $f((2n + 1) \pi) = 0$ for $n \in \mathbb{Z}.$

The graph of the function can be found here. Continue reading