# GeoGebra

## Fourier series of Sawtooth Function

This is a sample Fourier series used to represent a sawtooth function.

The series was built using the Sum[] command together with the Sequence[] command. In addition, the series formula is presented as text using LaTeX.SEO DallasFLAS INFORMASI TEKNOLOGI kumpulan i

The .ggb file is was developed collaboratively on the GeoGebra forum: "How to Input Long Formulae (as Fourier terms)"

## Fourier series of arbitrary functions

This is an initial attempt at a Fourier series generator for arbitrary functions. Fourier series

To use this tool, enter your function named f(x) in the Input Bar at the bottom of the applet. For example,

• $f(x) = x \,$ ... sawtooth function
• $f(x) = \mathrm{If}[x<0, 0, 3] \,$ ... step function
• $f(x) = \mathrm{If}[x<0, -x, x] \,$ ... triangle function

The domain of the defining function is given by the interval [xa,xb], thus the period is p = xbxa. We also define the wavenumber k = 2π / p.

Among the values displayed in the Algebra window are the lists "a" and "b", which are the coefficients of cosine and sine functions, respectively.

$a_n = \frac{2}{p}\int_{xa}^{xb} f(x) \cos(nkx) \, dx, \quad n \ge 1;\qquad a_0 = \frac{1}{p}\int_{xa}^{xb} f(x) \, dx$
$b_n = \frac{2}{p}\int^{xb}_{xa} f(x) \sin(nkx) \, dx, \,\quad n \ge 1$