# Fourier series expansion - calculus

A function is defined as followed:

see attachment

Where f(t+2)=f(t) that is, f(t) has period 2.

i) Draw a plot of the function f(t). Comment fully on whether the function is even or odd or none of these.

ii) Find the first four non-zero coefficients for the Fourier series expansion of the function f(t)

iii) Using eg. excel, draw a plot of the partial sum of the Fourier series which uses just there first four non-zero terms and comment on it in relation to your plot (i)

https://brainmass.com/math/basic-calculus/fourier-series-expansion-calculus-567236

#### Solution Preview

The function looks like:

This function is neither even function since , nor it is an odd function since

.

For example, while

However we can write the function as:

(1.1)

Where

(1.2)

And is an odd function and it looks like

The general expansion of a function over the symmetric interval is given by:

(1.3)

Where:

...

#### Solution Summary

The solution shows how to utilize parity to simplify the calculations of Fourier series coefficients.