WAVE SQUARED BY USING SOFTWARE DERIVE

The square wave function is defined in a piecewise way:

 − 1 , if - π < t < 0 f (t ) =  1 , if 0 < t < π For graphing it, we can follow these steps by using Derive: i) Put the expression:

ii) Click in the icon

if (−π < t < 0, - 1, if(0 < t < π , 1))

, and then, do it in

that, the graph will appear:

. After

iii)

Analogously , by putting

if (−2π < t < −π, 1, if(-π < t < 0, -1, if(0< t <π,1, if(π < t < 2π, -1, if(2π < t < 3π,1))))) we will obtain:

The representation in Fourier series of the mentioned function above is:

f(t) ≡

4

∞

∑ π n =1

sen ( 2 n − 1)t ( 2 n − 1)

which is obtained by help of Derive, by means of writing. Its plot is showed in last picture:

Fourier ( f (t ), t , - π , π , 20)