MATLAB.3
                
 Periodic Functions
We say f(x) is periodic with period m if f(x)=f(x+m) for all x.
Usually we are given a formula for f on a single period [a,b) with b-a=m.
To find f(x) for x not in [a,b) we first find the greatest integer multiple
of m less than or equal to x-a ,
 
 z=m*floor((x-a)/m)

(Here floor(t) is the MATLAB function giving the greatest integer <=t.)
Now y=x-z is in [a,b). The point is that f(y)=f(x) and we have a formula
for f(y).

example
Let f(x)=abs(x)   for -3<=x<3  and assume f(x) is 3-(-3)=6 -periodic.
To write a M-file for f type :

*************************************************************
function w=f(x)
z=6*floor((x+3)/6);
y=x-z;
w=abs(y);
*************************************************************
 
ASSIGNMENT  3 :
1. Let
f(x)=x^2 if-2<=x<2
and f(x) is 4-periodic.
Write f.m and graph f(x) on [-10,10].
 
2. Let
g(x)=x  if -2<=x<2
and g(x) is 4-periodic .
Write g.m and graph g(x) on [-10,10] .