problem1.html

problem1.mws

>    ## HW 1, EECS 207A, UCI, Fall 2004.
## by Nasser Abbasi
##
## Problem: Find fourier series approximation to f(x)=x^2 and
## print the fourier coefficients.
##
## We see as more terms as added, we get better approximation to f(x).

restart;
with(plots):
f:= x->x^2:
N:=9;
assume(n,integer);

denomA:=int(cos(n*x)^2,x=-Pi..Pi):
denomB:=int(sin(n*x)^2,x=-Pi..Pi):

a:=seq( int(f(x)*cos(n*x),x=-Pi..Pi)/denomA,n=1..N);
b:=seq( int(f(x)*sin(n*x),x=-Pi..Pi)/denomB,n=1..N);

a0:=int(f(x),x=-Pi..Pi)/denomA:

ff:=(n,x)-> a0/2 + sum( a[i]*cos(i*x),i=1..n) + sum( b[i]*sin(i*x),i=1..n);

A:=array(1..3,1..3):
k:=0:
for n from 1 to 3 do
    for m from 1 to 3 do
        k:=k+1;
        str := sprintf("n = %d",k);
        A[n,m]:=plot( {f(x),ff(k,x)} , x=-Pi..Pi,title=str,
                      linestyle=[DOT,DASH],thickness=[1,3],
                      color=[red,black] ):
    end do:
end do:
display(A);

>

Warning, the name changecoords has been redefined

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