![f(t) := PIECEWISE([0, t < 0],[1, -t < 0 and t < 1],[-1, 1 < t],[0, 2 < t])](images/m081.gif)
| > | restart:MAX:=200:A:=0:B:=2:p:=1/2*(B-A):pleft:=-.2:pright:=1.01:pup:=1.5:pdown:=0.5:P:=2*p:with(plots): |
Warning, the name changecoords has been redefined
| > | f(t):=piecewise(t<A,0, t>A and t<1/2*(B-A),1,t>1/2*(B-A), -1,t>B ,0);plot(f(t),t=-0.5..2); |
![[Maple Plot]](images/m082.gif)
| > | fperiodic:=proc(x) local y;y:=x; while y < A do y:=y+P;od; while y > B do y:=y-P;od;evalf(subs(t=y,f(t)));end;plot(fperiodic,-10..10); |
![[Maple Plot]](images/m084.gif)
| > | a[0]:=1/p*int(f(t),t=A..B); |
![a[0] := 0](images/m085.gif){kind=small}
| > | a[n]:=1/p*int(f(t)*cos(n*Pi*t/p),t=A..B); b[n]:=1/p*int(f(t)*sin(n*Pi*t/p),t=A..B); |
![a[n] := -2*sin(n*Pi)*(cos(n*Pi)-1)/n/Pi](images/m086.gif){kind=small}
![b[n] := 2*cos(n*Pi)*(cos(n*Pi)-1)/n/Pi](images/m087.gif){kind=small}
| > |
| > | ORIGINAL:=plot(f(t),t=pleft..pright,color=yellow,thickness=5,discont=true):FPERIODIC:=plot(fperiodic,pleft..pright,color=red):F:=plot(fs[N](t),t=pleft..pright,color=blue): |
| > | for N from 1 to MAX do fs[N](t):=1/2*a[0]+sum(a[n]*cos(n*Pi*t/p)+b[n]*sin(n*Pi*t/p),n=1..N):F[N]:=plot([fs[N](t),f(t)],t=pleft..pright,y=pup..pdown,color=[blue,red],numpoints=500):od: |
| > | S:=seq(F[N],N=1..MAX): |
| > | display(S,insequence=true); |
![[Maple Plot]](images/m088.gif)
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