Séries de Fourier

por

Milton Procópio de Borba

> restart;with(plots):

> T:=piecewise(x>=0 and x<=1,60*x, x>=1 and x<=2,20*x+40, x>=2 and x<=3,-80*x+240); 

Warning, the name changecoords has been redefined

T := PIECEWISE([60*x, -x <= 0 and x-1 <= 0],[20*x+4...

> G:=plot(T,x=0..3,color=black):

> display({G});

[Maple Plot]

> s[n]:=sin(n*Pi*x/3);

> bn:=2*int(T*s[n],x=0..3)/3;

s[n] := sin(1/3*n*Pi*x)

bn := 120*(-4*sin(n*Pi)+5*sin(2/3*n*Pi)+2*sin(1/3*n...

> for i to 30 do

> B:=subs(n=i,bn):

> b[i]:=evalf(B)

> od;

B := 120*(-4*sin(Pi)+5*sin(2/3*Pi)+2*sin(1/3*Pi))/P...

b[1] := 73.70724392

B := 30*(-4*sin(2*Pi)+5*sin(4/3*Pi)+2*sin(2/3*Pi))/...

b[2] := -7.897204706

B := 40/3*(-4*sin(3*Pi)+5*sin(2*Pi)+2*sin(Pi))/Pi^2...

b[3] := 0.

B := 15/2*(-4*sin(4*Pi)+5*sin(8/3*Pi)+2*sin(4/3*Pi)...

b[4] := 1.974301176

B := 24/5*(-4*sin(5*Pi)+5*sin(10/3*Pi)+2*sin(5/3*Pi...

b[5] := -2.948289757

B := 10/3*(-4*sin(6*Pi)+5*sin(4*Pi)+2*sin(2*Pi))/Pi...

b[6] := 0.

B := 120/49*(-4*sin(7*Pi)+5*sin(14/3*Pi)+2*sin(7/3*...

b[7] := 1.504229468

B := 15/8*(-4*sin(8*Pi)+5*sin(16/3*Pi)+2*sin(8/3*Pi...

b[8] := -.4935752941

B := 40/27*(-4*sin(9*Pi)+5*sin(6*Pi)+2*sin(3*Pi))/P...

b[9] := 0.

B := 6/5*(-4*sin(10*Pi)+5*sin(20/3*Pi)+2*sin(10/3*P...

b[10] := .3158881882

B := 120/121*(-4*sin(11*Pi)+5*sin(22/3*Pi)+2*sin(11...

b[11] := -.6091507762

B := 5/6*(-4*sin(12*Pi)+5*sin(8*Pi)+2*sin(4*Pi))/Pi...

b[12] := 0.

B := 120/169*(-4*sin(13*Pi)+5*sin(26/3*Pi)+2*sin(13...

b[13] := .4361375380

B := 30/49*(-4*sin(14*Pi)+5*sin(28/3*Pi)+2*sin(14/3...

b[14] := -.1611674430

B := 8/15*(-4*sin(15*Pi)+5*sin(10*Pi)+2*sin(5*Pi))/...

b[15] := 0.

B := 15/32*(-4*sin(16*Pi)+5*sin(32/3*Pi)+2*sin(16/3...

b[16] := .1233938235

B := 120/289*(-4*sin(17*Pi)+5*sin(34/3*Pi)+2*sin(17...

b[17] := -.2550423665

B := 10/27*(-4*sin(18*Pi)+5*sin(12*Pi)+2*sin(6*Pi))...

b[18] := 0.

B := 120/361*(-4*sin(19*Pi)+5*sin(38/3*Pi)+2*sin(19...

b[19] := .2041751909

B := 3/10*(-4*sin(20*Pi)+5*sin(40/3*Pi)+2*sin(20/3*...

b[20] := -.7897204706e-1

B := 40/147*(-4*sin(21*Pi)+5*sin(14*Pi)+2*sin(7*Pi)...

b[21] := 0.

B := 30/121*(-4*sin(22*Pi)+5*sin(44/3*Pi)+2*sin(22/...

b[22] := .6526615458e-1

B := 120/529*(-4*sin(23*Pi)+5*sin(46/3*Pi)+2*sin(23...

b[23] := -.1393331643

B := 5/24*(-4*sin(24*Pi)+5*sin(16*Pi)+2*sin(8*Pi))/...

b[24] := 0.

B := 24/125*(-4*sin(25*Pi)+5*sin(50/3*Pi)+2*sin(25/...

b[25] := .1179315903

B := 30/169*(-4*sin(26*Pi)+5*sin(52/3*Pi)+2*sin(26/...

b[26] := -.4672902192e-1

B := 40/243*(-4*sin(27*Pi)+5*sin(18*Pi)+2*sin(9*Pi)...

b[27] := 0.

B := 15/98*(-4*sin(28*Pi)+5*sin(56/3*Pi)+2*sin(28/3...

b[28] := .4029186074e-1

B := 120/841*(-4*sin(29*Pi)+5*sin(58/3*Pi)+2*sin(29...

b[29] := -.8764238278e-1

B := 2/15*(-4*sin(30*Pi)+5*sin(20*Pi)+2*sin(10*Pi))...

b[30] := 0.

> ser:=0:

> for n to 1 do

> ser:=ser+b[n]*sin(n*Pi*x/3):

> od:

> G1:=plot(ser,x=0..3):

> display({G,G1});

[Maple Plot]

> ser:=0:

> for n to 2 do

> ser:=ser+b[n]*sin(n*Pi*x/3):

> od:

> G2:=plot(ser,x=0..3,color=blue):

> display({G,G1,G2});

[Maple Plot]

> ser:=0:

> for n to 4 do

> ser:=ser+b[n]*sin(n*Pi*x/3):

> od:

> G4:=plot(ser,x=0..3,color=red):

> display({G,G4,G2});

[Maple Plot]

> ser:=0:

> for n to 5 do

> ser:=ser+b[n]*sin(n*Pi*x/3):

> od:

> G5:=plot(ser,x=0..3,color=blue):

> display({G,G4,G5});

[Maple Plot]

> ser:=0:

> for n to 7 do

> ser:=ser+b[n]*sin(n*Pi*x/3):

> od:

> G7:=plot(ser,x=0..3,color=red):

> display({G,G7,G5});

[Maple Plot]

> ser:=0:

> for n to 8 do

> ser:=ser+b[n]*sin(n*Pi*x/3):

> od:

> G8:=plot(ser,x=0..3,color=blue):

> display({G,G7,G8});

[Maple Plot]

> ser:=0:

> for n to 10 do

> ser:=ser+b[n]*sin(n*Pi*x/3):

> od:

> G10:=plot(ser,x=0..3,color=red):

> display({G,G10,G8});

[Maple Plot]

> ser:=0:

> for n to 30 do

> ser:=ser+b[n]*sin(n*Pi*x/3):

> od:

> G30:=plot(ser,x=0..3,color=blue):

> display({G,G10,G30});

[Maple Plot]