Maple Commands for Quiz 6
The following are Maple commands to generate the coefficients
of the Fourier series solution to problem 1 of quiz 7.
Note: the function f below is even about pi/2. Thus, the even indexed
coefficients, b[n], should be zero, should the sin(nx)
is odd about pi/2 when n is even.
> f:=x^2/Pi -x;
2
x
f := ---- - x
Pi
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> i:='i':for i from 1 to 10 do
> (2/Pi)*Int(f*sin(i*x),x=0..Pi)/sinh(2*i);b[i]:=evalf(");
> od;
Pi
/ / 2 \
| | x |
| |---- - x| sin(x) dx
| \ Pi /
/
0
2 -------------------------
Pi sinh(2)
b[1] := -.2234906718
-17
b[2] := -.4640597878*10
b[3] := -.0001488306059
-19
b[4] := .8077300294*10
b[5] := -.5887967528*10
b[6] := .1012928597*10
-8
b[7] := -.3930097914*10
b[8] := .1508175848*10
b[9] := -.3386819368*10
b[10] := .3700426818*10
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> i:='i':u:=x+Sum(b[i]*sinh(i*y)*sin(i*x),i=1..10);
/ 10 \
|----- |
| \ |
u := x + | ) b[i] sinh(i y) sin(i x)|
| / |
|----- |
\i = 1 /
> subs({x=.25,y=.33},u);evalf(");
/ 10 \
|----- |
| \ |
.25 + | ) b[i] sinh(.33 i) sin(.25 i)|
| / |
|----- |
\i = 1 /
.2313014166
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The following function is the exact solution to problem 2 of quiz 7.
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> v:=(9*r^2/65 - 9*16*r^(-2)/65)*sin(2*theta);
/ 2 144 \
v := |9/65 r - -----| sin(2 theta)
| 2|
\ 65 r /
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> r1:=sqrt(3+5);
r1 := 2sqrt(2)
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> theta1:=arctan(sqrt(5)/sqrt(3));
theta1 := arctan((1/3)sqrt(5)sqrt(3))
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> subs({r=r1,theta=theta1},v);evalf(");
54/65 sin(2arctan((1/3)sqrt(5)sqrt(3))
.8043888488
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