mapleL1-2002-text.mws

 Math 2250
 Maple Project 1, Math 2250
 Due date: September 9, 2002.

 Below appears the computer code in the problem notes,
 reproduced here for the purpose of copying with the mouse.
 All other text appears in mapleL1-2002.pdf (reference below).

References: Edwards-Penney, pages 55--57. File mapleL1-2002.pdf
            at URL http://www.math.utah.edu/~korevaar/

Notes on 1.1:
# Test LHS=RHS for u'+ku=kA.

M:=50:m:=20:t:='t':omega:='omega':u0:='u0':k:='k':
AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3)):
uh:=u0*exp(-k*t):
up:=k*int(exp(k*(x-t))*AA(x,omega),x=0..t):
u:=uh+up:
LHS:=diff(u,t)+k*u:
RHS:=k*AA(t,omega):
simplify(expand(LHS-RHS));

Notes on 1.2:

M:=50:m:=20:t:='t':omega0:=Pi/12:
AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3)):
plot(AA(t,omega0),t=0..24);


Notes on 1.3:

M:=50:m:=20:t:='t':u0:='u0':k:='k':omega:='omega':
AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3)):
uh:= u0*exp(-k*t):
up:= k*int(exp(k*(x-t))*AA(x,omega),x=0..t):
U:=unapply(uh+up,(t,u0,k,omega)):


u1:=U(t,40,0.3,Pi/12): u2:=U(t,50,0.3,Pi/12):
plot({u1,u2},t=0..72);


Notes on 1.4:

t:='t':omega:='omega':k:='k':
SS:=35-(15*k/(k^2+omega^2))*(k*cos(omega*(t-3))+omega*sin(omega*(t-3))):
AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3)):
LHS:=diff(SS,t)+k*SS:
RHS:=k*AA(t,omega);
simplify(LHS-RHS);


Notes on 1.5:

AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3)):
plot({U(t,69,0.3,Pi/12),AA(t,Pi/12)},t=0..48);

SS:=35-(15*k/(k^2+omega^2))*(k*cos(omega*(t-3))+omega*sin(omega*(t-3))):
AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3)):
uss:=unapply(SS,(t,k,omega)):
plot({uss(t,0.3,Pi/12),AA(t,Pi/12)},t=0..48);


Notes on 1.6:

with(plots):
AA:=(t,omega)->(M+m)/2-(M-m)*(1/2)*cos(omega*(t-3));
Uh:= u0*exp(-k*t):
Up:= k*int(exp(k*(x-t))*AA(x,omega),x=0..t);
U:=unapply(Uh+Up,(t,u0,k,omega)):
implicitplot(U(t,69,k,Pi/12)=30,t=0..72,k=0.2..0.5);
M:=50:m:=20:t:='t':u0:='u0':k:='k':omega:='omega':
plot3d({U(t,69,k,Pi/12),31},t=0..72,k=0.2..0.5);