# Maple code for Newton Cooling maple lab 1b S2005
#
#Notes on 1.3
 # Test LHS=RHS for u'+ku=kA.
 unassign('t','u0','omega','k'):
 myANS:=your hand-derived formula for u=uh+up:
 LHS:=diff(myANS,t)+k*myANS:
 RHS:=k*(33-13*cos(omega*(t-3))):
 simplify(expand(LHS-RHS));

#Notes on 1.4
 # No code

#Notes on 1.5
 with(plots): unassign('t','u0','k','omega'):
 AA:=(t,omega)->33-13*cos(omega*(t-3));
 U:=(t,u0,k,omega)-> your answer of u=uh+up from 1.3:

 plot({U(t,74,0.35,Pi/12),AA(t,Pi/12)},t=0..48);

#Notes on 1.6
 with(plots): unassign('t','u0','k','omega'):
 U:=(t,u0,k,omega)->your answer of uh+up from 1.3:
 implicitplot(U(t,74,k,Pi/12)=31,t=0..72,k=0.2..0.4);
 plot3d({U(t,74,k,Pi/12),30},t=0..72,k=0.2..0.4);