Covered today: More heat equation problems.

For next time: 10.5 - 1,2,4,9,12 (skip (d) on 12 if you want)

Maple commands:

• Once you've got your b_m's computed, enter them in like so:

  b := m -> (-100/(m*Pi)) * (cos(2*m*Pi/3) - cos(m*Pi/3));

  Or, you can let Maple compute them for you:

  b:= m -> (2/3) * int(50 * sin(m*Pi*x/3) , x=1..2);

• Now define u(x,t) in terms of the b_m's:

  u := (x,t) -> sum(b(m) * exp(-m^2*Pi^2*t/9) * sin(m*Pi*x/3) ,m=1..50);

• To look at cross-sections of u (like your book does), you can enter (for example)

  plot(u(x,0), x=0..3);

  or

  plot(u(1,t), t=0..10);

• In order to view a 3D plot of u, you need to invoke the plotting package. Type:

  with(plots);

  Then:

  plot3d(u(x,t), x=0..3, t=0..10);