News:

Homework solutions 1-3 are online. 4-5 will be posted Tuesday afternoon.
Week LecturePDF DueSol
1 1. Class hw1.pdf Fri 9/11 rsp Tue 9/15 solutions
2 2. Class hw2.pdf Mon 9/14 rsp Tue 9/15 solutions
3 3. Class hw3.pdf Wed 9/16 rsp Thu 9/17 solutions
4 4. Class hw4.pdf Fri 9/18 rsp Tue 9/22 solutions
5 5. Class hw5.pdf Mon 9/21 rsp Tue 9/22 solutions
6 6. Class hw6.pdf Wed 9/23 rsp Thu 9/24 solutions
7 7. Class hw7.pdf Fri 9/25 rsp Tue 9/29 solutions
8 8. Class hw8.pdf Mon 9/28 rsp Tue 9/29 solutions
9 9. Class hw9.pdf Fri 10/2 rsp Tue 10/6 solutions
10 10. Class hw10.pdf Mon 10/5 rsp Tue 10/6 solutions
11 11. Class hw11.pdf Wed 10/7 rsp Thu 10/8 solutions
12 12. Class hw12.pdf Fri 10/9 rsp Tue 10/13 solutions
13 13. Class hw13.pdf Wed 10/14 rsp Tue 10/13 solutions
14 14. Class hw14.pdf Fri 10/16 rsp Thu 10/15 solutions
15 15. Class hw15.pdf Mon 10/19 rsp Tue 10/20 solutions
16 16. Class hw16.pdf Wed 10/21 rsp Thu 10/22 solutions
17 17. Class hw17.pdf Fri 10/23 rsp Tue 10/27 solutions
18 18. Class hw18.pdf Mon 10/26 rsp Tue 10/27 solutions
19 19. Class hw19.pdf Wed 10/28 rsp Thu 10/29 solutions
20 20. Class hw20.pdf Fri 10/31 rsp Tue 11/03 solutions
21 21. Class hw21.pdf Mon 11/02 rsp Tue 11/03 solutions
22 22. Class hw22.pdf Fri 11/06 rsp Tue 11/10 solutions
23 23. Class hw23.pdf Mon 11/09 rsp Tue 11/10 solutions
24 24. Class hw24.pdf Wed 11/11 rsp Thu 11/12 solutions
25 25. Class hw25.pdf Fri 11/13 rsp Tue 11/17 solutions
26 26. Class hw26.pdf Mon 11/16 rsp Tue 11/17 solutions
27 27. Class hw27.pdf Wed 11/18 rsp Thu 11/19 solutions
28 28. Class hw28.pdf Fri 11/20 rsp Tue 11/24 solutions
29 29. Class hw29.pdf Mon 11/23 rsp Tue 11/24 solutions
30 30. Class hw30.pdf Mon 11/30 rsp Tue 12/01 solutions
31 31. Class hw31.pdf Wed 12/2 rsp Tue 12/03 solutions
Code for problem 4a). Find the value U[0.6.7]
f[x_]:=Sin[Pi 7x];
g[x_]:=5 Sin[5 Pi x];
U = NDSolveValue[
  {D[u[t,x],{t,2}]-D[u[t,x],{x,2}]==0,
  u[0,x]==f[x],
  Derivative[1,0][u][0,x] == g[x],
  DirichletCondition[u[t,x]==f[0],x==0],
  DirichletCondition[u[t,x]==f[1],x==1]},
  u,{t,0,1},{x,0,1}];
Animate[Plot[U[t,x],{x,0,1},
  PlotRange->{-2,2}],{t,0,1}]
Plot[U[t,0.5], {t, 0, 1}]
Code for problem 4b) We want to see U[t,0.6,0.7]
A = Rectangle[{0, 0}, {1, 1}]; Clear[t, x, y];
f[x_, y_] := Sin[2 Pi x] Abs[Sin[3 Pi y]];
g[x_, y_] := 3 Sin[Pi x] Sin[Pi y];
U = NDSolveValue[{D[u[t, x, y], {t, 2}] -
      Inactive[Laplacian][u[t, x, y], {x, y}] == 0,
    u[0, x, y] == f[x, y], Derivative[1, 0, 0][u][0, x, y] == g[x, y],
     DirichletCondition[u[t, x, y] == 0, True]},
   u, {t, 0, 2 Pi}, {x, y} \[Element] A];
Plot3D[U[4, x, y], {x, 0, 1}, {y, 0, 1}]
Animate[ContourPlot[U[t, x, y], {x, 0, 1}, {y, 0, 1}], {t, 0, 2 Pi}]
Example code for problem 5:
f[t_,x_]:=(1/Sqrt[t])*Exp[-x^2/(4t)];
Simplify[ D[f[t,x],t] == D[f[t,x],{x,2}]]