## News:

Homework solutions 1-3 are online. 4-5 will be posted Tuesday afternoon.Week | Lecture | Due | Sol | |
---|---|---|---|---|

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 |

- Homework is due at the beginning of class. Homework is due every class. TTh sections turn in two homework sets on Tuesdays and one on Thursday.
- Discussing mathematics can be effective in learning, and we encourage collaboration with other students for homework. We ask you however to turn in your own copy and list names of collaborators if you should have done a significant part of your homework in a group. Even if you work with others, it is a good strategy to work on homework problems first on your own. Honing your problem solving skills will have enormous benefits also in other fields.
- Use words to explain your work, if it is necessary. Show your work.
- We follow the honor code.

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}]]