Lecture Room: | B119 Van Vleck Hall |

Lecture Time: | 9:30–10:45 TuTh |

Lecturer: | Jean-Luc Thiffeault |

Office: | 503 Van Vleck |

Phone: | (608)263-4089 |

Email: | |

Office Hours: | Tues 1:00–2:00, Fri 1:20–2:20, or catch me after class |

**Is the final exam simply based on the material from the midterm exam (i.e., is it a cumulative final exam)?**

Just the material since the midterm.

**Can we use your notes, or do we simply have to use our own notes? I have my notes in my notebook. I just want to make sure I can use them. Ideally, I would like to have access to both sets of notes.**

You can use whaterver notes you want, as long as they are not photocopies or printouts of "other" documents. You can use a printout of notes you typed yourself.

**Can I write some additional notes by hand on separate pieces of paper?**

Yes.

**Did you say we can use our homework assignment solutions too?**

Yes.

The course introduces methods to solve mathematical problems that arise in areas of application such as physics, engineering and statistics.

See the official syllabus.

There two textbooks for the class:

- G. Strang,
**Introduction to Applied Mathematics**(Wellesley-Cambridge Press). ISBN: 0961408804. - C. M. Bender and S. A. Orszag,
**Advanced Mathematical Methods for Scientists and Engineers**(Springer). ISBN: 1441931872 or 0387989315.

Math 319 (ODEs), Math 321 (Vector and complex analysis), Math 322 (Sturm-Liouville, Fourier Series, intro to PDEs), Math 340 (Linear Algebra) or equivalent.

Every two weeks or so I will assign homework from the textbooks or otherwise and post it here.

Homework 1 (Due **Sept. 26** in class): Show that a symmetric
matrix is positive-definite if and only if its leading principal
minors (determinants of upper-leftmost *k* by *k*
submatrices along the diagonal) are positive. Problems from
Strang: **1.2**:
7,8,11; **1.3**:
2,6,7,8,11,17; **1.4**:
5,7,10,11,12; **1.5**:
6,7,11,12,13,23,24.

Homework 2 (Due **Oct. 10** in class): Problems from
Strang: **1.6**:
2,3,5,6; **2.1**:
2,3,6,12; **2.2**:
2,4; **2.4**:
1,4,10,11,12,17.

Homework 3 (Due **Oct. 24** in class): Problems from
Strang: **3.1**:
1,2,4,5,6; **3.2**:
2,3,10,12; **3.3**:
3,4,5; **3.6**:
1,2,9,11,14. *[Note for 3.6.9: M refers to the multiplier you use
for the question, and m to the one on page 245. In part (c), he
means for what values of the length constraint is there no
solution.]*

Homework 4 (Due **Nov. 7** in class): Problems from
Strang: **4.1**: 10,11,18,19,20,26,30. **4.3**:
5,6,7,10,21,27. **4.4**: 10,15,17,21,22,23. **4.5**: 2,3,5,8,9.

Homework 5 (Due **Nov. 26** in class): Problems from
Strang: **6.1**: 18,20,21,22. **6.2**:
2,3,5,6,8,11,12,13,14,19. Bender&Orszag: **4.4**
(p. 201) 43,49,51,59.

Homework 6 (Due **Dec. 12** in class): Problems from
Bender&Orszag: **7** (p. 361)
1,4,9,10,12,18,28,36(a),36(d). **9** (p. 479)
1,3,4,6,17,19,29(a),31. **10** (p. 539) 2,5,8,23.

There will be a **midterm** and a **final
exam**. Homework will be collected for credit, but not
graded in detail. The final grade will be computed according to:

Homework | 10% |

Midterm | 40% |

Final exam | 50% |

Midterm exam | Thursday October 31, 2013 at 9:30–10:45 (in class) |

Final exam | Thursday December 12, 2013 at 17:00–19:00 (room B139) |

lecture |
date(s) |
sections |
topic |

1 | 09/03 | Strang 1.1–1.3 | Matrices and pivoting |

2 | 09/05 | Strang 1.4 | Minimum principles; Springs! |

3 | 09/10 | Strang 1.5 | Eigenvalues and dynamical systems |

4 | 09/12 | Strang 1.6 | Incidence matrices of graphs |

5 | 09/17 | Strang 2.1–2.2 | Fundamental equations for equilibrium |

6 | 09/19 | Strang 2.2, 2.4 | Duality; Trusses |

7 | 09/24 | Strang 2.4 | Trusses (cont'd) |

8 | 09/26 | Strang 3.1 | The continuous case |

9 | 10/01 | Strang 3.2, 3.3, 3.6 | The continuous case (cont'd) |

10 | – | – | skip this material |

11 | 10/03 | Strang 3.6, 4.1 | Principle of least action; Analytic methods |

12 | 10/08 | Strang 4.1, 4.3 | Analytic methods (cont'd); Fourier transforms |

13 | 10/10,10/15 | Strang 4.4 | Complex variable methods |

14 | 10/15 | Strang 4.4, 4.5 | Complex variable methods (cont'd) |

15 | 10/17 | Strang 4.5 | Complex methods (end) |

15 | 10/22 | Strang 4.5 | Complex methods (really the end) |

16 | 10/24 | Strang 6.1, 6.2 | Stability |

17 | 10/29,11/05 | Strang 6.2; B&O 4.4 | Phase plane analysis |

– | 10/31 | – | midterm |

18 | 11/05 | Strang 6.2; B&O 4.5 | Chaos part 1:
maps
[note
on Poincaré–Bendixson
theorem; Matlab code] |

19 | 11/11 | Strang 6.2; B&O 4.5 | Chaos part 2: flows |

20 | 11/14 | B&O 7.1, 7.2 | Perturbation methods |

21 | 11/19 | B&O 7.2, 7.4 | Singular perturbations |

– | 11/21 | – | Guest lecturer: Marko Budisic |

22 | 11/26 | B&O 7.4 | Asymptotic matching |

23 | 12/03 | B&O 9.1 | Boundary layer theory |

24 | 12/05 | B&O 9.1, 9.2, 9.3 | Boundary layer theory (cont'd) |

25 | 12/05 | B&O 9.4 | Boundary layer theory (cont'd) |

26 | 12/10 | B&O 10.1, 10.2 | WKB theory |

– | 12/12 | – | discussion (final at 5pm) |