Jean-Luc Thiffeault

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

Textbooks

Prerequisites

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

Homework

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.

Course Policy and Grading

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:

Exam Dates

Schedule of Topics

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)

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

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)

Math 703: Methods of Applied Mathematics I: Fall 2013

Final Exam

FAQ

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