|Lecture Room:||B119 Van Vleck Hall|
|Lecture Time:||9:30–10:45 TuTh|
|Office:||503 Van Vleck|
|Office Hours:||Tues 1:00–2:00, Fri 1:20–2:20, or catch me after class|
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:
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:
|Thursday October 31, 2013 at 9:30–10:45 (in class)|
|Final exam||Thursday December 12, 2013 at 17:00–19:00 (room B139)|
|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|
|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)|