Syllabus
(The tentative schedule)
| Week 1 | ||
|---|---|---|
| Mon 16 Sept | 1.1-1.3: Discrete maps, fixed points, cobwep plots,
stability |
Worksheet 1 Solutions |
| Weds 18 Sept | 1.4-1.5: Periodic points, logistic maps, bifurcation
diagram |
Worksheet 2 Solutions |
| Thurs 19 Sept | Learn how to use Matlab: download intro53.m
|
|
| Fri 20 Sept |
1.6-1.7: "Periodic table" of logistic map 4x(1-x), sensitive dependence on initial conditions | Worksheet 3 Solutions |
| Week 2 | ||
| Mon 23 Sept |
1.8: Itineraries Notes on change to theta Sensitivity code for f(x) = 3x(mod 1) |
Worksheet 4 Solutions |
| Weds 25 Sept |
2.1-2.2: Poincare maps, Sinks, Sources and Saddlesexplormap2d.m
explorbasin2d.m
iterdisc2d.m |
|
| Thurs 26 Sept |
2.3-2.4: Linear maps and coordinate changes |
Worksheet 5 Solutions |
| Fri 27 Sept |
Visit by Tristan Perich |
|
| Week 3 | ||
| Mon 30 Sept |
2.5: Nonliner maps and the Jacobian | |
| Weds 2 Oct |
2.6: Stable/unstable manifolds | Worksheet 6 Solutions |
| Thurs 3 Oct |
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|
| Fri 4 Oct | 2.7: disc under linear
map iterdisc2d.m |
Worksheet 7 Solutions |
| Week 4 | ||
| Mon 7 Oct |
3.1-3.2: Lyapunov Exponents, Chaotic orbits, binary | Worksheet 8 Solutions |
| Tues 8 Oct | Midterm 1, 5:00-7:00
pm, Kemeny 201 Exam 1
Solutions
Old midterms: 2007 midterm 1 solutions 2009 midterm 1 solutions 2011 midterm 1 solutions |
|
| Weds 9 Oct |
3.3: Conjugacy and the Logistic Map | |
| Thurs 10 Oct |
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| Fri 11 Oct |
3.4: Transistion Graphs and Fixed points | Worksheet 9 Solutions |
| Week 5 | ||
| Mon 14 Oct |
4.1: Cantor Sets
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|
| Weds 16 Oct |
4.2: Probabilistic constructions of fractals Iterated function system Chaos games |
Worksheet 10 Solutions |
| Thurs 17 Oct |
4.3: Fractals from deterministic systems | |
| Fri 18 Oct |
4.4: Fractal Basin Boundaries The quadratic map |
Worksheet 11 Solutions |
| Week 6 | ||
| Mon 21 Oct |
4.5-4.6: Fractal dimension, The box-counting dimension Mandelbrot movie |
Worksheet 12 Solutions |
| Weds 23 Oct |
4.7: Correlation dimension |
|
| Thurs 24 Oct |
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|
| Fri 25 Oct |
5.1-5.2: Lyapunov exponents, numerical computation of
the exponent |
|
| Week 7 | ||
| Mon 28 Oct |
5.2 Numerical computation of the Lyapunov exponent |
|
| Tues 29 Oct | Project 1-2 page description due. | |
| Weds 30 Oct |
7.1-7.2: 1-D linear and nonlinear differential equations | |
| Thurs 31 Oct |
|
|
| Fri 1 Nov |
7.3-7.4: Nonlinear systems of ODEs, stability.
code: potential1d.m. |
Math 23 worksheets on 1st order systems Math23: Worksheet 20 Math23: Worksheet 21 |
| Week 8 | ||
| Mon 4 Nov |
7.5 Motion in potential field | Worksheet 13 Solutions |
| Tues 5 Nov | ||
| Weds 6 Nov |
7.6: Damping in potential field, damped
pendulum.
Lyapunov functions |
|
| Thurs 7 Nov |
Midterm 2, 5:00-7:00
pm, Kemeny 201 Exam 2
Solutions
Old midterms: 2007 midterm 2 solutions 2009 midterm 2 solutions 2011 midterm 2 solutions |
|
| Fri 8 Nov |
8.1: Range of flow limit behaviors in R and R2: Poincare-Bendixson theorem | |
| Week 9 | ||
| Mon 11 Nov |
8.2: Chaos in ODEs: Lorenz attractor. | |
| Weds 13 Nov |
9.6:Measuring Lyapunov exponent in flows lyapflow (needs lorenz_time1map.m) |
|
| Thurs 14 Nov |
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| Fri 15 Nov | Student presentations |
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| Week 10 | ||
| Mon 18 Nov | Student presentations |
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| Weds 13 Nov |
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| Thurs 14 Nov |
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| Fri 22 Nov | Projects are due |
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