Math 53: Schedule, topics and worksheets

week   date    readingdaily topics & demosworksheets
1Sep 24 Th Intro, 1.1-1.4 Discrete maps, fixed points, stability, cobweb plot. Periodic orbits. cobweb, periodic
29 Tu1.5-1.7Logistic family of maps, bifurcation diagram, `Periodic table' of logistic map 4x(1-x), sensitive dependence on initial conditionstable
30 W X-hrintro53.m Matlab technique (by now you'll have installed it; bring your laptop)
2Oct 1 Th1.8, 2.1(HW1 due) Itineraries (proof of small subintervals) itineraries
6 Tu2.2-2.4Poincare section, 2D maps, sinks, sources, saddles, linear maps, stability (review), Jacobean. [if you need it, 4-5:30pm Intro to Matlab class, Berry Instr Ctr; sign-up reqd] 2dlinear
7 W X-hr-
38 Th2.5Nonlinear maps, fixed point stability, Henon example.
13 Tu2.6-2.7, Challenge 2Stable/unstable manifolds, disc under linear map iterdisc2d.m, periodic orbits on linear map on a torus. manifolds
14 W X-hrmidterm review
415 Th3.1-3.2Lyapunov exponents, chaotic orbits. torus
20 Tu(lecture moved to Wed X-hr)
21 Wed X-hr3.3Binary, conjugacy, uses for logistic mapbinary
Midterm 1: Wed Oct 21, 6-8pm, Kemeny 007 (solutions), practise exam (solutions) On: everything up to and including 3.1, apart from Matlab.
522 Th3.4, 4.1 Dense orbits, transition graphs and counting periodic orbits. Fractals: Cantor sets. applet, difference of two cantor sets. transgraph
27 Tu4.3, 4.2 Fractals from tent map, logistic map with a>4. Fractals from probabilistic games. Sierpinski gasket, game 1,2probgames
629 Th4.4-4.5(Project choice due Fri). Julia and Mandelbrot sets, Devaney movies, Fractal dimension.mandel
Nov 3 Tu4.6-4.7 Fractal dimension. Box-counting dimension. Computing box-counting. Correlation dimension boxdim
4 W X-hr
75 Th5.1-5.2, 7.1-7.2 Lyapunov exponent for maps in Rn and their numerical measurement, lyap2d. Flows: linear (review).
10 Tu7.3-7.5Project 2-page descriptions due. Nonlinear systems of ODEs, stability. Motion in potential field. code: potential1d.m. potential
11 W X-hrreview for midterm 2
812 Th7.6, Ch.9, 8.1 Damping in potential field, damped pendulum. Lyapunov functions. Range of flow limit behaviors in R and R2: Poincare-Bendixson theorem.
17 Tu8.2, 9.6 Chaos in ODEs: Lorenz attractor. Measuring Lyapunov exponent in flows lyapflow (needs lorenz_time1map.m)
18 W X-hrlast-minute review
Midterm 2: Wed Nov 18, 6-8pm, Kemeny 007 (solutions), practise exam (solutions)
919 ThCh. 13Delay embedding henon_timedelay.m. Hamiltonian mechanics and flows: double pendulum (applets 1, 2), Liouville's Theorem on volume-preservation. Autocorrelation of time-series (henon_autoc.m) liouville
24 Tu (no lecture)
.................................. Nov 25 W - 29 Su Thanksgiving recess...............................
Dec 1 TuProject Presentations in lecture slot.
2 W X-hrRest of presentations
104 FrProject write-ups due (noon)
5 Sa - 9 W: Exam period (no final exam)