NEW:
Lorenz attactor links: Mathematica
plotting tool
with sliders (needs Mathematica or free Player); cool
fly through visualization
(uses Shockwave);
nice pictures
and auralization.
Chua circuit links:
Chua's Scholarpedia page;
another nice page.
Cool
Mathematica Chaos "demos" on dozens of topics (need Mathematica or
free Player).
Informal notes on the
flow map
and matrix exponential.
Instructor: Debra Lewis
Office: 359B Baskin Engineering
Phone: 459-2718
E-mail: lewis at ucsc dot edu
(checked more often than voicemail or gmail)
and/or DebraKLewis at gmail dot com
TA: Patrick Schultz
Office: 354 Baskin Engineering
E-mail: pschultz at math at ucsc dot edu
Office hours: Tu 10-12, Th 4-5, and by appointment
Lecture: MWF 12:30PM-1:40PM, Earth & Marine B214
Lab: Tu 2:00PM-3:10PM, Soc Sci 1 135 (Mac); W 2:30-4:30PM SS1 135 (PC);
F 10:30-12:00AM SS1 135 (PC).
Office hours: By appointment (the labs serve as my regularly scheduled office hours).
Course web page: http://people.ucsc.edu/~lewis/Math145
(here)
Chaos: An Introduction to Dynamical Systems, by
Kathleen Alligood, Timothy Sauer, and James Yorke
Cobweb plots (notebook,
PDF)
(4/1/08).
Homework 1 cobweb plots and fixed point approximation (notebook,
PDF)
(4/3/08).
Logistic map bifurcation plot (notebook,
PDF), and periodic orbit calculations for a = 4
(notebook,
PDF) (4/10/08).
Sensitive dependence on initial conditions (notebook,
PDF) (4/14/08).
Poincare maps for a spring model (notebook,
PDF) (4/21/08).
Some simple linear algebra (notebook,
PDF) (4/23/08).
Some stability plots (images of circles) for the Henon map (notebook,
PDF) (4/23/08).
Some very disorganized calculations related to finding the fixed points and
period two orbits for the Henon map and determining their stability
(notebook,
PDF) (5/1/08). (Sorry, but the lengthier version from Monday's lab got trashed;
hopefully this has some of the key pieces.)
A possible approach to approximating Lyapunov exponents
(notebook,
PDF) (5/14/08).
ADDITIONAL NOTES, SCANNED MATERIALS FROM TEXTS, ETC.
Wikipedia article on the
Mandelbrot set,
including fourteen levels of zoom.
Java Julia Set Generator.
Midterm solution possibilities (handwritten and probably hard to read!)
and the midterm
itself.
Some sections from Linear Algebra, by Michael O'Nan:
eigenvalues and vectors, symmetric matrices,
Jordan Normal Form (4/23/08).
Some informal notes on the
Jordan Normal Form (4/23/08).
If you'd like to try using the Virtual Lab (e.g. to use the UCSC Mathematica
licenses), here's some information:
Instructional computing's
Virtual Computer Labs
website has information about installing Remote Desktop Connection and using the Virtual Lab.
Once Microsoft Remote Desktop Connection is installed on your machine (Mac
users: it seems to be OK for now to ignore the "Beta out of date" message), you should be able
to access the virtual lab by launching Remote Desktop Connection and logging
into windows.ic.ucsc.edu; after you've typed in your username and password
several times, you should see a Windows-style "desktop".
Start> Math, Stats, and Graphing takes you to the mathematical packages folder;
to launch Mathematica, choose Mathematica 6.0 > Mathematica 6.
Good luck!
VERY TENTATIVE SCHEDULE
| Monday | Wednesday | Friday |
| March 31: 1.1-2 1-D maps and cobweb plots | April 2: 1.3 Stability of fixed points | April 4: 1.4 Periodic points |
| April 7: 1.5 Logistic maps | April 9: 1.6 Logistic maps cont. | April 11: 1.7 Sensitive dependence on I.C.s |
| April 14: 1.8 Itineraries | April 16: "Lab visit": beetle populations | April 18: 2.1 2-D systems: models |
| April 21: 2.1-2 Models cont., sinks etc. | April 23: 2.3-4 Linear maps, coordinate changes | April 25: 2.5 Nonlinear maps, the Jacobean matrix |
| April 28: 2.6 Stable and unstable manifolds | April 30: 2.7 Ellipses | May 2: MIDTERM |
| May 5: 3.1-2 Lyapunov exponents and chaotic orbits | May 7: 3.2-3 Chaotic orbits cont., the logistic map | May 9: 3.3 The logistic map cont. |
| May 12: 3.4 Transition graphs | May 14: 3.5 Basins of attraction | May 16: 4.1 Cantor sets |
| May 19: 4.2 Probabilistic construction of fractals | May 21: 4.3-4 Fractals in deterministic systems, basin boundaries | May 23: 4.5 Fractal dimension |
| May 26: HOLIDAY | May 28: 9.1 Lorentz equations | May 30: 9.2 Lorentz equations cont. |
| June 2: 9.3-4 Roessler attractor, Chua's circuit | June 4: 9.6 Lyapunov exponents in flows | June 6: TBD (presentations?) |
HOMEWORK POLICIES
Late homework will be discounted and, at the discretion of the grader and/or the instructor, may not be accepted.
Your homework should be neatly written and well-organized, with the pages securely fastened together and your name on every page. Many of the exercises involve several nontrivial steps; make it clear to your readers (and yourself!) what it is you're doing at each step.
Clearly number the exercises and try to submit them in numerical order; if any problems are out of sequence, indicate that at the beginning of the assignment. (You don't need to solve them in order, just submit them in order.) The grader should not have to hunt through several pages to find a particular problem.
Computer difficulties do not justify late or incomplete assignments.