My office phone, 523-6878, goes straight to voice mail.
You can send me e-mail at
Jim.Swift@nau.edu.
Here is my weekly schedule.
Please feel free to contact me any time via e-mail with any
questions about the math, or with any feedback about the class.
You can always come to my office, AMB 110, during these times:
M: 1:45-4:00
W: 1:45-4:00
You can always send me e-mail, drop in to my office,
or make an appointment if these times aren't convenient.
Darryl Nester's Slope Field Applet. Here is the Slope Field App, Old Interface
Chart of letters of the Greek alphabet.
The Lorenz Equations
Newton's Law of Cooling, Scaling and other Dynamical Systems (January 22-29)
Homework 1 is due at the beginning of class on Monday, January 27.
You can send a pdf before class starts, or bring hardcopy to class.
Here are some comments about the dead body cooling problem.
Introduction (January 13-17)
Dynamical systems: PDEs, ODEs and iterated maps.
Monday: Each of these can be conservative or dissipative. This allows a
classification
of dynamical systems.
Wednesday, Friday?: We will investigate these ODEs with parameters
Newon's Law of Cooling,
\(\displaystyle \frac{du}{dt} = -k (u-A)\),
the simple harmonic oscillator, \(\displaystyle m\frac {d^2 u}{dt^2} = - k u\),
the simple pendulum, \(\displaystyle m\frac {d^2 \theta}{dt^2} = -\frac{mg}{L} \sin(\theta)\),
and
the van der Pol oscillator, \(\displaystyle \frac {d^2 y}{dt^2} = - y + \varepsilon (1-y^2) \frac{dy}{dt}\).
Friday?: The Lorenz Attractor
Here is a link to the 1963 paper by Lorenz.
My page on the
Lorenz attractor.
Mark McClure visualization Shows convection cells and has the round button (rounds \(\pi\) to 3.142, etc.)
Hendrik Wernecke Simulation. Simple app with only STOP, Reset, and a slider for \(\rho\). This uses Euler's method.
Malin Christersson simulation. Swarms of butterflies!
All of those programs have their drawbacks. Twenty years ago we had better web-based demonstrations
written by dynamical systems experts, but most don't run today. Peter Scott's home page has a link to a page on the Lorenz equations. He has a C++ program that integrates the Lorenz equations that runs in linux.
A possible program project for this course would be to get this program to run on
your laptop or the classroom computer,
and demonstrate the program for the class.
Double Pendulum Simulation by Eric Neumann
