Tues. 9/2

MAIN POINTS
The beginning of the first chapter serves as an overview of the history of chaos/dynamics. Then it turns to some examples of differential equations— an oscillator, the heat equation, and then defines the generalized case of a differential equation. The text introduces dummy variables to put equations in standard form, and defines the difference between linear and nonlinear systems (whether the x variables on the right hand side are all in the first power or not). The text defines autonomous vs. nonautonomous systems (systems with the time variable explicit or not), the trajectory, and phase space.

Ch. 2 defines a first-order system as a function of one variable. It gives the example of dx/dt=sinx, which it explains graphically. Stability is defined as whether or not a small peturbation will be rectified, or if it will cause a drastic change in trajectory in the movement of the peturbation. It gives a number of examples of systems, particularly population growth, which uses a logistic equation.

CHALLENGES:
I'm a little unclear on the precise definition of a logistic equation— and how the limitations are incorporated into the system.

REFLECTION:
We did a quick exercise on Chaos in Scientific Computation. I also read the book by Gleick at some point in High School. As for the differential equations, I have little experience working with them apart from using the Runge-Kutte method, etc.