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# Modeling and Computation, Spring 2004

### Content

### Chapter 1: Finite Difference Equations

- functions, iterations, and cobweb plots
- fixed points, cycles and their stability
- bifurcation diagrams, bifurcation points, Feigenbaum's constant
- solving f(x)=0 for x using bisection and Newton's method

### Chapter 2: Boolean Networks and Cellular Automata

- Cellular automata models for diffusion and forrest fires
- Stephen Wolfram's experiment, Conway's game of life

### Chapter 3: Self Similarity and Fractals

- the Brocolli fractal, Serpinski's gasket in 2D and 3D
- dimension, the Cantor set and the Mandelbrot set

### Chapter 4: One Dimensional Differential Equations

- exponential growth, Newton's law of cooling, logistic growth
- data fitting using linear least squares
- fixed points and their stability
- Euler's method, Heun's method, Taylor series methods

### Chapter 5: Two Dimensional Systems of DEs

- simple harmonic motion, damped harmonic motion,
- the Lotka-Volterra system, a virus model, room heating models,
- partial derivatives, Taylor series and least squares approximation.
- the phase plane, fixed points and their stability.

#### Textbook

*Non-Linear Dynamics* by Kaplan and Glass.

#### Software

The course will involve extensive use of Maple, a mathematical software package, for the assignments and exams. The university has a site license for Maple. Maple is installed on the PCs and MACs in the assignment lab, the CECM lab, university open labs and the library. Maple is available from the computer shop for about $200.