# Mathematical Modeling and Computation

MACM 202, Fall 2005

### Textbook and Content

*Non-Linear Dynamics* by Kaplan and Glass.

- Chapter 1: Finite Difference Equations
- Chapter 2: Boolean Networks and Cellular Automata
- Chapter 3: Fractals and Dynamics
- Chapter 4: First Order Differential Equations
- Chapter 5: First Order Systems of Differential Equations

### Software

We will use Maple extensively for calculations and programming in this course. The university has a site license. Maple is installed on the PCs and MACs in the assignment lab, university open labs and the library. Maple is available from the microcomputer store for about $200. The Maple worksheet (see Handouts below) contains notes on how to use Maple. Please print a copy and read through it even if you have used Maple before.

### Maple Worksheets

- (MapleNotes.mws) Maple notes in Maple worksheet format
- (cobweb.mws) Code for creating cobweb plots
- (bifurc.mws) Code for creating bifurcation plots
- (program.mws) Notes on programming in Maple
- (newton.mws) Code for solving f(x)=x using Newton's method
- (network.mws) Code for networks and automata package
- (setlist.mws) Notes on sets and lists
- (arrays.mws) Notes on arrays
- (run1dca.mws) Code for running a 1D cellular automaton
- (graphics.mws) Maple 2D and 3D graphics primitives.
- (broccoli.mws) Code for drawing the broccoli fractal.
- (drawtree.mws) Code for drawing a tree in 2D.
- (randwalk.mws) Code for constructing random walks.
- (karafrac.mws) Code for drawing the Karatsuba fractal.
- (fit.mws) Maple procedure for data fitting using least squares.
- (dsolve1.mws) dsolve applied to first order DEs.
- (DEplot1.mws) DEplot for first order DEs.
- (dsolve2.mws) dsolve applied to second order DEs.
- (MCCHWP.mws) dsolve and DEplot for systems of DEs.
- (PDplots.mws) Plots of partial derivatives and Taylor series of f(x,y).
- (MCCHWP.mws) Local stability analysis of the modified Lotka-Volterra system.

### Assignments in Adobe .pdf format