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Spring 2005

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Instructor:	Warren Weckesser 314 McGregory, (315) 228-7228 Email: wweckesser-at-mail-dot-colgate-dot-edu
Office Hours:	Monday, Wednesday: 1:30-3:30 PM
Lecture:	M,W,F 9:20-10:10, McGregory 215
Web Page:	https://math.colgate.edu/~wweckesser/math312/

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Course Information (in PDF format)

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Final Project

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Lecture Notes and Supplements

First order differential equations; population models; the logistic equation

The Solow growth model (economics); direction field; stability of an equilibrium

Solving first order DEs: separable; linear

Second order differential equations; nondimensionalizing a DE; the projectile problem

Nondimensionalize the logistic equation; dimensional analysis and the Buckingham Pi Theorem applied to the pendulum

Finding eigenvalues and eigenvectors of 2x2 matrices

Linear Two-dimensional Systems of Differential Equations. Includes finding the general solution and sketching phase portraits.

Some notes on using the PPLANE Java applet

One Dimensional Maps

Linear 2D Maps

Periodic Drug Doses

Linearization

Competing Species

"The Coin and Die Game"

Markov Chains (Updated, 30 April 2005)

Some notes on using MATLAB

Converting a map that depends on older states to a simple map

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Homework

Note: Unless otherwise noted, homework is due by 5:00 PM on the given due date.

Assignment	Due Date
Homework 1	Friday, Jan. 28
Homework 2	Friday, Feb. 11
Homework 3	Friday, Feb. 25
Homework 4	Friday, April 8
Homework 5	Friday, April 22

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Web Applications, Solvers, Applets, and Links

Solvers for Specific Systems of Differential Equations Linear System Solver (2x2) SIR Model of Disease Spread SIR Model of Disease Spread (with Birth and Death Rates) SIQR Model of Disease Spread Rinaldi's "Laura and Petrarch" Model Phase Plane Java Applets DFIELD and PPLANE :: PPLANE is the Phase Plane applet. Phase Portraits for ODEs

Linear Map Iterators Linear 3D Map Iterator Additional Solvers Periodic Drug Dose Discrete Predator-Prey One-dimensional Maps 1D Map Iterator :: Dan Schult's web page for computing iterates of 1D maps The Logistic Map :: Andrew Burbank's elegant Java applet Time Series of Logistic Map :: Another nice Java applet. This one shows both the "cob web" diagram, and the plot of xn vs. n.

Monopoly and Markov Chains Monopoly in the view of mathematics This link animates the results of Monte Carlo simulations and Markov Chain iterations. Probabilities in the Game of Monopoly This page shows the (very large) transition matrix! Monopoly Revisited by Ian Stewart Small World Links The Small World Phenomenon :: A Wikipedia article The Oracle of Kevin Bacon The Erdös Number Project