Introduction to Continuous Mathematical Modeling

Course Description

Textbook

Topics in Mathematical Modeling by K.K. Tung (pdf).

The following additional books include many of the topics we will address and are highly recommended additional resources:

• Mathematical Models: Mechanical Vibrations, Population Dynamics, and Traffic Flow. by R. Haberman, SIAM, 1998.
• Differential Equations and Their Applications by M. Braun, Springer-Verlag, 1983 (or later). Includes discussion of combat models, predator-prey models, competition models, and several other interesting applications.
• Nonlinear Dynamics and Chaos by S.H. Strogatz, Addison Wesley, 1995. Includes in depth discussion of bifurcations, phase plane analysis, conservative systems, and the Romeo and Juliet model of love affairs, as well as the topic of chaos. (This is written at a level slightly above the level the instructor will take for the course.)
• Mathematical Biology I: An Introduction (3rd Ed.) by J.D. Murray, Springer-Verlag, 2002.

For a review of differential equations, you may be interested in reading the AMATH 568 class notes written by Professor Nathan Kutz. They provide a review which is more than sufficient for our purposes in this class. (pdf)

Syllabus

• Introduction to continuous models: compound interest and mortgages.

• Biological and ecological population models, exponential growth and decay, logistic growth.

• Phase plane analysis, equilibria, stability, and bifurcations.

• Models of species interation, predator and prey.

• Conflict models, competition models, war games, marriage and divorce.

• Physical sciences models, potential energy, conserved quantities, orbits.

• Traffic models, method of characteristics, wave propogation.

• The Lorenz equations and chaos.

• Carbon dating and the age of the earth.

Schedule

Grading

You may view your homework and project grades on-line.