
Math 636  Mathematical Modeling 



San Diego State University  This page last updated 03Sep01 

This course will examine mathematical modeling primarily from a dynamical systems point of view using the text listed above and a collection of material that I have developed and will post on this website. The course will begin with some applications from my website looking at population models using data from classical yeast experiments. The text will be used to support the modeling efforts developed on the web. The course will examine models of physical systems, including spring problems, pendulums, and heat flow, and other applications from the biological sciences. The majority of the modeling efforts use techniques from the qualitative theory of differential equations. Whenever possible, this course will show how to connect the theoretical models to real data. Later in the semester, I plan to venture away from the text to provide additional material on mathematical modeling in areas such as parameter identification or Monte Carlo simulations (probabilistic modeling). Every attempt will be made to provide you with this additional material on the Web through this website.
The grading of this course will be based on your performance on the homework assignments, takehome exams, and a project. I have yet to determine the weighting of each of these, but your homework will be a major portion of the grade (5060%), so it is important to keep current on assignments. There will be a penalty for homework that is late. Homework will be due on Friday (usually), and late homework will be assessed a 20% penalty for unexcused late work up until the homeworks are returned to class, after which homework will not be accepted. At present, I am planning 2 takehome exams with one in the middle and one at the end of the class. You will choose a project based on your interests that will be presented both orally and in written form near the end of the semester.
Mathematical modeling
The diagram above shows the basics of how you should visualize mathematical modeling as you cycle between the real world, the mathematical model, and empirical data.
This course will rely on many of your past courses in mathematics, especially differential equations and linear algebra (and Calculus of course). In addition, there will a strong computational component to the class. You will have access to the BA 120 computer lab, and I will present some numerical methods in Excel, Maple, and MatLab. (Some introduction to each of these will be provided.) Below we see the output of a model for a damped spring using Maple to simulate the system.
More information on the damped oscillator and its solution in Maple with a movie of the solution curves rotating can be found by clicking on the picture. This movie is part of the advertisement for the Math 241 course on Maple.