Mathematical Modeling
Fall 1999
Bard Ermentrout
Coordinates:
- Lectures: Thackeray 525 MWF 11:00-11:50
Grading Policy
All homework is due the week
following the assignment.
Grades will be based on:
- Written homework 25%
- Projects 25%
- Two Exams 50%
The book is Mathematical Models in Biology by
Leah Edelstein-Keshet, but I will be supplementing the material with
lots of other things.
Syllabus
The syllabus is rather flexible at this point and will develop as the
course goes on. I will first determine how much preparatory material
is required. There is no extra knowledge required about bniology and I
will introduce all the concepts as needed. Here is a rough outline of
what I will cover in the course.
- Models using discrete dynamics
- Introductory models (chapt 1)
- Nonlinear difference equations - fixed points, stability, etc
(chapt 2) Try the XPP for maps
tutorial
- Population models (chapt 3)
- Markov Chains (random linear equations)
- Other models from neural networks to economics
- Ordinary differential equations
- Chemical models - the law of mass action
- Growth models (chapter 4,5,6) Try the tutorial
Phase planes and populations
- Mechanics and the Euler-Lagrange equations
- Population and disease (chapter 6)
- Active media (chapt 8)
- Other types of equations - delay and PDEs (chapt 9,10?)
Additional Info
A central part of the course will be a project in which you choose
some sort of physical, social, or biological system and create a
mathematical model of it to explain some aspect of the system. For
example, in the past, some students have looked at chemical
oscillation models, some have modeled simple mechanical toys, some
have modeled vampires. By the middle of the term, you should be
thinking about a project.
There will homework of several varieties. Much of it will be taken
from the book but there will be a substantial amount of homework which
you can do on the computer that will allow you to simulate different
systems. I will describe
these later on in the term, but they will likely involve your using
the computer and your brains to solve some applied problems that arise
in applications.
I have not specified any particular software package
to use for the course but I will introduce you to a piece of software
that I wrote that allows you to solve and animate ODEs, PDEs, and all
the kinds of equations you will encounter in the course. It is
available for both Windows 95 and Unix platforms and is free. Some of
the projects may involve the use of software; I will introduce its use
to you during the course of the semester. The software is available in
some of the labs.
XPP/WinPP
Go to my home page to download the latest versions of my
software. Here is a quick guide as well as
some practice problems. There is a fuller tutorial available for UNIX as well
as one for the Windows
95 version.