Mathematical Biology
Spring 2020
Bard Ermentrout
Coordinates:
 Lectures: Lawrence 231 TH 4:005:15
Grading Policy
All homework is due the week
following the assignment.
Grades will be based on:
 Written homework 40%
 Project 20%
 Two Exams 40% (Take home)
The book is A Course in Mathematical Biology de Vries et al
Syllabus
 Week 1 (1/71/9). Scaling and dimensional analysis. This may bleed into week 2.
 Week 2 (1/171/16) Chapter 1 and start Chapt 2 of book
 Week 3 Continue to study Chapt 2 in book.
 Homework 3 Due 1/30 (Note the HW gives the wrong due date  it is Thursday 1/30)
 Week of Jan 27. Finish up discrete models and turn to Chapter 3, ODE models.
 Week of Feb 3 More ODEs, epidemic models, population biology, etc
 Homework 4 due Feb 6
 Qualitative stability notes
 Week of Feb 10  molecular modeling, game theory.
 Homework 5  Due on Feb 13
 Week of Feb 17  finish up game theory  some PDEs chapt 4 in book
 Week of Feb 24 More PDEs  reaction diffusion equations pattern formation
 Homework 7 Due Feb 27
 Midterm will be given Feb 27 and collected on Mar 3 (I have changed the dates of the Midterm as I will be out of town on Friday/Saturday 2/212/22 with no chance to check email, so you would not be able to ask questions)
Additional Info
 Extremely brief Maple tutorial

Differential equations using the computer

Project
A central part of the course will be a project in which you choose
some 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 neurons, some
have modeled vampires. By the middle of the term, you should be
thinking about a project. The project should have the following components:
 Introduction to the problem
 Approach to modeling
 Model development and equations
 Analysis and simulation (if appropriate)
 Conclusions based on the analysis
All totaled, should be about 35 pages including figures. You will give a 10 minute prsentation during the last week of class before FINALS. The project does not have to be original in that you can find a model in a paper as long as you show that you have done the analysis and simulations.

Homework
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.

Software
XPPaut info
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 Mac, Windows, and Unix platforms and is free. Some of
the problem may be easier with 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, but I can show you how to put it on your laptops.
Since MATLAB is available (free or cheap for students), you are also encouraged to use that.