MATH 563: Advanced Mathematical Methods for the Biological Sciences
TTH010:10 - 11:30, 3096 EH

Instructor:

 Trachette Jackson
3856 East Hall
tel: 734-764-8537
fax: 734-763-0937
tjacks@umich.edu
office hours: MW 01:00-02:00 3856 EH

Course description Textbook Syllabus MATLAB Help Homework Handouts

Course Description

Mathematical biology is a fast growing and exciting modern application of mathematics which has gained worldwide recognition. This course will focus on the derivation, analysis, and simulation of partial differential equations (PDEs) which model specific phenomena in molecular, cellular, and population biology. A goal of this course is to understand how the underlying spatial variability in natural systems influences motion and behavior. Mathematical topics covered include derivation of relevant PDEs from first principles; reduction of PDEs to ODEs under steady state, quasi-steady state, and traveling wave assumptions; solution techniques for PDEs and concepts of spatial stability and instability. These concepts will be introduced within the setting of classical and current problems in biology and the biomedical sciences such as cell motion, transport of biological substances, and biological pattern formation. Above all, this course aims to enhance the interdisciplinary training of advanced undergraduate and graduate students from mathematics and other disciplines by introducing fundamental properties of partial differential equations in the context of interesting biological phenomena.

Textbook

There is no single text that is entirely appropriate for a course such as this one; however, it is strongly recommended that students purchase one of the following texts: Mathematical Biology II: Spatial Models and Biomedical Applications, James D. Murray or Mathematical Models in Biology, Leah Edelstein-Keshet, 1988. The former is the second edition of a well written and classic text in mathematical biology by one of the pioneers of this field. This book is intended for students with a strong mathematical background; whereas the latter is geared more towards students who have not already seen certain advanced mathematical techniques for analyzing biological models. Material for this course will be taken from both texts as well as the current literature. An excellent text for background in PDEs is Elementary Applied Partial Differential Equations by Haberman.

Syllabus

MATLAB Help

Homework

Follow links in the table below to obtain a copy of the homework in Adobe Acrobat (PDF) format.

Computer Lab Assignments Homework Assignments
Lab #1(PDF)
Lab #2(PDF)
Homework #1 (PDF)
Homework #2 (PDF)
Homework #3 (PDF)
Homework #4 (PDF)
Homework #5 (PDF)

Handouts