MAC 6933
 Mathematical Biology -Spring 2006


Course: MAC-6933
Mathematical Biology 
(CRN 12684)


Instructor: Mahbubur Rahman


4:30-5:45  TR
Class  Bldg. 3/Rm. 1371


Office:  Bldg. 14/ Room 2718

Office hour: 11:00-12:00noonTR/Appointment




 Tentative Materials

1. Deterministic single species population dynamics. Methods for the study of linear and nonlinear discrete and continuous dynamical systems. Cobwebbing with 1 dimensional difference equations; periodic points and their linearized stability. Introduction to numerical chaos to standard quadratic/Ricker map.


2. Population dynamics of interacting species. Host parasitoid interactions, Predator-prey systems, competition. Nulliclines/direction field for planar systems of ODES. Hopf bifurcation for two dimensions. Bendixon-dulac criterion, Liapunov functions.


3. Population dynamics in structured populations. Deterministic matrix and partial differential equations formulation of birth and death process. Perron-Frobenius Theorem and discussion of dynamics of x_{n+1}=Lx_{n} for low dimensional negative Leslie matrix.


4. Standard models in epidemiology/immunology.





1. Mathematical Models in Population Biology and Epidemiology

by Fred Brauer, Carlos Castillo-Chavez, Springer, ISBN-0387989021



Additional References:


1. Infectious Diseases of Humans by Roy M. Anderson and Robert M. May, Oxford University Press, 2002


2. Mathematical Models in Biology (Paperback)
by Leah Edelstein-Keshet, Society of Industrial and Applied , 2005, ISBN-0898715547


3. Differential Equations and Mathematical Biology
by D. S. Jones, B. D. Sleeman, Chapman & Hall, 2003, ISBN-1584882964


Grade Allocation :

2 Exams : 40 % 
Final Exam(Comprehensive):  30 % 

Homework- 30 %


The plus & minus `` will be included only to improve your grades

90 to 100 %A

80 to89 %B

70 to79 %C

60 to 69 %D

Below 60 %F


Important Deadlines:

         Last day to withdraw   March 26th

         Holidays (no classes or office hours)   January 16th , March 20th-March 25th .

         Exam 1: February. 14, 2006(Tuesday)

         Exam 2: April. 6, 2006(Thursday)

         Final Exam is Thursday, April 27, 3:00-4:50pm. 

HOMEWORK: is required. Problems to be turned in are assigned in class.