MAC 6933
Mathematical Biology Spring 2006
Course: MAC6933 

Instructor: Mahbubur Rahman 


4:305:45
TR 

Office: Bldg. 14/ Room 2718 Office hour: 11:0012:00noonTR/Appointment 


email: mrahman@unf.edu 

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,
Predatorprey systems, competition. Nulliclines/direction field for
planar systems of ODES. Hopf bifurcation for two dimensions. Bendixondulac
criterion, Liapunov functions.
3. Population dynamics in
structured populations. Deterministic matrix and partial
differential equations formulation of birth and death process. PerronFrobenius
Theorem and discussion of dynamics of x_{n+1}=Lx_{n} for low dimensional
negative Leslie matrix.
4. Standard models in epidemiology/immunology.
Text:
1. Mathematical Models in Population Biology and
Epidemiology
by Fred Brauer, Carlos CastilloChavez, Springer, ISBN0387989021
Additional References:
1. Infectious Diseases of Humans by Roy M. Anderson
and Robert M. May,
2. Mathematical Models in Biology
(Paperback)
by Leah EdelsteinKeshet,
Society of Industrial and Applied , 2005,
ISBN0898715547
3.
Differential Equations and Mathematical Biology
by D. S. Jones, B. D. Sleeman,
Chapman & Hall, 2003, ISBN1584882964
Grade
Allocation :
2
Exams : 40 % 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 16^{th} , March 20^{th}March 25^{th} .
· Exam 1: February. 14, 2006(Tuesday)
· Exam 2: April. 6, 2006(Thursday)
· Final Exam is Thursday, April 27, 3:004:50pm.
HOMEWORK: is required. Problems to be turned in are assigned in class.