Mathematical Modeling in the Biological Sciences

Spring Semester 1997
BIOL 379.01 (2 credits), W, 6:00PM-8:00PM, Wickersham 109
Dr. Buchanan
Office: Wickersham 113, Phone: 872-3659, FAX: 871-2320
Office Hours: 8AM-9AM (MTu_ThF), 10AM-11AM (W), or by appointment

Dr. Ostrovsky
Office: Roddy 259, Phone: 872-3425, FAX: 872-3985
Office Hours: 3PM-6PM (M), 8AM-9AM (Tu), 5PM-6PM (W)

The students will explore biological applications of mathematical modeling. A tentative schedule for the topics to be covered is listed below. Topics covered in this course will include models of population interactions, age-structured populations, genetics, muscle mechanics, ecology, and epidemics. Students will make use of mathematical software to rapidly carry out some of the more tedious calculations in the Mathematics Department's computer laboratory.
MATH 161 (Calculus I) is a prerequisite for this course.
Students are expected to attend all class meetings. If you must be absent from class you are expected to complete class requirements (tests and/or homework assignments) prior to the absence. Students who miss a test or assignment should provide a valid excuse, otherwise you will not be allowed to make up the missed work. Tests should be made up within one week of their scheduled dates.
Students are expected to do their homework and participate in class. Homework will be assigned during every class meeting. Selected homework problems will be handed in later for grading. Students should submit all homework by the date due. Late homework will not be accepted without valid excuse.
If you feel that an error was made in the grading of a test or homework assignment, you should explain the error on a separate sheet of paper and return both it and the work to me within a week after the assignment is returned to you. Course grade will be calculated as follows.
Mid-term test 1/3
Homework assignments 1/3
Final project and presentation 1/3

The course letter grades will be calculated as follows.

90-100 A
80-89 B
70-79 C
60-69 D
0-59 F

Course Contents

01/29 Linear and nonlinear difference equations applied to a single species, equilibrium points, stability, periodic orbits, cobweb diagrams.
02/05 Linear and nonlinear differential equations applied to a single species, exponential growth, the logistic equation, equilibrium points, stability, harvesting.
02/12 Linear and nonlinear difference equation models of two interacting species, equilibrium points, asymptotic behavior, introduction to matrix algebra.
02/19 More matrix algebra, eigenvalues and eigenvectors, determinant, characteristic polynomials, Perron-Frobenius theorem, diagonalization, basis vectors, applications to population interactions.
02/26 Leslie models, genetics models of autosomal inheritance, age stratification in a population.
03/05 Numerical taxonomy.
03/12 Genetic drift, sex-linked genes.
03/19 Differential equation models of two interacting populations, models of epidemics, vector field diagrams, nullclines, invariant regions, equilibrium points, stability, stable and unstable manifolds.
03/26 Spring break.
04/02 Evolutionary ecology, optimal phenotypes.
04/09 Muscle mechanics
04/16 Plant growth analysis, allometry, curve fitting.
04/23 Models of biochemistry and physiology, chemical kinetics, ligand-receptor interactions, parameter estimation, Hill plots, a model of dialysis.
04/30 Phyllotaxis and the Fibonacci sequence.
05/07 Models of spatial distributions, the game of life, random walks.

Final Word:
Modeling is a skill best learned by doing. You can only learn a limited amount by studying existing models. You will learn the most by trying out models of your own design or at the least modifying existing models. Do not expect perfection from early versions of models. Modeling is in part an exercise in refinement. What you learn from this course and your final grade depend mainly on the amount of work you put forth.

Page maintained by: Robert.Buchanan

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