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The course
will cover basic techniques of
deterministic modeling. Models drawn
from mathematical biology will be used as "case studies" to motivate
and illustrate the mathematical methods as well as to introduce
classical areas
of mathematical biology such as population dynamics, biological
kinetics and
pattern formation. We will start by
studying discrete time models described by difference equations and
then focus
on continuous time models given by ordinary differential equations
(ODEs). The course will emphasize
techniques from
ODEs, primarily the analysis of qualitative behavior of systems of
equations. Lastly, we will study models
with two independent variables described by partial differential
equations, in
particular, reaction-diffusion equations. The
first half of the course will focus on models from
population
biology, which provide examples of models that are amenable to analysis
with
the techniques covered in class. Later
in the semester, models from cell biology and development will be
discussed.
Faculty whose research is related to topics discussed in class will be
invited
to give guest lectures. The class will
include a computer laboratory that will teach the basics of programming
in
Matlab and provide the computational tools necessary for simulating,
analyzing
and fitting models. |
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LAB HANDOUTS:
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HOMEWORK:
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LAB
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SOLUTIONS: |
Midterm
Exam Solutions Project |