Mathematical models (in science
and engineering), and their analysis
MATH 235, Instructor: T. Lakoba.
In this course, several models of classical and modern science will be
considered
starting, as much as possible, from first principles. The emphasis
will be made
on mathematical techniques which are often used by
applied mathematicians,
physicists, and engineers in their research. These techniques lie in
the
foundation of
mathematical modeling, and hence any prospective researcher in
this field needs
to be well-versed in them. Examples of such techniques are:
linearization, Taylor series,
and the eigenvector expansion. Most of the techniques
considered in this course
are covered, to various extent, in the basic undergraduate
mathematics courses.
The goal of this course is to elevate the students' passive familiarity
with these
techniques to the level where they can actively use them.
Students will work through the mathematical details of analysis
presented in the
Notes for the course, and then practice applying these techniques to
similar models
in Homework problems. Students will not
be expected to construct mathematical
models themselves.
The course will include two projects: a
midterm and a final, where students will have
to demonstrate their acquired mastery of basic
mathematical techniques by reading a
contemporary research paper (with some
mathematical content) and making a
presentation about it to the class.