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.