Linear Algebra with Applications to Differential Equations.
Instructor: Dave Feldman
College of the Atlantic
The first half of this class will consist of a rapid tour of the
key elements of linear algebra. We will cover vector and matrix
algebra, linear vector spaces and subspaces, basis and dimension, the
determinant, and eigenvalues and eigenvectors. We will then consider
first-order linear differential equations---first scalar equations and
then systems of equations. We will see that linear algebra is an
indispensable tool for solving systems of linear differential
equations and understanding the geometric structure of their solutions.
In addition to covering basic theory, we will consider a handful of
case studies that illustrate the power of the mathematical techniques
we are learning. These case studies will be drawn from across the
sciences. The particular case studies we examine will depend on
student interests.
Students who successfully complete this course will gain a solid
introduction to the calculational techniques and key constructions and
ideas of linear algebra. Students will also learn techniques for
solving and understanding systems of linear differential equations.
Additionally, this course serves as an introduction to formal
mathematics; students will gain experience working at a level of
generality and abstraction a bit above that encountered in a typical
introductory calculus sequence.
Evaluation will be based on weekly programming exercises.
Pre-requisites: Calculus I and II, or the equivalent.
Class size: no limit. *QR* *ES*. Intermediate. No lab fee.
