MATH 320(!): Linear Algebra and Differential Equations (honors-level), 2016-2017


Course Details:

Instructor: Saverio Spagnolie

Lectures: MWF 9:55-10:45am (Fall 2016) and TR 1-2:15pm (Spring 2017) in Van Vleck Hall B239

Course websites are on Canvas: Fall 2016 and Spring 2017

Preliminaries (or: is this course for you?)

Course Content:

Math 320! focuses on Equilibrium and Dynamics of Linear systems, in short: Ax=b and dx/dt=Ax-b, and does not try to be a full course on ODEs AND a full course on Linear Algebra. In practice however, Math 320! covers more material than regular math 320.

Math 320! introduces and uses modern computation tools such as Python/Numpy, not just "by hand" calculations on elementary number problems. We will discuss and use numerical methods early in the course to build practical insight into ODEs. Examples of simple ODEs, systems of ODEs and nonlinear ODEs, are discussed and illustrated.

Math 320! focuses on explicit applications such as coupled mass-spring systems and coupled heat transfer problems, including non-dimensionalization and reduction to relevant parameters (not discussed in regular 320). We will discuss eigenvalue problems as motivated by the differential system dx/dt = Ax-b, but goes beyond standard 320 coverage by showing that typical applications lead to systems of the form B dx/dt = A x - b with diagonal B and symmetric A. We will learn strategies for dealing with situations when A or B are singular or defective, and provide physical examples of such singular or defective systems.

Math 320! discusses the importance of symmetry for eigenvalues and eigenvectors and shows how to preserve that symmetry. Math 320! shows how these results apply to diagonalization of the mass-spring systems, heat transfer problems, tensor of inertia, stress tensor and quadratic forms.

Math 320! is a mathematics course. It does include simple proofs of key concepts, for example that eigenvectors corresponding to distinct eigenvalues are linearly independent, that symmetric matrices have real eigenvalues with orthogonal eigenvectors, etc. Students are expected to understand those proofs as they underlie a deeper and lasting understanding of the concepts. Homework and exams may include some such proofs, but mostly consists of solutions and analysis of explicit problems.

Can I take this course?

Anyone who has satisfied the prerequisites may enroll in this course. Officially the prerequisite is Math 222, but familiarity with vectors (as seen in Math 234) would be helpful. Students do not have to be "honor" students to take the course. Neither is 320! "honors optional" (%); students do not have the choice to do/not do/request/ignore extra "honors" material. 320! is "honors-level", the coverage and content is somewhat deeper than regular sections. Honor students get honors credit automatically.