This is the first semester of a two-semester course sequence. In this first semester, the classical theory of differential equations is developed, focussing on existence and uniqueness of solutions, continuous dependence on data, Lyapunov stability, Floquet theory, periodic solutions and the Poincare-Bendixon Theorem, dissipation and passivity. As time allows, the basic framework for differential-algebraic equations (DAEs) will be introduced as well
In the second semester, material on DAEs will continue to be developed and the focus will shift toward boundary value problems, Hamiltonian systems, regular/singular perturbations, asymptotic expansions, and boundary layers.
Course Instructor: Christopher Beattie
Office hours will be held in McBryde 552; times will be announced in the second week of classes. Additional meeting times can be arranged by appointment. Walk-ins are encouraged.
The main reference texts for this course are available for download at the links provided below, free of charge with a VT account.
Supplemental reading material may be distributed occasionally via the Canvas website.
Either MATLAB or Octave may be used for the computational exercises in this course. MATLAB can be purchased from the Software Distribution Office located in 3240 Torgerson Hall; Octave is a freely available, open source package with similar capabilities as MATLAB. Note that MATLAB is available on the computers at the Math Emporium.
There will be two in-class quizzes and a take-home final exam each worth 15% of the grade. The remainder of the grade will be determined from individual or group projects that include homework exercises and computational studies.
A final grade of 92% or higher will guarantee an A.
You are encouraged to discuss regular individual homework assignments with other members of the class, however any write-ups or scripts that are submitted for grading should be your own work. Group projects should be worked on only with group members, and no more than three people may work as a group. Naturally, no collaboration is allowed on quizzes.
Failure to follow these guidelines, and giving or receiving unauthorized aid or assistance on homework, on in-class quizzes, or on the take-home final are Virginia Tech Honor System violations and cases will be filed.