MATH 612, Spring 2003
Ordinary Differential Equations

Course information

Course:	MATH 612: Ordinary Differential Equations
Time/Place:	MW 7:00pm-8:15pm, MP 401
Instructor:	Dr. Rouben Rostamian
Office:	MP 417
Phone:	410-455-2458
Email:	rostamian@umbc.edu
Office hours:	MW 6:00-7:00 and by appointment

Course Description

This subject of this is course is an introduction to the qualitative analysis of ordinary differential equations and dynamical systems.

Textbook

Differential Equations and Dynamical Systems by Lawrence Perko will serve as the main textbook for this course. We will cover approximately half of the book, consisting of chapters 1 and 2 and parts of chapter 3.

Syllabus

Topics will include:

• General solution of systems of linear ODEs, qualitative behavior and stability.
• Existence and uniqueness of solutions of systems of nonlinear ODEs, continuous dependence on initial data, maximal interval of existence.
• Phase space and the flow defined by a differential equation, linearization, Liapunov functions.
• The Stable Manifold Theorem, The Hartman-Grobman Theorem, Center Manifold Theory.
• Limit sets and attractors, periodic orbits, limit cycles, Poincare-Bendixon Theorem, LaSalle's Invariance Principle

Prerequisites: MATH 225, MATH 301, MATH 302 or permission of instructor.

Grading

Course grade will be based on performance on frequent homework assignments throughout the semester.

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