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Qualitative Ordinary Differential Equations


Course Description

Transform methods, linear and nonlinear systems of ordinary differential equations, stability, and chaos.

Additional Requirements for Graduate Students:
Extra problems which are more difficult or more theoretical on homework.


Athena Title

Qual Ordinary Differ Equations


Prerequisite

MATH 2700 and [MATH 3000 or (MATH 3200 and MATH 3300) or MATH 3500 or MATH 3500H]


Semester Course Offered

Offered fall


Grading System

A - F (Traditional)


Course Objectives

Students will learn to solve constant coefficient ordinary differential equations by using the Laplace and Fourier transform. Students will also learn how to qualitatively examine the solutions of ordinary differential equations. Students will be able to graphically distinguish between stable and chaotic behavior of solutions of differential equations.


Topical Outline

1. One-dimensional dynamical systems. 2. Bifurcations, flows on the circle. 3. Linear systems of differential equations, analysis of the phase plane. 4. Limit cycles, bifurcations in 2-dimensional systems. 5. Liapunov exponents.


Syllabus