Recent Changes

• Changed Sat 5 May 2007 11:53:08 IST

  • Corrected some typos in the posted solutions.

• Changed Thu 19 Apr 2007 22:25:09 IST

  • Posted information on the exams.

• Changed Sun 18 Mar 2007 15:38:53 GMT

  • Posted solutions to assignment due 7 February 2007

• Changed Tue 30 Jan 2007 19:54:47 GMT

  • Posted problems due 7 February.

• Changed Tue 9 Jan 2007 11:41:36 GMT

  • Posted solutions to problems due 8 December.

Older changes are recorded in the change log.

Course Content

The course covers introductory material from the theory of ordinary differential equations. There are three main parts of the theory of ODE's:

• finding exact solutions,
• qualitative description of solutions, and
• finding (approximate) numerical solutions.

The course concentrates on the first two.

A much more detailed outline follows. This is subject to change, depending on how the course is going.

• Introduction
  • Terminology
    • Order of an Equation
    • Scalar Equations vs. Systems
    • Linear vs Nonlinear
  • Invariants
  • Symmetry
• Examples
  • Trigonometric Functions
  • Elliptic Functions
  • Van der Pol's Equation
  • Legendre Equation
  • Bessel's Equation
  • Celestial Mechanics
• The Gronwall Inequality
• Well Posedness
  • Existence
    • Local
    • Global
  • Uniqueness
  • Continuous Dependence on Initial Conditions
  • Stability
• First Order Linear Systems
  • Matrix Viewpoint
  • Existence
  • Uniqueness
  • Homogeneous Equations
  • Inhomogenous Equations
  • Linear Constant Coefficient
  • Method of Undetermined Coefficients
• Stability
  • Definition
  • Stability Criterion for Linear Constant Coefficient Systems
  • Autonomous Systems
  • Lyapunov's Method

Text

The course will roughly follow the book The Qualitative Theory of Ordinary Differential Equations, an Introduction by Fred Brauer and John A. Nohel. Buying the book is not strictly required, but it would be a good idea.

Tutorials

There are no tutorials in the usual sense.

Exams

There will be an annual exam on 24 May in Luce Hall from 2pm to 4pm. The exam will look more or less like the early exam I gave to a student who was going abroad in the second semester or like the Scholarship Exam. The Schol is, of course, harder then the annual exam will be. If you prefer PostScript to PDF, then click here and here.

Assignments

Assignments

	Questions		Solutions
	PostScript	PDF	PostScript	PDF
Due 25 October	a1.ps	a1.pdf	s1.ps	s1.pdf
Due 15 November	a2.ps	a2.pdf	s2.ps	s2.pdf
Due 8 December	a3.ps	a3.pdf	s3.ps	s3.pdf
Due 5 February	a4.ps	a4.pdf	s4.ps	s4.pdf

Please direct comments, queries and corrections to stalker@maths.tcd.ie.