School of Mathematics
School of Mathematics
Course 216 - Ordinary Differential Equations
2006-07 (SF Mathematics & TP
)
Lecturer: Dr. John Stalker
Requirements/prerequisites:
Duration: 11 weeks.
Number of lectures per week: 3 including tutorials
Assessment:
End-of-year Examination: Annual examination in May/June.
Description:
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.
- Introduction
- Terminology
- Order of an Equation
- Scalar Equtions 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
- 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
Textbooks:
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 agood idea.
Sep 25, 2006
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On 25 Sep 2006, 13:02.