**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

- Terminology
- 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

- Existence
- 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

Sep 25, 2006

File translated from T

On 25 Sep 2006, 13:02.