Module Overview

Ordinary Differential Equations

This module introduces the various types of ordinary differential equations, the situations in which they arise and how they are solved.

Module Code

MATH 3802

ECTS Credits


*Curricular information is subject to change

Linear Ordinary Differential Equations: Definition. Existence and Uniqueness theorem for initial-value problems. Dimension of the solution space (linear independence of functions, vector space, Wronskian). Abel’s formula. Variation of parameters (reduction of order).

Laplace Transform: Transforms of derivatives and integrals, of periodic functions and the various shifting theorems. Convolution theorem. Application to constant coefficient linear ordinary differential equations.

Power Series: Solution in series of second order linear differential equations. Singular points of such an equation. Cauchy-Euler equation.

Orthogonal Systems of Functions: Fourier series. Linear operators, adjoint and self-adjoint operators. Eigenvalue problems. Sturm-Liouville problems and the orthogonality property of the solutions.

Lectures supported by tutorials.

Module Content & Assessment
Assessment Breakdown %
Formal Examination70
Other Assessment(s)30