This module introduces the various types of ordinary differential equations, the situations in which they arise and how they are solved.
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 Examination | 70 |
| Other Assessment(s) | 30 |