Differential Equations module (MA31002)

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Credits

15

Module code

MA31002

About the module

This module provides an in-depth study of Differential Equations aimed at Level 3 students. This module is mandatory for all Level 3 students on Mathematics (including Mathematics combined) degrees. If you have questions about this module please contact your Advisor of Studies.

Prerequisites

Students taking this module must have achieved a pass mark in each of the modules MA21001 and MA22001, or equivalents.

Indicative Content

  • First Order Differential Equations

    Separable equations, Linear equations with constant coefficients, Linear equations with variable coefficients, integrating factors, Homogeneous equations, Exact equations and integrating factors.

  • Second Order Differential Equations

    Homogeneous equations with constant coefficients, Fundamental solutions of linear homogeneous equations, Linear independence and the Wronskian (including Abel′s formula), Reduction of order and reduction to the normal form, Nonhomogeneous equations, Method of undetermined coefficients, Initial conditions.

  • Systems of First Order Linear Equations

    Transformation of an nth order equation to a system of n first order equations, Homogeneous linear systems with constant coefficients, Fundamental sets of solutions and fundamental matrices, the Wronskian and Abel′s formula, The exponential of a matrix, Nonhomogeneous linear systems, Variation of parameters, Homogeneous linear systems of two first order equations with constant coefficients, Stability and the phase plane.

  • Partial Differential Equations and Fourier Series

    Fourier series of functions of one variable, Dirichlet′s Conditions, Technique for determining Fourier coefficients (even/odd functions). Gibbs′ phenomena. Introduction to Partial Differential Equations, Technique of separation of variables with application to initial and boundary value problems.

Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via an exam (80%) and coursework (20%).

Credit Rating

This module is a Scottish Higher Education Level 3 or SCQF level 9 module and is rated as 15 SCOTCAT credits or 7.5 ECTS credits.