MT3504 Differential Equations

Academic year

2024 to 2025 Semester 1

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 9

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Planned timetable

9.00 am Mon (odd weeks), Wed and Fri

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr D W Rees Jones

Dr D W Rees Jones
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module Staff

Dr Irene Kyza

This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

The object of this module is to provide a broad introduction to analytical methods for solving ordinary and partial differential equations and to develop students' understanding and technical skills in this area. This module is a prerequisite for several other Honours options. The syllabus includes: existence and uniqueness of solutions to initial-value problems; non-linear ODE's; Green's functions for ODE's; Sturm-Liouville problems; first order PDE's; method of characteristics; classification of second order linear PDE's; method of separation of variables; characteristics and reduction to canonical form.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2503

Assessment pattern

Written Examination = 100% (2-hour final exam = 90%, class test = 10%)

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks) and 1 tutorial (x 10 weeks).

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Understand the basic solution methods for first and second order ordinary differential equations (ODEs)
  • Be able to discuss existence and uniqueness of solutions to ODEs
  • Be able to solve inhomogeneous second order ODEs using Green functions
  • Find solutions of linear second order PDEs using the method of separation of variables
  • Find solutions of first order PDEs using the method of characteristics and combining the coupled ODEs arising
  • Classify second order PDEs as hyperbolic, parabolic or elliptic, as well as understand the concepts of domain of dependence and range of influence