3H: Mathematical Methods MATHS4075

• School: School of Mathematics and Statistics
• Credits: 20
• Level: Level 4 (SCQF level 10)
• Typically Offered: Semester 1
• Available to Visiting Students: Yes

Short Description

This course aims to give students an understanding of linear differential equations (both ordinary and partial) including the construction of their solutions by a variety of techniques.

Timetable

34 x 1hr lectures and 12 x 1hr tutorials in a semester.

None

Excluded Courses

Mathematical Methods I (86PP)
Mathematical Methods II (86PQ)

Assessment

90% Examination, 10% Coursework.

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? Not applicable

Reassessments are normally available for all courses, except those which contribute to the Honours classification. For non Honours courses, students are offered reassessment in all or any of the components of assessment if the satisfactory (threshold) grade for the overall course is not achieved at the first attempt. This is normally grade D3 for undergraduate students and grade C3 for postgraduate students. Exceptionally it may not be possible to offer reassessment of some coursework items, in which case the mark achieved at the first attempt will be counted towards the final course grade. Any such exceptions for this course are described below.

Course Aims

The course Mathematical Methods aims to give a comprehensive treatment of techniques for the solution of linear ordinary differential equations, including eigenvalue problems, and commonly occurring partial differential equations given initial and boundary conditions that are appropriate for each type of equation. The techniques to be covered include series solutions, Green's function methods, the method of separation of variables, and the method of characteristics.

Intended Learning Outcomes of Course

By the end of this course students will be able to:

■ classify differential equations according to order, degree and linearity;

■ construct exact solutions to second order linear differential equations by a variety of techniques, including Wronskians and integrating factors;

■ construct series solutions for second order ordinary differential equations about ordinary and regular singular points;

■ construct Green's functions and handle delta functions for simple systems of equations;

■ solve simple eigenvalue/boundary value problems;

■ establish the orthogonality of eigenfunctions and use this property to construct an eigenfunction expansion.

■ solve a first order linear or quasilinear partial differential equation;

■ determine the regions of the xy-plane in which the general second order partial differential equation in two dimensions is hyperbolic, parabolic or elliptic and subsequently reduce the equation to its canonical form and determine the characteristic equations;

■ solve partial differential equations by the method of separation of variables for given initial and/or boundary conditions.

None