Mathematics 3S: Mathematical Methods MATHS3019

  • Academic Session: 2023-24
  • School: School of Mathematics and Statistics
  • Credits: 20
  • Level: Level 3 (SCQF level 9)
  • Typically Offered: Semester 1
  • Available to Visiting Students: Yes

Short Description

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


Lectures at 9.00 am on Mondays, Tuesdays, Wednesdays and some Thursdays. Tutorials weekly, at a time to be arranged.

Requirements of Entry

Mathematics 2A and 2D at Grade D3 or better.
Please note: this is one of a package of level-3 courses in Mathematics leading to a designated degree in Mathematics.
Full details of the requirements for a designated degree can be found in the University Calendar.
The requirements or the designated degree include a second-year curriculum that includes Mathematics 2A, 2B, 2D and another level 2 Mathematics course. An average grade of D3 over these 4 level-2 courses is required.

Excluded Courses

Mathematical Methods  (85JM)


90% Examination, 10% Coursework.

Main Assessment In: April/May

Are reassessment opportunities available for all summative assessments? No

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 introduce students to techniques for the solution of linear ordinary differential equations and commonly occurring partial differential equations given initial and boundary conditions that are appropriate for each type of equation.

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;

■ 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.

Minimum Requirement for Award of Credits

Students will be deemed to have completed the course (gaining 20 credits and at least a Grade H) if they have: a 70% or better record of attendance at tutorials; handed in written work; taken the degree (or resit) exam.

Students who have not satisfied the above requirements may still be deemed to have completed the course subject to approval by the Head of School. Explanations are required for absences of more than a few days.