View Specification DocumentMathematics 2D: Mathematical Methods and Modelling MATHS2033
- Academic Session: 2026-27
- School: School of Mathematics and Statistics
- Credits: 10
- Level: Level 2 (SCQF level 8)
- Typically Offered: Semester 2
- Available to Visiting Students: Yes
- Collaborative Online International Learning: No
- Curriculum For Life: No
Short Description
This course aims to introduce aspects of the theory and methods used in mathematical modelling. Topics covered in the course include: dynamical systems and integral transforms. It is an essential course for intending honours students. The emphasis is on methods and applications.
Timetable
2 x lectures per week. Fortnightly tutorials.
Requirements of Entry
Mathematics 1 at at least grade D3.
Co-requisites
Mathematics 2A: Multivariable Calculus, Mathematics 2B: Linear Algebra.
Assessment
One degree examination (80%) (1 hour 30 mins); coursework (20%).
Main Assessment In: April/May
Are reassessment opportunities available for all summative assessments? No
It is the default expectation that all courses will offer opportunities for reassessment or deferred assessment. Where it is not possible to offer this in some assessment components, the grade achieved at the first attempt will be counted towards the final course grade, and any exceptions for this course are described below.
[No exceptions]
Course Aims
This course aims to introduce aspects of the theory and methods used in mathematical modelling. The course first aims to provide an introduction to dynamical systems associated with mathematical models. Students will learn to construct the solution of the ordinary differential equations arising in such models and qualitatively analyse these solutions. The course then aims to provide an introduction to Fourier series, Fourier and Laplace transforms, including their use in simplifying and solving differential equations.
Intended Learning Outcomes of Course
By the end of this course, students will be able to:
■ Analyse dynamical systems consisting of a single dependent variable and which are modelled using ordinary differential equations.
■ Analyse the stability of equilibrium points in first order autonomous ordinary differential equations and construct phase portraits for single dependent variable dynamical systems.
■ Solve linear systems of autonomous ordinary differential equations using the matrix exponential and identify phase portraits of two-dimensional systems.
■ Compute Fourier series, Fourier and Laplace transforms, including the use of their elementary properties to simplify and solve differential equations.
■ State the definitions, results and formulae presented in lectures; apply and adapt these to solve suitable problems.