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MT2507 Mathematical Modelling

Academic year

2025 to 2026 Semester 2

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 8

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 (weeks 2, 4, 6, 8, 11), Tue and Thu

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

Module coordinator

Prof D H Mackay

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

Module Staff

Prof Duncan Mackay; Dr Tom Elsden

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

Module description

This module provides an introduction to a variety of techniques that are used throughout applied mathematics. It discusses how to translate physical problems into mathematics and covers such topics as differential equations, dynamics, numerical methods and Fourier series. It illustrates how these are used when solving problems. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2503

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 hours of lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 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

  • Analyse mathematical models of real-world problems based on ordinary differential equations
  • Use numerical methods to solve problems associated with mathematical modelling
  • Apply a range of programming skills in Python to make use of these numerical methods in practice
  • Demonstrate that they have acquired the mathematical skills to use Fourier series to analyse periodic functions

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics please consult the School Handbook, at /mathematics-statistics/students/ug/module-choices-2000/

MT2507 Mathematical Modelling

Academic year

2026 to 2027 Semester 2

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 8

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 (weeks 2, 4, 6, 8, 11), Tue and Thu

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

Module coordinator

Prof D H Mackay

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

Module Staff

TBD

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

Module description

This module provides an introduction to a variety of techniques that are used throughout applied mathematics. It discusses how to translate physical problems into mathematics and covers such topics as differential equations, dynamics, numerical methods and Fourier series. It illustrates how these are used when solving problems. It is recommended that students in the Faculties of Arts and Divinity take an even number of the 15-credit 2000-level MT modules.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST PASS MT2503

Assessment pattern

2-hour Written Examination = 70%, Coursework = 30%

Re-assessment

2-hour Written Examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 hours of lectures (x 10 weeks), 1-hour tutorial (x 5 weeks), 1-hour examples class (x 5 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

  • Analyse mathematical models of real-world problems based on ordinary differential equations
  • Use numerical methods to solve problems associated with mathematical modelling
  • Apply a range of programming skills in Python to make use of these numerical methods in practice
  • Demonstrate that they have acquired the mathematical skills to use Fourier series to analyse periodic functions

Additional information from school

For guidance on module choice at 2000-level in Mathematics and Statistics see our Module choices at 1000 and 2000 level page.

Syllabus

  • Revision of ODEs: separable 1st order ODEs, integrating factors, homogeneous linear 2nd order ODEs with constant coefficients, inhomogeneous linear 2nd order ODEs with constant coefficients. Simple applications: radioactive decay, logistic ODE.  Nonlinear coupled ODEs: application, e.g., predator-prey models, etc., stationary states, linearization.
  • Phase plane analysis.
  • Dynamics: Newton’s laws, motion under constant gravitational force (1D, 2D), friction, use of total energy.
  • Numerical methods: applied to previous nonlinear ODEs, Newton-Raphson (1D, 2D) for calculating stationary states, solution of nonlinear ODEs with numerical methods to supplement phase plane analysis.
  • Fourier series: Use of 2D Laplace equation for potential in Cartesian coordinates as motivation, sine and cosine as a system of orthogonal functions, definition of Fourier Coefficients, examples of Fourier series.