Module Code - Title:

MS4408 - MATHEMATICAL MODELLING

Year Last Offered:

2026/7

Hours Per Week:

Lecture

2

Lab

0

Tutorial

1

Other

0

Private

6

Credits

6

Grading Type:

N

Prerequisite Modules:

MS4403

MS4404

MS4407

Rationale and Purpose of the Module:

To learn the techniques of advanced mathematical modeling or real phenomena with examples from the physical, biological, chemical and financial sciences.

Syllabus:

Review of modelling skills, applications from: classical models (e.g. heat transfer), continuum models , financial models, statistical models, mathematical biology, advanced models.

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

1. Demonstrate an understanding of the concept of a mathematical model and the procedure by which such models are formulated. 2. Demonstrate a basic knowledge of conservation laws and develop classical models on this basis. 3. Demonstrate an understanding of dimensional analysis and the process of non-dimensionalisation, scaling and asymptotic simplification of systems of equations. 4. Demonstrate an understanding of basic physical modelling concepts such as the law of mass-action, advection-diffusion, quasi-steady approximations, boundary layers, similarity solutions, stability of solutions, oscillations. 5. Solve generic problems arising in heat and fluid transport, chemical kinetics, porous flow, biology.

Affective (Attitudes and Values)

N/A

Psychomotor (Physical Skills)

N/A

How the Module will be Taught and what will be the Learning Experiences of the Students:

Normal mathematics lectures. Students will have homework (not for credit), a mid-term text worth 5%, 5% for participation in tutorial problem solving sessions and a final exam worth 90%.

Prime Texts:

A.B. Tayler (1986) Mathematical models in applied mechanics , OUP

S. Howison (2005) Practical applied mathematics , CUP

A.C. Fowler (1997) Mathematical models in the applied sciences , CUP

J. David Logan (1996) Applied mathematics , Wiley

N.D. Fowles & J.J. Mahony (1994) An introduction to mathematical modelling , Wiley

C.C. Lin & L.A. Segel (1988) Mathematics applied to problems in the natural sciences , SIAM

Other Relevant Texts:

G. Strang (1986) Introduction to applied mathematics , Wellesley-Cambridge

J. Keener (1995) Principles of applied mathematics , Addison-Wesley

Programme(s) in which this Module is Offered:

BACHELOR OF SCIENCE IN ECONOMICS AND MATHEMATICAL SCIENCES

BACHELOR OF SCIENCE IN ECONOMICS AND MATHEMATICS

BACHELOR OF SCIENCE IN FINANCIAL MATHEMATICS

BACHELOR OF SCIENCE IN MATHEMATICAL SCIENCES

BACHELOR OF SCIENCE IN MATHEMATICS AND PHYSICS

MASTER OF SCIENCE IN MATHEMATICAL MODELLING

Semester(s) Module is Offered:

Module Leader:

Stephen.OBrien@ul.ie