Module Code - Title:

MS4408 - MATHEMATICAL MODELLING

Year Last Offered:

2025/6

Hours Per Week:

Lecture

2

Lab

0

Tutorial

1

Other

0

Private

6

Credits

6

Grading Type:

N

Prerequisite Modules:

MS4404

MS4407

MS4403

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%.

Research Findings Incorporated in to the Syllabus (If Relevant):

Prime Texts:

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

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

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

J. David Logan (1996) Applied mathematics , Wiley

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

S. Howison (2005) Practical applied mathematics , CUP

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:

Semester(s) Module is Offered:

Module Leader:

Stephen.OBrien@ul.ie