Module Code - Title:

MS4627 - MATHEMATICS OF NATURAL PHENOMENA

Year Last Offered:

2025/6

Hours Per Week:

Lecture

2

Lab

1

Tutorial

1

Other

0

Private

7

Credits

6

Grading Type:

N

Prerequisite Modules:

MA4607

MS4404

Rationale and Purpose of the Module:

To introduce the concepts of modelling natural phenomena (biological and geophysical systems)

Syllabus:

Evolutionary game theory: populations, strategies, evolutionary success Dimensional analysis: scaling, similarity. Fractals Waves: frequency, wave vector, phase velocity, group velocity Stability: steady solution of PDEs and small perturbations, harmonic disturbances, normal modes Boundary layer theory: flow near a plate, the Blasius problem

Learning Outcomes:

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

1. Understand the basic concepts of the evolution game theory (strategy, payoff matrix, fitness, population, dynamics equations, evolutionary stable population). Be aple to apply them to two- and three-strategy games, including the stability analysis of such. 2. Understand basic concepts associated with fractals, such as self-similarity and fractal dimension. 3. Understand the concept of dimensional analysis and be able to apply it to physical problems. 4. Understand the basic concepts of wave theory (amplitude, frequency, wavevector, phase velocity, group velocity), and be able to apply them to common waves types, such as electromagnetic and water waves. 5. Understand the basic ideas of hydrodynamic stability associated with harmonic disturbances and normal modes. 6. Understand the concept of a boundary layer associated with a small parameter in an ODE. Applications to the Blasius problem (flow near a plate).

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:

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

Prime Texts:

J.W. Weibull (1995) Evolutionary game theory , MIT Press

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

P.G. Drazin, W.H. Reid (1981) Hydrodynamic stability , Cambridge University Press

Other Relevant Texts:

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

Michael.Vynnycky@ul.ie