2023-2024 / OCEA0014-1

# Mathematical analysis and modelling methods applied to the environment

20h Th, 20h Pr

### Number of credits

 Master in oceanography (120 ECTS) 4 crédits

English language

### Organisation and examination

Teaching in the first semester, review in January

### Units courses prerequisite and corequisite

Prerequisite or corequisite units are presented within each program

### Learning unit contents

Mathematical basic concepts and tools applied to the analysis and modeling of physical, biological and chemical aspects of the environment. in particular, a focus is put on theoritical and mathematical ecology with a lot of practical examples.

The course will involve the follwoing chapters:

1) Concepts and tools of mathematical analysis: revision of basic mathematics: function, limit and asymtotic behavior, derivative function (simple, composite and material, taylor expansion), primitive and integration, basics of modelling (mass balance equation), (moving) averaging of continuous function, ..Remediation exercices will be organized.

2) Dimensional analysis: dimensions, principle of dimensional homogeneity, characteristic length and time scales. Dimensionnal analysis, Pi theorem, systematic determination of dimensionless products, ..

3) Dynamical modelling with one equation: the malthusian growth model, Verhulst logistic model, equilibrium and stability, linear perturbation analysis, solution of basic ordinary differential equations,

4) Dynamic modelling with interactions: modelling of biochemical transformation, composed reactions, prey-preadtor, species competition, serach for steatdy state solution, space phase analysis, and analyse the stability (linear pertrubation, determination of the Jacobian matrix).

### Learning outcomes of the learning unit

Introduction to the basics of mathematical modelling and data analysis.

### Prerequisite knowledge and skills

Calculus and matrix algebra, basic differential equations, solving linear systems, ...

Refresher exercises in mathematics are organized.

### Planned learning activities and teaching methods

Lectures introducing the theoretical aspects + applications and exemples.

### Mode of delivery (face to face, distance learning, hybrid learning)

Face-to-face learning.

Slides of the lectures and exercices are available on eCampus.

Exam(s) in session

Any session

- In-person

written exam ( open-ended questions )

A written test in january (first session). The stduent has to be able to define the theoritical concepts seen during the lecture and to use the mathematical methods for answering practical examples and to interpret the results of the analysis. Questions will be similar to those seen during the theoritical and practical sessions.

A written test in August/September (retake) similar to that in January.

The examination will be organized only in person.

### Contacts

Prof. Marilaure Grégoire

Département d'Astrophysique, Géophysique et Océanographie

MAST-FOCUS research group

B5a Sart-Tilman

mgregoire@uliege.be

### Items online

Theory and applications
Lecture notes (in French).