Duration
20h Th, 20h Pr
Number of credits
| Master in geography : climatology (120 ECTS) | 3 crédits | |||
| Master in geography, global change (120 ECTS) | 3 crédits | |||
| Master in oceanography (120 ECTS) | 4 crédits |
Lecturer
Language(s) of instruction
English language
Organisation and examination
Teaching in the first semester, review in January
Schedule
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 practical examples using R.
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) Interpolation: unidimensional and multi-dimensional interpolation, linear estimation, objective analysis,
4) Analysis of time series: generalities, Fourier series and transform, filtering,
5) Dynamical modelling with one equation: the malthusian growth model, Verhulst logistic model, equilibrium and stability, linear perturbation analysis, solution of basic ordinary differential equations,
6) 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). R exercices will be organized.
7) Modelling with partial differential equations: continuity equations, adevctionn-diffusion eqaution in 3D and 1D , spectral window,
Learning outcomes of the learning unit
Introduction to the basics of mathematical modelling.
Prerequisite knowledge and skills
Calculus and matrix algebra.
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.
Organisational adjustments related to the current health context
Recommended or required readings
Slides of the lectures will be available.
Assessment methods and criteria
Below you will find information on the evaluation methods planned for in-person and remote exams as well as those planned for hybrid sessions. Depending on how the health crisis evolves, the chosen method will be communicated to you no later than one month before the start of the exam session.
A written test in january (first session).
A written test in August/September (retake).
This written test will be organized on line via eCampus because the sanitary conditions do not allow a written examination in presence.
Work placement(s)
Organizational remarks
First quadrimestre
Contacts
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).