ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 102 Hours of tutorials: 6 Expository Class: 18 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary subject Master’s Degree RD 1393/2007 - 822/2021
Departments: Applied Mathematics, External department linked to the degrees
Areas: Applied Mathematics, Área externa M.U en Matemática Industrial
Center Faculty of Mathematics
Call: Second Semester
Teaching: With teaching
Enrolment: Enrollable | 1st year (Yes)
- Know the role of mathematical models in the study of environmental sciences.
- Know some models related to the description of biological communities.
- Know some models related to the spread of pollution.
Topic 1: Introduction.
1.1. Modeling process.
1.2. Mathematical model.
1.3. Numerical simulation.
1.4. Types of models
Topic 2: The first steps: Models of biological communities.
2.1. Communities of one specie.
2.2. Communities of two species.
2.3. Population dynamics models structured by age.
Topic 3: Mathematical models in geophysics: introduction to fluids.
3.1 Basic concepts. The Euler and Navier-Stokes equations.
3.2 Adimensional numbers.
3.3 Incompressible flows. Boussinesq approximation for natural convection problemes.
3.4 Selection of models and numerical methods.
Topic 4: Transport and diffusion models. Polution.
4.1 Transport and diffusion.
4.2 Phenomena involved in polution studies.
4.3 Some control polution problems.
Topic 5: Shallow water models.
5.1 Gravitational flow with free surface.
5.2 The Saint-Venant equations.
5.3 Erosion and sediment transport.
Topic 6: Water polution.
6.1 Adsorption and absortion.
6.2 Simplified polution models.
Topic 7: Alternative shallow water models.
7.1 Models for dispersive flows.
7.2 Multilayer models.
Topic 8: Further mathematical models in environmental engineering.
8.1 Subsurface flows. Richards equation.
8.2 GPR model for continuum mechanics.
Basic:
C.R. Hadlock, Mathematical modeling in the environment, Mathematical Association of America, 1998.
N. Hritonenko – Y. Yatsenko, Mathematical modeling in economics, ecology and the environment, Kluwer Academic Publishers, 1999.
J. Pedlosky, Geophysical fluid dynamics, Springer Verlag, 1987.
Complementary:
S.C. Chapra, Surface water-quality modelling, WCB/McGraw Hill, 1997.
P.L. Lions, Mathematical topics in fluid mechanics. Vol. 2: Compressible models, Clarendon Press, 1998.
G.I. Marchuk, Mathematical models in environmental problems, North-Holland, 1986.
J. D. Murray, Mathematical Biology. Springer-Verlag, 1993.
J.C. Nihoul, Modelling of marine systems, Elsevier, 1975.
L. Tartar, Partial differential equation models in oceanography, Carnegie Mellon Univ., 1999.
R.K. Zeytounian, Meteorological fluid dynamics, Springer Verlag, 1991.
Basic:
CG4: To have the ability to communicate the findings to specialist and non-specialist
audiences in a clear and unambiguous way.
CG5: To have the appropriate learning skills to enable them to continue studying in a
way that will be largely self-directed or autonomous, and also to be able to
successfully undertake doctoral studies.
Specific:
CE1: To acquire a basic knowledge in an area of Engineering / Applied Science, as a
starting point for an adequate mathematical modelling, using well-established
contexts or in new or unfamiliar environments within broader and multidisciplinary
contexts.
CE4: To be able to select a set of numerical techniques, languages and computer tools,
suitable for solving a mathematical model.
CE7: To know how to model complex elements and systems or in poorly established
fields, which lead to well-posed/formulated problems.
The class is a combination of master sessions (where the teacher will present the
theoretical contents of the subject) and problems and/or exercises solving sessions (in these
hours the teacher will solve problems for the different topics and will introduce new
mathematical approaches from a practical point of view).
The copetences related to this teaching methodology are: CG4, CG5, CE1, CE4, CE7
The student will also be asked to solve some problems proposed by the teacher in order to apply the acquired knowledge.
The copetences related to this teaching methodology are: CE1, CE4, CE7.
CRITERIA FOR THE 1ST EVALUATION OPPORTUNITY:
1-Problem solving and / or exercises (50% of the grade):
a) Attendance and active participation in class.
b) Exercises and / or works that will be proposed in the classroom.
2-Final exam of the course (50% of the grade).
CRITERIA FOR THE 2nd EVALUATION OPPORTUNITY:
The same as for the 1st evaluation opportunity
Problem solving: 28 HP 45 HNP 73 T
Master sessions: 28 HP 45 HNP 73 T
Final exam: 4 HP 0 HNP 4 T
The student is recommended to use online tutoring for any doubt related to this subject.
UNIVERSITIES FROM WHICH IT IS TAUGHT: Universidade de Santiago, Universidade da Coruña
CREDITS: 6 ECTS credits
TEACHER / COORDINATOR: José Manuel Rodríguez Seijo (jose.rodriguez.seijo [at] udc.es (jose[dot]rodriguez[dot]seijo[at]udc[dot]es))
TEACHER: Saray Busto Ulloa (saray.busto.ulloa [at] usc.es (saray[dot]busto[dot]ulloa[at]usc[dot]es))
Saray Busto Ulloa
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- saray.busto.ulloa [at] usc.es
- Category
- Researcher: Ramón y Cajal
| Thursday | |||
|---|---|---|---|
| 16:30-19:30 | Grupo /CLE_01 | Spanish | Computer room 5 |