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: Propagation models for pollution.
3.1. Mathematical models concerning the air environment.
3.1.1. Basics.
3.1.2. Transport and diffusion models.
3.2. Mathematical models relating to the aquatic environment.
3.2.1. Model classification.
3.2.2. General models of adsorption and sedimentation.
3.2.3. Three-dimensional models.
3.2.4. Two-dimensional shallow water models.
3.2.5. One-dimensional models for rivers and canals.
3.2.6. Zero-dimensional models.
Topic 4: Control of environmental processes.
4.1. Formulations.
4.2. Realistic examples.
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.
Specific Competences:
-A1: Achieve basic knowledge in an area of Engineering / Applied Sciences, as a starting point for adequate mathematical modeling, both in well-established contexts and in new or little-known environments within broader and multidisciplinary contexts.
-A2: Model specific ingredients and make the appropriate simplifications in the model that facilitate its numerical treatment, maintaining the degree of precision, in accordance with previously established requirements.
-A5: Be able to validate and interpret the results obtained, comparing with visualizations, experimental measurements and / or functional requirements of the corresponding physical / engineering system.
-A6: Be able to extract, using different analytical techniques, both qualitative and quantitative information from the models.
Basic Competences:
-B1: Know how to apply the knowledge acquired and their ability to solve problems in new or little-known environments within broader contexts, including the ability to integrate into multidisciplinary R&D teams in the business environment.
-B2: Possess knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context, knowing how to translate industrial needs in terms of R + D + i projects in the field of Industrial Mathematics.
-B4: Know how to communicate the conclusions, together with the knowledge and ultimate reasons that support them, to specialized and non-specialized audiences in a clear and unambiguous way.
-B5: Possess the learning skills that allow them to continue studying in a way that will have to be largely self-directed or autonomous, and be able to successfully undertake doctoral studies.
-Problem solving:
The class is a combination of a magisterial session (the teacher will present in this type of classes the theoretical contents of the subject) and problem solving and / or exercises (in these working hours the teacher will solve problems in each of the topics and will introduce new methods of resolution not contained in the master classes from a practical point of view).
The student must also solve problems proposed by the teacher in order to apply the knowledge acquired.
- Master session:
The class is a combination of a magisterial session (the teacher will present in this type of classes the theoretical contents of the subject) and problem solving and / or exercises (in these working hours the teacher will solve problems in each of the topics and will introduce new methods of resolution not contained in the master classes from a practical point of view).
- Objective test:
There will be a final exam of the course.
-Master session: (Competences A1 A2 A5 A6 B2 B5 B1 B4)
Attendance and active participation in class will be taken into account. (25%)
-Solving problems: (Competences A2 A5 A6 B5 B1)
Individual theoretical exercises. (25%)
- Objective test: (Competencies B2 B1 B4) (50%)
CRITERIA FOR THE 1ST EVALUATION OPPORTUNITY:
1-Problem solving and / or exercises (50% of the grade):
a) Attendance and active participation in class.
b) individual theoretical exercises: Exercises and / or works that the teacher will propose 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
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The student is recommended to use online tutoring when solving the exercises.
UNIVERSITIES FROM WHICH IT IS TAUGHT: Universidade de Santiago, Universidade de Coruña
CREDITS: 6 ECTS credits
TEACHER / COORDINATOR: Miguel A. Vilar Rivas (miguel.vilar [at] usc.es (miguel[dot]vilar[at]usc[dot]es))
TEACHER 1: José Manuel Rodríguez Seijo (jose.rodriguez.seijo [at] udc.es (jose[dot]rodriguez[dot]seijo[at]udc[dot]es))
As it is a subject of an inter-university master's degree, teaching is virtual, so for scenarios 2 and 3 no adaptation is contemplated except for the place from where the training is given or received.
Saray Busto Ulloa
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- saray.busto.ulloa [at] usc.es
- Category
- Researcher: Ramón y Cajal