Mathematical Modelling

It presents the general methodology of mathematical modelling and specific examples related to different areas of applied sciences and engineering. The program can travel along different topics related to models of discrete and continuous mathematics: numerical equations, difference equations, differential equations, optimization, etc.

1. Tensor algebra and tensor analysis. (8 expositive hours)
2. The material point. (4 expositive h)
3. Basic concepts about continuum mechanics. (7 expositive h)
4. Introduction to fluid mechanics. (10 expositive h)
5. Introduction to solid mechanics. (6 expositive h)

Basic bibliography:

A. BERMÚDEZ DE CASTRO, R. MUÑOZ SOLA. Modelización Matemática. Departamento de Matemática Aplicada. USC.
M. E. GURTIN. An Introduction to Continuum Mechanics. Academic Press. New York, 1981.
O. LÓPEZ POUSO. "An Introduction to Continuum Mechanics" de M. E. Gurtin. Ejercicios resueltos (capítulos I-VI).
Publicacións docentes do Departamento de Matemática Aplicada, USC. 2002.

Complementary bibliography:

A. BERMÚDEZ. Continuum Thermomechanics. Birkhäuser. Basel. 2005. (Available online.)
J. CALDWELL, D. K.S. NG. Mathematical Modelling : Case Studies and Projects. Kluwer. Boston. 2004. (Available online.)
A. J. CHORIN, J. E. MARSDEN - A Mathematical introduction to fluid dynamics. Springer-Verlag. New York. 1993. (Available online.)
M. MESTERTON-GIBBONS. A Concrete approach to mathematical modelling. Addison-Wesley Publishing Company. Redwood. 1989.

GENERAL COMPETENCES
CG1 – To know the more important concepts, methods, and results of the different branches of Mathematics, together with some historical perspective of its development.
CG2 – To gather and to interpret data, information, and relevant results, to obtain conclusions and to write reasoned reports in scientific or technological problems (or other field problems) that require the use of mathematical tools
CG4 – To communicate, by writing and in oral form, knowledges, procedures, results, and ideas in Mathematics both to a specialized public and to a non- specialized one.
CG5 – To study and learn in autonomous form, with organization of time and resources, new knowledge, and techniques in any scientific or technological discipline.

TRANSVERSAL COMPETENCES
CT1 – To use bibliography and research tools of general bibliographic resources as well as specific of Mathematics ones, including the access by Internet.
CT2 – To manage, in an optimal way, the time of work and to organize the available resources, establishing priorities, alternative ways and identifying logical errors in decision-making.
CT3 – To check or to reject in a reasoned form the arguments of other people.
CT4 – To work in interdisciplinary teams, contributing with order, abstraction, and logical reasoning.
CT5 – To read scientific texts both in mother tongue and in others of importance in the scientific field, especially English.

SPECIFIC COMPETENCES
CE1 – To understand and to use the mathematical language.
CE4 – To identify errors in wrong reasonings by proposing proofs or counterexamples.
CE5 – To assimilate the definition of a new mathematical object, to relate it with others already known, and to be able to use it in different contexts.
CE6 – To be able to abstract the properties and substantial facts of a problem, distinguishing them of those purely occasional or circumstantial ones.
CE7 – To propose, analyze, validate, and interpret models of simple real situations, using the mathematical tools more adapted to the pursued goals.
CE8 – To schedule and execute algorithms and mathematical methods to solve problems in the academic technician, financial or social fields.
CE9 – To use computer applications of statistical or numerical analysis and symbolic calculation, graphic visualization, optimization, and scientific software, in general, to make mathematical experimentation and to solve problems

Expositive, interactive seminar classes and face-to-face tutorials. We will encourage students to participate in class, especially in the interactive ones. In the course created in the Virtual Campus (Moodle) there will be available the notes elaborated by the teachers and the collection of problems. To solve the models we can make use, if any, of the MATLAB package.

The overall rating is the highest of the following marks:
-The final exam grades.
-The weighted average of the final exam (70%) and the continuous assessment (30%).
The continuous evaluation will consist of one non-releasing control.

The continuous evaluation will be kept for the second opportunity.

The final examination and the continuous evaluation control will be the same for all the groups.

The evaluation of the competences, both at the first and the second opportunity, will be carried out in the final examination and in the continuous evaluation. More specifically:
-In the final examination all the competences developed in the subject will be evaluated.
-In the continuous evaluation, the competences CG4, CE1, CE4, CE6, CE7 and CE8.


The qualification of an assessment opportunity in which the student does not present or does not pass the established aims will be fail. If the student does not carry out any evaluable academic activity according to the established in the program, he/she will be marked as “NON PRESENTADO.”

In order to obtain a “Matrícula of Honor”, the numerical final note and the continuous assessment will be considered.

For fraudulent cases, either carrying out exercises or exams, we will apply what is collected in the "Norm of evaluation of the academic performance for students and revision of qualifications".

Hours: expositive 35, interactive seminar 21, tutorials 2.
Individual study or in group 52
Problems solving 30
Recommended reading, library, or similar activities 10

TOTAL VOLUME OF WORK = 58 +92 = 150 hours

1.To attend class.
2.To self work both with the class exercises and the problem worksheets
3.To review the basic concepts and methods of Algebra and Mathematical Analysis.
4.To make use of tutorials.
5.To appeal to the bibliography.
6.To study regularly.