ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician, English
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Applied Mathematics
Areas: Applied Mathematics
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable
It presents the general methodology of mathematical modeling 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, deterministic and stochastic differential equations, partial differential equations, optimization, etc.
1. Tensor algebra and tensor analysis. (About 4 expositive hours)
2. The material point. (2 expositive h)
3. The harmonic oscillator. (4 expositive h)
4. Generalities about continuum mechanics. (4 expositive h)
5. Introduction to fluid mechanics. (4 expositive h)
6. Introduction to solid mechanics. (4 expositive h)
7. Heat transfer in solids. (2 expositive h)
Basic bibliography:
A. BERMÜDEZ DE CASTRO y 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:
N. BELLOMO, E. DE ANGELIS, M. DELITALA. Mathematical Modelling in Applied Sciences. SIMAI e-lecture notes ISSN
1970-4429.
A. BERMÚDEZ. Continuum Thermomechanics. Birkhäuser. Basel. 2005
J. BERRY, K. HOUSTON. Mathematical Modelling. Edward Arnold. London. 1995
J. CALDWELL and D. K.S. NG. Mathematical Modelling: Case Studies and Projects. Kluwer. Boston. 2004
D. EDWARDS, M. HAMSON. Guide to Mathematical Modelling. Industrial Press. New York. 2007
N. D. FOWKES and J. J. MAHONY. An Introduction to Mathematical Modelling. John Wiley and Sons. Chichester. 1994
R. ILNER. Mathematical Modelling. A Case Studies Approach. AMS. Providence. 2005
J.N. KAPUR. Mathematical Modelling. New Age International Publishers. New Delhi. 2005
M.S. KLAMKIN. Mathematical Modelling. SIAM. Philadelphia. 1987.
M. MESTERTON-GIBBONS. A Concrete approach to mathematical modelling. Addison-Wesley Publishing Company.
Redwood. 1989
G. F. SIMMONS, Ecuaciones Diferenciales, McGraw-Hill, 1993
E. VAN GROESEN, J. MOLENAAR. Continuum Modeling in the Physical Sciences. SIAM. Philadelphia. 2007
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. As an exercise, students should state and solve simple models of some real problems to be proposed. This task will attempt to encourage student participation in classes, especially in interactive ones.
The teachers will publish bulletins of problems in the course website. The notes elaborated by the teachers will also be available at the course website. To solve the models we can make use, if any, of the MATLAB package or of computer programs written in any another programming language
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 non-releasing controls and / or the completion of questionnaires. The final exam will be face-to-face.
The continuous evaluation will be kept for the second opportunity.
The evaluation of the competences will be carried out in the final examination together with the controls that are considered in the continuous evaluation. More specifically:
-In the final examination all the competences developed in the subject will be evaluated.
-In the controls, 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 26, interactive seminar 26, tutorials 2.
Individual study or in group 50
Problems solving 25
Programming / testing and other work in the computer 5 Recommended reading, library, or similar activities 10
TOTAL VOLUME OF WORK = 54 +90 = 144 hours
1.To try to understand what is studied. To this respect, students should be able to solve by themselves the exercises proposed in class and in the worksheets.
2.To review the basic concepts and methods of Algebra and Mathematical Analysis. In particular, to review the analytical methods of solving ordinary differential equations.
3.To make use of tutorials.
4.To appeal to bibliographical references.
5.To study regularly.
Contingency plan to adapt this guide to the “Bases” document which develops a safe face-to-face teaching environment on the 2020-2021 academic year (approved by the USC Government Council in a regular session held on June 19, 2020).
1. The teaching methodology and the evaluation system described above would correspond to Scenario 1: adapted normality (without restrictions on physical attendance) following the USC Guidelines for the development of safe classroom teaching.
2. If the scenario were Scenario 2: distancing (partial restrictions on physical presence), both headings should adapt to said Guidelines: both the expository and interactive classes will be taught preferably from the classroom. They can also be carried out virtually, depending on the circumstances. The tutorials will be telematic.
The evaluation system would not change except for the final exam that would have to be done electronically using the Virtual Campus and the Teams platform.
3. If the scenario were Scenario 3, both expository and interactive teaching will be completely telematic with synchronous mechanisms, through the Microsoft Teams application. The scheduling of tutorials will be done electronically.
The evaluation system would not change except for the final exam that would have to be done electronically using the Virtual Campus and the Teams platform.
Alfredo Bermudez De Castro Lopez-Varela
Coordinador/a- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813192
- alfredo.bermudez [at] usc.es
- Category
- Professor: University Professor
Rafael Muñoz Sola
- Department
- Applied Mathematics
- Area
- Applied Mathematics
- Phone
- 881813182
- rafael.munoz [at] usc.es
- Category
- Professor: University Lecturer
| Monday | |||
|---|---|---|---|
| 16:00-17:00 | Grupo /CLE_01 | Spanish | Classroom 07 |
| Tuesday | |||
| 18:00-19:00 | Grupo /CLIS_01 | Spanish | Ramón María Aller Ulloa Main Hall |
| 19:00-20:00 | Grupo /CLIS_02 | Spanish | Ramón María Aller Ulloa Main Hall |
| Wednesday | |||
| 16:00-17:00 | Grupo /CLE_01 | Spanish | Classroom 07 |
| Thursday | |||
| 18:00-19:00 | Grupo /CLIS_01 | Spanish | Ramón María Aller Ulloa Main Hall |
| 19:00-20:00 | Grupo /CLIS_02 | Spanish | Ramón María Aller Ulloa Main Hall |
| 01.15.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 02 |
| 01.15.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 03 |
| 01.15.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 01.15.2021 16:00-20:00 | Grupo /CLE_01 | Ramón María Aller Ulloa Main Hall |
| 06.21.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |