| Study programme competencies |
| Code | Study programme competences |
| B1 | Posuír e comprender coñecementos que acheguen unha base ou oportunidade de ser orixinais no desenvolvemento e/ou aplicación de ideas, a miúdo nun contexto de investigación |
| B2 | Que os estudantes saiban aplicar os coñecementos adquiridos e a súa capacidade de resolución de problemas en ámbitos novos ou pouco coñecidos dentro de contextos máis amplos (ou multidisciplinares) relacionados coa súa área de estudo |
| B3 | Que os estudantes sexan capaces de integrar coñecementos e enfrontarse á complexidade de formular xuízos a partir dunha información que, sendo incompleta ou limitada, inclúa reflexións sobre as responsabilidades sociais e éticas vinculadas á aplicación dos seus coñecementos e xuízos |
| B4 | Que os estudantes saiban comunicar as súas conclusións e os coñecementos e razóns últimas que as sustentan a públicos especializados e non especializados dun modo claro e sen ambigüidades. |
| B9 | Adquirir unha formación metodolóxica que garantice o desenvolvemento de proxectos de investigación (de carácter cuantitativo e/ou cualitativo) cunha finalidade estratéxica e contribúan a situarnos na vangarda do coñecemento. |
| C4 | Desenvolverse para o exercicio dunha cidadanía aberta, culta, crítica, comprometida, democrática e solidaria, capaz de analizar a realidade, diagnosticar problemas, formular e implantar solucións baseadas no coñecemento e orientadas ao ben común. |
| C6 | Valorar criticamente o coñecemento, a tecnoloxía e a información dispoñible para resolver os problemas cos que deben enfrontarse. |
| C7 | Asumir como profesional e cidadán a importancia da aprendizaxe ao longo da vida. |
| C8 | Valorar a importancia que ten a investigación, a innovación e o desenvolvemento tecnolóxico no avance socioeconómico e cultural da sociedade. |
| Learning aims | |||
| Subject competencies (Learning outcomes) | Study programme competences | ||
| Knowledge of elementary tensor calculus | BC1 BC2 BC3 BC4 BC9 |
CC4 CC6 CC7 CC8 |
|
| Ability to work with curves and surfaces and study their geometric properties: curvature, geodesics, ... | BC1 BC2 BC3 BC4 BC9 |
CC4 CC6 CC7 CC8 |
|
| Aplication of tensor calculus to the formulation of partial differential equations from Physics. | BC1 BC2 BC3 BC4 BC9 |
CC4 CC6 CC7 CC8 |
|
| Contents |
| Topic | Sub-topic |
| Curves | Parametrized curves. Regular curves. Arc length. Curvature. Torsion. Frenet trihedron. Famous curves. |
| Surfaces | Parametrized surfaces. Regular surfaces. Tangent plane. First fundamental form. Surface area. Second fundamental form. Gauss curvature and mean curvature. Ruled surfaces and minimal surfaces. Apendix: bilinear forms and quadratic forms |
| Tensors | Definition and properties. Einstein notation. Tensor fields. Operations with tensors. |
| Mathematics of continuum mechanics. Conservations laws | - Continuum cinematics - Gradient of strain tensor. Green-Saint Venant Strain tensor - Transformation of areas and volumes - Reynolds theorem of transport. - Mass conservation law. - Law of conservation of momentum - Thermodinamics. Law of conservation of energy - Control volumens and conservation laws |
| Partial differential equations | - Partial differential equations. Boundary conditions. - Constituive laws - Heat conduction. Fourier's law. Heat equation for solids. - Fluid mechanics. Derivation of some important equations in fluid mechanics. Equations for incompressible fluids. - Elastic solids. Cauchy Theorem. Stress and strain tensors. Principal components. Eigenvalues and eigenvectors. Partial differential equationspara for elastic solids. |
| Planning | |||
| Methodologies / tests | Ordinary class hours | Student’s personal work hours | Total hours |
| Seminar | 15 | 15 | 30 |
| Supervised projects | 0 | 3 | 3 |
| Objective test | 3.5 | 0 | 3.5 |
| Guest lecture / keynote speech | 30 | 45 | 75 |
| Personalized attention | 1 | 0 | 1 |
| (*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. | |||
| Methodologies |
| Methodologies | Description |
| Seminar | Technique of group work which purpose is the in-depth study of a subject. It involves discussion, participaction, edocuments elaboration and the conclussion reached by all the components of the seminar. |
| Supervised projects | Methodology designed to promote authonomous learning of the students, always under the teacher's guide. It is a technique based on the assumption by the students of the responsability of their learning. This learning technique is based in two basic elements: the authonomous learning and the continous monitoring of this learning by the teachers. |
| Objective test | Written test to asses the obtained competencies. It is an instruments of meassure, rigorously developed, that allows to evaluate knowledges, capacities, skills, performances, aptitudes, attitudes, etc. |
| Guest lecture / keynote speech | Oral presentation complemented with the use of audiovisual media and the introduction of some questions to the students, in order to transmit knowledge and provide learning |
| Personalized attention |
|
|
| Assessment | ||
| Methodologies | Description | Qualification |
| Supervised projects | Students who wish to, can choose a topic from among those proposed by the teachers of the subject. They will do a work on this subject to deepen their concepts and techniques, and that they will have to expose later. This work will be qualified and will allow to pass the subject. | 50 |
| Objective test | At the end of the course, these students that have not done the proposed works or that want to obtain a better qualification, will do a written exam in the data fixed by the school. | 50 |
| Assessment comments | ||
|
The works will be corrected and and attending to this corrections students will be qualified. If a student does not present the proposed work or if he wants to obtain a better qualifications he will be able to give up the obtained qualification and realize the final written exam |
||
| Sources of information |
| Basic |
Alexandre J. Chorin,Jerrold E. Marsden. (2000). A Mathematical Introduction to Fluid Mechanics. Texts in Applied Mathematic, Springer
M. Gurtin (1981). An introduction to continuum mechanics. Academic Press
Manfredo P. do Carmo (1995). Geometría diferencial de curvas y superficies. Alianza Universidad Textos
M. Gurtin, Eliot Fried, Lallit Anand (2010). The mechanics and thermodynamics of continua. Cambridge
José A. Pastor González, Mª Ángeles Fernández Cifre (2010). Un curso de geometría diferencial. Consejo Superior de Investigaciones Científicas
Rutherford Aris (1962). Vectors, tensors, and the basic equations of fluid mechanics.. Prentice-Hall |
|
|
|
| Complementary | |
|
|
| Recommendations | |
| Subjects that it is recommended to have taken before |
| Subjects that are recommended to be taken simultaneously |
| Subjects that continue the syllabus |
| Other comments | |