| Study programme competencies |
| Code | Study programme competences |
| B1 | CB06 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 | CB07 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 |
| B4 | CB09 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. |
| B5 | CB10 Que os estudantes posúan as habilidades de aprendizaxe que lles permitan continuar estudando dun modo que haberá de ser en boa medida autodirixido ou autónomo. |
| B6 | G01 Capacidade para resolver problemas complexos e para tomar decisións con responsabilidade sobre a base dos coñecementos científicos e tecnolóxicos adquiridos en materias básicas e tecnolóxicas aplicables na enxeñaría naval e oceánica, e en métodos de xestión. |
| Learning aims | |||
| Learning outcomes | Study programme competences | ||
| Ability to work with curves and surfaces and study their geometric properties: curvature, geodesics, ... | BC1 BC2 BC4 BC5 BJ1 |
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| Aplication of tensor calculus to the formulation of partial differential equations from Physics. | BC1 BC2 BC5 |
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| Knowledge of elementary tensor calculus | BC1 BC2 |
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| Capability to face typical problems in the context of naval engineering using basic differential geometry of curves and surfaces. | BC1 BC5 BJ1 |
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| Contents |
| Topic | Sub-topic |
| Os seguintes temas desenvolven os contidos establecidos na ficha da Memoria de Verificación, que son: | XEOMETRÍA DIFERENCIAL E TENSORES: Curvas: - Triedro de Frenet.- Recta tanxente, normal e binormal.- Curvatura e torsión. Superficies: - Curvatura de Gauss e curvatura media. - Xeometría intrínseca: xeodésicas. Tensores. SERIES DE FOURIER: - Funcións ortogonais. -Series de Fourier. - Series de Fourier de cosenos e senos. ECUACIÓNS DIFERENCIAIS EN DERIVADAS PARCIAIS: -Ecuacións en derivadas parciais clásicas e problemas de valor na fronteira. - Resolución analítica. Resolución numérica: método de elementos finitos. |
| 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. Tensor fields. The metric tensor. Second fundamental form. Christoffel symbols. Gauss curvature and mean curvature. Ruled surfaces and minimal surfaces. Appendix 1: Einstein notation. Appendix 2: bilinear forms and quadratic forms. |
| 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 - 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 | Competencies | Ordinary class hours | Student’s personal work hours | Total hours |
| Guest lecture / keynote speech | B1 B2 B5 B6 | 24 | 36 | 60 |
| Problem solving | B1 B2 B4 B5 B6 | 12 | 12 | 24 |
| Supervised projects | B2 B4 B5 B6 | 0 | 24 | 24 |
| Objective test | B1 B2 B4 B5 B6 | 3.5 | 0 | 3.5 |
| 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 |
| 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 |
| Problem solving | 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. |
| Personalized attention |
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| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Objective test | B1 B2 B4 B5 B6 | 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 |
| Supervised projects | B2 B4 B5 B6 | 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 |
| Assessment comments | |||
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The works will be corrected and attending to this corrections students will be qualified. If a student does not present the proposed work or if he/she wants to obtain a better qualifications, he/she will be able to give up the obtained qualification and do the final exam in the 1st or the 2nd opportunity. |
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| 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 |
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| Complementary | |
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| 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 | |
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In order to get a sustainable neighbourhood and attain the aim of action number 5: “Docencia e investigación saudábel e sustentábel ambiental e social” of the "Plan de Acción Green Campus Ferrol", the homework of this course will attend to the following: • Preferably, virtual homework will be used, when printing is not required. • In the case that paper is needed, then: - No plastic materials will be used. - Printing will be done both sides. - Recycled paper will be used as possible. In general, a sustainable use of natural resources will be done. Moreover, ethic principles related to sustainability will be followed. |