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Teaching GuideTerm Higher Polytechnic University College |
| Mestrado Universitario en Enxeñaría Naval e Oceánica (plan 2012) |
 Subjects |
| Advanced mathematics |
| Contents |
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| Identifying Data | 2017/18 | |||||||||||||
| Subject | Advanced mathematics | Code | 730496015 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Official Master's Degree | 1st four-month period |
First | Optativa | 4.5 | ||||||||||
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| 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. |
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