| Mestrado Universitario en Enxeñaría Naval e Oceánica (plan 2012) |
 Subjects |
| Ampliación de matemáticas |
| Contents |
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| Identifying Data | 2014/15 | |||||||||||||
| Subject | Ampliación de matemáticas | 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 |
| 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. |
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