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Teaching GuideTerm Higher Polytechnic University College |
| Grao en Enxeñaría Naval e Oceánica |
 Subjects |
| Mathematics 2 |
| Contents |
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| Identifying Data | 2016/17 | |||||||||||||
| Subject | Mathematics 2 | Code | 730G05005 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 2nd four-month period |
First | FB | 6 | ||||||||||
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| Topic | Sub-topic |
| Vector spaces | Euclidean spaces R^2 and R^3. Operations: sum, product by real numbers. Vector subspaces. Direct sum. Linear combination, span. Linear independence. System of generators. Basis and dimension. Theorem of the basis. Coordinates, change of coordinates. Applications to systems of linear equations. |
| Linear maps | Correspondences. Maps. Linear maps. Properties of linear maps. Matrix associated to a linear map. Applications to systems of linear equations. |
| Diagonalization of endomorphisms | Invariant subspaces. Eigenvalues and eigenvectors. Diagonalizable endomorphisms. |
| Integrals over paths | Paths in R^2 and R^3. Parametrizations. Path integrals of scalar functions. Line integrals of vector fields. Gradient vector fields. Green's Theorem. |
| Integrals over surfaces | Parametrized surfaces. Surface integrals. Rotational and divergence. Stokes's Theorem. Divergence Theorem. |
| Appendix: the free software program MAXIMA | Practical sessions with the free software program MAXIMA |
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