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Teaching GuideTerm Polytechnic University Collage |
| Grao en Enxeñaría Electrónica Industrial e Automática |
 Subjects |
| Alxebra |
| Contents |
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| Identifying Data | 2015/16 | |||||||||||||
| Subject | Alxebra | Code | 770G01006 | |||||||||||
| 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 |
| Path Integral | Paths in Rn. Reparameterizations. Line integrals of scalar functions. Applications of the integrals of scalar functions. Integrals of vector fields. Gradient type functions. Green theorem. |
| Surface integral | Cross product. Sufaces in R3. Area of a surface. Integral of a scalar function. Oriented surfaces. Integral of vector fileds. Divergence. Gauss Theorem. Curl. Stokes Theorem. |
| Vector spaces | The vector space Rn. Operations: vector addition, scalar multiplication. Vector subspaces. Direct sum. Linear combination, linear span. Linear independence. Spaning set. Basis and dimension. Theorems about basis. Coordinates, change of coordinates. |
| Linear maps | Linear maps. Properties of the linear maps. Kernel and Image of a linear map. Operations with linear maps. Matrix associated to a linear map. |
| Diagonalization | Invariant subspaces. Eigenvalues and eigenvectors. Characteristic polynomial. Diagonalizable endomorphism. |
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