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Teaching GuideTerm Higher Polytechnic University College |
| Grao en Enxeñaría Naval e Oceánica |
 Subjects |
| Mathematics 1 |
| Contents |
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| Identifying Data | 2022/23 | |||||||||||||
| Subject | Mathematics 1 | Code | 730G05001 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 1st four-month period |
First | Basic training | 6 | ||||||||||
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| Topic | Sub-topic |
| The R^n space | - The complex plane. Operations with complex numbers. Polar form. - Vector structure: The linear spaces R^2 and R^3. Linear subspaces. Bases and dimension. Coordinates. Systems of linear equations. - Metric structure: Scalar product, norm and distance. - Topological structure: Topological classification of points and sets. Polar, cylindrical and spherical coordinates. |
| Linear maps | Maps. Linear maps. Basic properties of linear maps. Matrix associated to a linear map. Diagonalization of endomorphisms: invariant subspaces, eigenvalues and eigenvectors, diagonalizable endomorphisms. |
| Differential Calculus | Topology in R. Functions of one variable. Continuity. Smooth functions of one variable. Taylor polynomial. Parametrized curves in R^n. Reparametrizations. |
| Integral Calculus | Riemann sums. Integrable functions. Main theorems in integral calculus: Mean value theorem, Fundamental theorem and Barrow's rule. Computation of primitive functions. Polynomial interpolation. Numerical integration: Simpsons' rule. Computation of volumes. Length of curves and line integrals of scalar functions. |
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