| Study programme competencies |
| Code | Study programme competences |
| A1 | FB1 Capacidade para a resolución dos problemas matemáticos que poidan formularse na enxeñaría. Aptitude para aplicar os coñecementos sobre: álxebra lineal; xeometría; xeometría diferencial; cálculo diferencial e integral; ecuacións diferenciais e en derivadas parciais; métodos numéricos; algorítmica numérica; estatística e optimización. |
| B1 | CB1 Que os estudantes demostren posuír e comprender coñecementos nunha área de estudo que parte da base da educación secundaria xeral e adoita encontrarse a un nivel que, aínda que se apoia en libros de texto avanzados, inclúe tamén algúns aspectos que implican coñecementos procedentes da vangarda do seu campo de estudo |
| B2 | CB2 Que os estudantes saiban aplicar os seus coñecementos ao seu traballo ou vocación dunha forma profesional e posúan as competencias que adoitan demostrarse por medio da elaboración e defensa de argumentos e a resolución de problemas dentro da súa área de estudo |
| B3 | CB3 Que os estudantes teñan a capacidade de reunir e interpretar datos relevantes (normalmente dentro da súa área de estudo) para emitiren xuízos que inclúan unha reflexión sobre temas relevantes de índole social, científica ou ética |
| B5 | CB5 Que os estudantes desenvolvan aquelas habilidades de aprendizaxe necesarias para emprenderen estudos posteriores cun alto grao de autonomía |
| B7 | B5 Ser capaz de realizar unha análise crítica, avaliación e síntese de ideas novas e complexas |
| C1 | C3 Utilizar as ferramentas básicas das tecnoloxías da información e as comunicacións (TIC) necesarias para o exercicio da súa profesión e para a aprendizaxe ao longo da súa vida. |
| C4 | C6 Valorar criticamente o coñecemento, a tecnoloxía e a información dispoñible para resolver os problemas cos que deben enfrontarse. |
| C5 | C7 Asumir como profesional e cidadán a importancia da aprendizaxe ao longo da vida. |
| Learning aims | |||
| Learning outcomes | Study programme competences | ||
| Abilities in differential and integral calculus. | A1 |
B1 B2 B3 B5 B7 |
C1 C4 C5 |
| Being able to solve mathematical problems with applications in engineering. Abilities in geometry and differential geometry | A1 |
B1 B2 B3 B5 B7 |
C1 C4 C5 |
| Contents |
| Topic | Sub-topic |
| The space R^n | The vector space R^n. Scalar product: norms and distances. Classification of points and sets. Topology of R^n: bounded set, extrema. Coordinates systems: polar, cylindrical and spherical coordinates. |
| Functions of several variables | Scalar and vector functions. Level sets. Continuity. Continuity in compact sets. |
| Differenciation of funcions of several variables and applications | Directional derivative. Partial derivatives: properties and practical computing. Differential map of a function. Gradient, relation with partial derivatives. Relation between the differential map and partial derivatives: jacobian matrix. Higher order partial derivatives. Introduction to vector calculus. Taylor theorem for scalar functions. Critical points. Classification. Hessian matrix. Conditioned extremes: dimension reduction, Lagrange multipliers method. Implicit function theorem and inverse function theorem. |
| Integration of funcions of one and several variables | Riemann sums. Integrable functions. Integral Calculus Theorems: Mean Value Theorem, Fundamental Theorem and Barrow's rule. Primitive Calculus. Polinomial interpolation. Numerical integration. Compound Simpson's Rule. Application of integral calculus to computing arc lengths, volumes of revolution and surface areas of revolution. Double integrals. Triple integrals. Variable change in double and triple integrals. Application of integrals: calculation of areas and volumes. |
| Complex numbers | The field of complex numbers. Operations: sum, produt. Module and argument. Polar form. Operating in polar form. |
| Planning | ||||
| Methodologies / tests | Competencies | Ordinary class hours | Student’s personal work hours | Total hours |
| Guest lecture / keynote speech | A1 B2 B3 B5 B7 C4 C5 | 30 | 45 | 75 |
| Problem solving | A1 B1 B2 B3 B5 B7 C5 C4 | 26 | 39 | 65 |
| Mixed objective/subjective test | A1 B1 B2 B3 B5 B7 C1 C4 C5 | 6 | 0 | 6 |
| Personalized attention | 4 | 0 | 4 | |
| (*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. | ||||
| Methodologies |
| Methodologies | Description |
| Guest lecture / keynote speech | The course will be developed during the regular classes where the professor will explain the main concepts and results of the subject. |
| Problem solving | This classes are organiized in such a way that we practice how to solve the proposed problems. |
| Mixed objective/subjective test | Three exams will be carried out during the course. The first one will be a partial exam where only some of the chapters will be considered. A final exam will be done at the end of the semester. Furthermore a computer exam will be carried out. |
| Personalized attention |
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| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Problem solving | A1 B1 B2 B3 B5 B7 C5 C4 | After the completion of a thematic block, small collections of representative exercises will be proposed for evaluation. | 10 |
| Mixed objective/subjective test | A1 B1 B2 B3 B5 B7 C1 C4 C5 | These consist on written exams to assess the knowledge of the course by the students. The exames will be divided into 2 parts and the final qualification will be the addition of the qualification obtained in each of them. 1) The first one will be done during the teaching period by means of a partial exam. It will likely involve contents of chapters 1, 2, 3 and 4. Students passing this exam, will not need to repeat the corresponding questions in the final exams. Otherwise, this part will be recoverable in the final exams. 2) The final exam will be carried out in the period of final exams. It will be include contents of the second part of the subject and a second chance to pass the first part. In case of passing any of these two parts, either in the partial or in the final exam of january, the qualification is retained for the present course until the exam of the second oportunity. |
90 |
| Assessment comments | |||
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<p>Students with recognition of part-time dedication and academic exemption from attendance will be graded under the same conditions than other students, as explained above.</p>
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| Sources of information |
| Basic |
García, A. et al. (2007). Cálculo I. Teoría y Problemas de Análisis Matemático en Una Variable. Madrid. Clagsa
García, A. et al. (2007). Cálculo II. Teoría y Problemas de Análisis Matemático en Varias Variables. Madrid. Clagsa
Burgos Román, Juan de (2007). Cálculo infinitesimal de una variable. Madrid. McGraw-Hill
Soler, M., Bronte, R., Marchante, L. (1992). Cálculo infinitesimal e integral. Madrid
García Castro, F., Gutiérrez Gómez, A. (1990-1992). Cálculo Infinitesimal. I-1,2. Pirámide. Madrid
Tébar Flores, E. (1977). Cálculo Infinitesimal. I-II. Madrid. Tébar Flores
Coquillat, F (1997). Cálculo Integral. Madrid. Tebar Flores
Spiegel, M. R. (1991). Cálculo Superior. Madrid. McGraw-Hill
Marsden, J., Tromba, A. (2010). Cálculo vectorial. ADDISON WESLEY
Larson, R., Hostetler, R., Edwards, B. (2013). Calculus. . Brooks Cole
Salas, L., Hille, E., Etgen, G. (2003). Calculus. vol I-II. Madrid. Reverté
De Diego, B. (1991). Ejercicios de Análisis: Cálculo diferencial e intergral (primer curso de escuelas técnicas superiores y facultades de ciencias). Madrid. Deimos
Varios (1990). Problemas de Cálculo Infinitesimal. Madrid. R.A.E.C. |
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| Complementary | |
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There are many interesting webpages that can help with this subject, here we cite just a few:
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| Recommendations | ||||
| Subjects that it is recommended to have taken before |
| Subjects that are recommended to be taken simultaneously |
| Subjects that continue the syllabus | ||||
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| Other comments | |
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In order to get a sustainable neighbourhood and attain the aim of action number 5: “Docencia e investigación saudábel e sustentábel ambiental e social” of the "Plan de Acción Green Campus Ferrol", the homework of this course will attend to the following: • Preferably, virtual homework will be used, when printing is not required. • In the case that paper is needed, then: - No plastic materials will be used. - Printing will be done both sides. - Recycled paper will be used as possible. In general, a sustainable use of natural resources will be done. Moreover, ethic principles related to sustainability will be followed. |