| Study programme competencies |
| Code | Study programme competences |
| A1 | Skill for the resolution of the mathematical problems that can be formulated in the engineering. Aptitude for applying the knowledge on: linear algebra; geometry; differential geometry; differential and integral calculation; differential equations and in partial derivatives; numerical methods; algorithmic numerical; statistics and optimization |
| B1 | That the students proved to have and to understand knowledge in an area of study what part of the base of the secondary education, and itself tends to find to a level that, although it leans in advanced text books, it includes also some aspects that knowledge implicates proceeding from the vanguard of its field of study |
| B2 | That the students know how to apply its knowledge to its work or vocation in a professional way and possess the competences that tend to prove itself by the elaboration and defense of arguments and the resolution of problems in its area of study |
| B5 | That the students developed those skills of learning necessary to start subsequent studies with a high degree of autonomy |
| B6 | Be able to carrying out a critical analysis, evaluation and synthesis of new and complex ideas. |
| C4 | Recognizing critically the knowledge, the technology and the available information to solve the problems that they must face. |
| Learning aims | |||
| Learning outcomes | Study programme competences | ||
| To identify mathematical concepts and tools to solve problems that can appear in an engineering context. | A1 |
B1 B2 B5 B6 |
C4 |
| To show the ability of using techniques of Linear Algebra, Geometry and Calculus to be applied in problem solving. | A1 |
B1 B2 B5 B6 |
C4 |
| Contents |
| 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. |
| Planning | ||||
| Methodologies / tests | Competencies | Ordinary class hours | Student’s personal work hours | Total hours |
| Guest lecture / keynote speech | A1 B5 B6 C4 | 30 | 30 | 60 |
| Problem solving | A1 B1 B2 B5 B6 C4 | 30 | 30 | 60 |
| Supervised projects | A1 B1 B2 B5 B6 C4 | 0 | 16 | 16 |
| Mixed objective/subjective test | A1 B1 B2 B5 B6 C4 | 5 | 5 | 10 |
| 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. |
| Supervised projects | Homework that professors is going to asses during the course. |
| 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 |
| Mixed objective/subjective test | A1 B1 B2 B5 B6 C4 | Written exams to assess the knowledge of the subject by the students. The subject will consist on two parts and the final qualification of the subject will be the addition of the qualifications obtained at each of them. 1) The first part will be performed during the teaching period and will involve all the chapters studied until the celebration of the exam. If the student passes this exam, the qualification is retained until the end of the present course. This part will be recoverable in the final exam (second chance), to be held in July. 2) The second (and final) exam will be carried out in the period of final exams. It will involve 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 exam or in the final exam of January, the qualification is retained for the present course until the exam of second opportunity. To pass the subject is compulsory to obtain at least 30% of the maximum grade in each part. |
80 |
| Supervised projects | A1 B1 B2 B5 B6 C4 | Students must do an autonomous work related with the contents of the subject and following specific guidelines. | 20 |
| Assessment comments | |||
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The students with recognition of part-time dedication and academic exemption from attendance will be assessed through the objective tests in the same conditions as the rest of the students. The second opportunity and the extraordinary exam in december will be graded following the same criteria than in the first one. Fraudulent behaviour will result in a "0" qualification in the subject for the two opportunities. |
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| Sources of information |
| Basic |
Burgos, J. (1993). Álgebra lineal. McGrawHill
Grossman, S. I. (1995). Álgebra Lineal con Aplicaciones.. Mcgraw-Hill
Lay, D. C. (2007). Álgebra lineal y sus aplicaciones. Addison-Wesley
Larson, R., Edwards, B.H., Calvo, D. C. (2004). Álgebra lineal.. Pirámide Ediciones
Granero Rodríguez, F. (1991). Álgebra y Geometría Analítica. Mcgraw-Hill
González Rodríguez, R. (2022). Álxebra linear. Historia, teoría e práctica.. Universidade de Vigo
García, A. et al. (2007). Cálculo I. Teoría y Problemas de Análisis Matemático en Una Variable. 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
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
Ladra, M., Suárez, V., Torres, A. (2003). Preguntas test de Álgebra Lineal y Cálculo Vectorial. E. U. Politéctica
Villa Cuenca, A. (1994). Problemas de Álgebra.. CLAGSA
Gómez Bernúdez, C. (2015). Problemas de Álxebra Linear.. Andavira
Gómez Bernúdez, C, Gómez Gratacos, F. (2018). Problemas de Cálculo. Anvavira |
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| Complementary | |
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Resources from the webpage http://maxima.sourceforge.net/ are recommended for dealing with Maxima software. |
| 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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Students are encouraged to attend the "Course 0" with preliminaries in the contents of the couse. 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. - Unnecessary printed drafts will be avoided. In general, a sustainable use of natural resources will be done. Moreover, ethic principles related to sustainability will be followed. |