| 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 | ||
| 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 |
| Sets and functions in R^n | Scalar and vector functions. Level sets. Continuity. Continuity in compact sets. |
| Differential Calculus | Directional derivative. Partial derivative. Differential of a function. Gradient vector. Jacobian matrix. Higher order derivatives. Introduction to vector calculus. Taylor polynomial for scalar functions. Critical points. Hessian matrix. Conditional extreme values. Lagrange multipliers. |
| Integral Calculus. | Double integrals. Triple integrals. Change of variables. Applications to the computation of areas and volumes. |
| Differential Geometry | Parameterized curves and line integrals. Integrals of vector functions. Gradient functions and conservative vector fields. Green's theorem. Parameterized surfaces. Rotational and divergence. Surface integrals. Stokes theorem. Divergence theorem. |
| 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 |
| Mixed objective/subjective test | A1 B1 B2 B5 B6 C4 | 8 | 8 | 16 |
| Supervised projects | A1 B1 B2 B5 B6 C4 | 0 | 10 | 10 |
| Problem solving | A1 B1 B2 B5 B6 C4 | 30 | 30 | 60 |
| 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 | Oral exhibition complemented with the use of audiovisual means and some questions headed to the students, with the purpose to transmit knowledges and facilitate the learning |
| Mixed objective/subjective test | Written exam used for the evaluation of the learning, whose distinctive stroke is the possibility to determine if the answers given are or no correct. It constitutes an instrument of measure, elaborated rigorously, that allows to evaluate knowledges, capacities, skills, performance, aptitudes, attitudes, etc |
| Supervised projects | Homework that professors are going to asses during the course. |
| Problem solving | Technic by means of which one has to solve a specific problematic situation related to the contents of the subject. |
| Personalized attention |
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| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Mixed objective/subjective test | A1 B1 B2 B5 B6 C4 | Written exam will be used to assess learning of the contents of the subject. The exam consists of three parts, the first one will be performed during the course as a partial exam. This part will be eliminnatory and retrievable. The second part will be developed throughout the course by making homework and will be graded by assessing gained competences. The third part will be performed during the usual period of final exams and will assess the first, second and third parts. | 80 |
| Supervised projects | A1 B1 B2 B5 B6 C4 | Homework that professors are going to asses during the course. | 20 |
| Assessment comments | |||
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Students with recognition of part-time dedication and academic exemption The second opportunity will be developed in the same conditions as the first one. |
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| Sources of information |
| Basic |
Hwei P. Hsu (1987). Análisis Vectorial. Addison-Wesley
Marsden, J., Tromba, A. (2004). Cálculo Vectorial. Addison-Wesley
Larson, R., Hostetler, R., Edwards, B. (1999). Cálculo y Geometría Analítica, Vol. 2. McGraw-Hill
Salas, L., Hille, E.,Etgen, G. (2013). Calculus, vol I-II. Reverté
Gómez Bernúdez, C, Gómez Gratacos, F. (2018). Problemas de Cálculo. Andavira |
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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 | ||
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| Subjects that are recommended to be taken simultaneously | |
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| Subjects that continue the syllabus | |
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| Other comments | |
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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. |