| 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 |
| 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 | 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 |
| Problem solving | Technic by means of which one has to solve a specific problematic situation related to the contents of the subject. |
| Supervised projects | Homework that professors are going to asses during the course. |
| 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 |
| 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 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 |
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. |