| Study programme competencies |
| Code | Study programme competences |
| A6 | Capacidade para a resolución dos problemas matemáticos que se poidan suscitar 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. |
| A9 | Capacidade de visión espacial e coñecemento das técnicas de representación gráfica, tanto por métodos tradicionais de xeometría métrica e xeometría descritiva como mediante as aplicacións de deseño asistido por ordenador. |
| B1 | Capacidade de resolver problemas con iniciativa, toma de decisións, creatividade e razoamento crítico. |
| B2 | Capacidade de comunicar e transmitir coñecementos, habilidades e destrezas no campo da enxeñaría industrial. |
| B3 | Capacidade de traballar nun contorno multilingüe e multidisciplinar. |
| B4 | Capacidade de traballar e aprender de forma autónoma e con iniciativa. |
| B6 | Capacidade de usar adecuadamente os recursos de información e aplicar as tecnoloxías da información e as comunicacións na enxeñaría. |
| C1 | Expresarse correctamente, tanto de forma oral coma escrita, nas linguas oficiais da comunidade autónoma. |
| C6 | Valorar criticamente o coñecemento, a tecnoloxía e a información dispoñible para resolver os problemas cos que deben enfrontarse. |
| Learning aims | |||
| Learning outcomes | Study programme competences | ||
| Modeling and solving mathematical problems in the field of engenengineering. | A6 |
B1 B2 B3 B4 B6 |
C1 C6 |
| Possessing own scientific mathematical skills, enabling it to ask and answer some math questions. | A6 |
B1 B2 B3 B4 B6 |
C1 C6 |
| Create linear models that approximate problems to solve. Having ability to apply knowledge of Linear Algebra and Differential Geometry. | A6 A9 |
B1 B2 B3 B4 B6 |
C1 C6 |
| Understand mathematical models that explain the behavior of a fluid in a 1-dimensional space. | A6 |
B1 B2 B3 B6 |
C1 C6 |
| Knowing how to use numerical methods in solving some mathematical problems that arise. | A6 |
B1 B2 B3 B6 |
C1 C6 |
| Knowing the thoughtful use of tools symbolic and numeric computation. | A6 |
B4 B6 |
C6 |
| Contents |
| Topic | Sub-topic |
| Path Integral | Paths in Rn. Reparameterizations. Line integrals of scalar functions. Applications of the integrals of scalar functions. Integrals of vector fields. Gradient type functions. Green theorem. |
| Surface integral | Cross product. Sufaces in R3. Area of a surface. Integral of a scalar function. Oriented surfaces. Integral of vector fileds. Divergence. Gauss Theorem. Curl. Stokes Theorem. |
| Vector spaces | The vector space Rn. Operations: vector addition, scalar multiplication. Vector subspaces. Direct sum. Linear combination, linear span. Linear independence. Spaning set. Basis and dimension. Theorems about basis. Coordinates, change of coordinates. |
| Linear maps | Linear maps. Properties of the linear maps. Kernel and Image of a linear map. Operations with linear maps. Matrix associated to a linear map. |
| Diagonalization | Invariant subspaces. Eigenvalues and eigenvectors. Characteristic polynomial. Diagonalizable endomorphism. |
| Planning | ||||
| Methodologies / tests | Competencies | Ordinary class hours | Student’s personal work hours | Total hours |
| Guest lecture / keynote speech | B2 B3 B4 C1 | 21 | 42 | 63 |
| Document analysis | A9 B4 B6 | 0 | 7 | 7 |
| Directed discussion | A6 B1 C1 | 12 | 12 | 24 |
| Mixed objective/subjective test | A6 B1 B4 C1 C6 | 4 | 14 | 18 |
| Laboratory practice | A6 A9 B4 B6 | 6 | 0 | 6 |
| Problem solving | A6 C6 | 12 | 18 | 30 |
| Personalized attention | 2 | 0 | 2 | |
| (*)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 | We present the contents of the subject. Examples of applications are developed and related activities are proposed. |
| Document analysis | We discuss the different notations in mathematics. The sources of information are commented: books, magazines, webpages. |
| Directed discussion | The students debate about how to solve problems. They discusse if the results achieved are meaningless. |
| Mixed objective/subjective test | Its aim is to determine the degree of knowledge that students get at classes and with their personal study. It may consist of an explanation of any content of the course, the answer of test questions, the resolution of theoretical and practical issues and developing solutions to issues involving deep knowledge of the subject. |
| Laboratory practice | Its aim is to apply computer programs to solve problems commented in the lectures. |
| Problem solving | With them we move from theory to practice. Specific problems of the subject developed in the lectures are solved. |
| Personalized attention |
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| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Problem solving | A6 C6 | We will formulate practical issues in which students have to seek a solution to a given problem. | 20 |
| Mixed objective/subjective test | A6 B1 B4 C1 C6 | They are tests made for measuring the level of knowledge of the subject by students. They do not have a defined profile, as they can range from test questions in which the student must only choose one answer among the options proposed, or solving problems involving an action strategy or theoretical questions that reflect the degree of knowledge of the subject. | 75 |
| Laboratory practice | A6 A9 B4 B6 | Students should know the functioning of a computer program that helps resolve mechanical problems raised previously. | 5 |
| Assessment comments | |||
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<p> The final grade of the subject consists of three parts:</p><p>i) Problem solving: It's made through written tests and the development of classes in the classroom, where the teacher assesses individually the degree of knowledge of the subject of each student. This part represents 20% of the grade.</p><p>ii) performing laboratory practice, where students will learn to use the software that provides the teacher. This part represents 5% or qualification.</p><p>iii) Mixed objective/subjective test. This part represents 75% of the grade for students, of which 5% is evidence of laboratory practices.</p>
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| Sources of information |
| Basic |
Grossman, S. (1995). Álgebra lineal con aplicaciones. McGraw-Hill
Nakos, G. y otros (1999). Álgebra lineal con aplicaciones. Thomson
Granero Rodríguez, F. (1991). Álgebra y geometría analítica. McGraw-Hill
Besada Morais, M. y otros (2008). Calculo vectorial e ecuacións diferenciais. Servizo publicacións da Universidade de Vigo
Roberto Benavent (2010). Cuestiones sobre Álgebra Lineal. Paraninfo
Guillem Borrell i Nogueras (2008). Introducción a Matlab y Octave. http://iimyo.forja.rediris.es/matlab/
Prieto Sáez, E. y otros (1995). Matemáticas I: economía y empresa. Centro de estudios Ramón Areces
Ladra González y otros (2003). Preguntas test de álbegra lineal y cálculo vectorial. J.B.Castro Ambroa y Copybelén |
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| Complementary | |
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| Recommendations | |
| Subjects that it is recommended to have taken before |
| Subjects that are recommended to be taken simultaneously | |
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| Subjects that continue the syllabus | |
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| Other comments | |
| <p> The student must know the content of the subjects of Mathematics studied at ESO and high school. Those students from Profesional Learning should study the basic concepts related to applications, functions and integration of real functions of real variable, which are contained in the curricula of high school, and are not in Profesional Learning. </p> |