| Study programme competencies |
| Code | Study programme competences |
| A1 | Capacidad para plantear y resolver los problemas matemáticos que puedan plantearse en el ejercicio de la profesión. En particular, conocer, entender y utilizar la notación matemática, así como los conceptos y técnicas del álgebra y del cálculo infinitesimal, los métodos analíticos que permiten la resolución de ecuaciones diferenciales ordinarias y en derivadas parciales, la geometría diferencial clásica y la teoría de campos, para su aplicación en la resolución de problemas de Ingeniería Civil. |
| B2 | Resolver problemas de forma efectiva. |
| B3 | Aplicar un pensamiento crítico, lógico y creativo. |
| C1 | Reciclaje continúo de conocimientos en el ámbito global de actuación de la Ingeniería Civil. |
| C4 | Entender y aplicar el marco legal de la disciplina. |
| C6 | Compresión de la necesidad de analizar la historia para entender el Presente. |
| C8 | Facilidad para la integración en equipos multidisciplinares. |
| Learning aims | |||
| Learning outcomes | Study programme competences | ||
| To know and to understand the basic theory of linear algebra required in civil engineering , especially the study of vector spaces. | A1 |
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| Know, understand and manage elementary mathematical notation. | A1 |
B3 |
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| Learn to express with precision and rigor. | A1 |
C1 |
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| Learn to use the basic techniques of mathematical reasoning. | A1 |
B2 B3 |
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| Understanding the importance of justifying the thesis and results in science . | A1 |
B3 |
C4 C6 |
| Develop critical thinking and analytical skills . | A1 |
B2 B3 |
C4 C8 |
| Learn to pose and solve mathematical problems of Linear Algebra, | A1 |
B2 B3 |
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| Contents |
| Topic | Sub-topic |
| I. Preliminars. |
1. Correspondences and maps. 1.1 Sets Definiction and notation. Operations with sets. 1.2 Correspondences. Maps. Definition, properties and classification. 2. Combinatorics. 2.1. Product rule. 2.2. Variations. 2.3. Permutations. 2.4. Combinations. |
| II. Matrices and determinants. | 1. Matrices. 1.1 Basic definitions. 1.2 Operations with matrices. 1.3 Special matrices. 2. Determinants. 2.1 Preliminars on permutacions. 2.2 Determinant of a square matrix: definition and properties. 2.3. Development of a determinant by adjoints. 2.4. Rank of a matrix. 2.5. Inverse of a matrix. 3. Equivalence and congruence of matrices. 3.1 Elementary transformations. 3.2 Row equivalence of matrices. 3.3 Column equivalence of matrices. 3.4 Matrix equivalence. 3.5 Matrix congruence. 4. Systems of linear equations. 4.1 Cramer's rule. 4.2 Rouche-Frobenius' Theorem. 4.3 Gaussian elimination. |
| III. Vectorial spaces. | 1. Vectorial spaces and subspaces. 1.1 Definition and properties. 1.2 Vectorial subspaces. 2. Spanning systems. Free linear systems. Basis. 2.1 Linear combinations of vectors. 2.2 Linear dependence and indepdence of vectors. 2.3 Basis, dimension and coordinates. 2.4 Rank of a vector set. 2.5 Change of basis. 2.6 Equations of a subspace. 2.7 Dimension formula. 3. Linear maps. 3.1 Definitions and properties. 3.2 Matrix form of a linear map. 3.3 Change of basis. 3.4 Kernel and image of a linear. 3.5 Composition fo homomorphisms. 4. Endomorphisms. 4.1 Introduction. 4.2 Eigen values and eigen vectors. 4.3 Diagonalization by similarity. 4.4 Triangularization by similarity. Jordan form |
| Planning | ||||
| Methodologies / tests | Competencies | Ordinary class hours | Student’s personal work hours | Total hours |
| Guest lecture / keynote speech | A1 B2 B3 | 27 | 32 | 59 |
| Seminar | A1 B2 B3 | 27 | 33 | 60 |
| Mixed objective/subjective test | A1 B2 B3 | 3 | 3 | 6 |
| Problem solving | A1 B2 B3 | 0 | 10 | 10 |
| Workbook | A1 B2 B3 | 0 | 10 | 10 |
| Personalized attention | 5 | 0 | 5 | |
| (*)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 | New mathematic concepts will be developed from examples familiar for the students, or explaining the questions are wished to be solved with them; from this their common caracthers will be abstracted causing its more accuracy deffinition. The theory which allows to solve the questions described at the beginning will be developed after. Students participation is desirable, sharing their doubts or comments as the class progresses. |
| Seminar | Simultaneously to the theoretical development of the matter collections of exercics are given. The goal is allowing students to practise the knowledge adquierd at theorical classes. At seminars the most important problems will be discussed. |
| Mixed objective/subjective test | Exam where concepts are methods of the subjets are evaluated. |
| Problem solving | Each student must solve individually some of the proposed problems. |
| Workbook | Before the beginning of each item, some notes about the contents are avaiable for the students. The notes are intended as a complement of teacher's explanations. A previous reading of students familiarize them with an outline of what they will study. |
| Personalized attention |
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| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Problem solving | A1 B2 B3 | Each student must solve individually some of the proposed problems. | 10 |
| Mixed objective/subjective test | A1 B2 B3 | Exam where concepts are methods of the subjets are evaluated. | 90 |
| Assessment comments | |||
| Sources of information |
| Basic |
Juan de Burgos (2000). Álgebra Lineal. McGraw-Hill
Fuentes, Salete y Cruces (1980). Álgebra vectorial y Tensorial. ETSICCP Madrid
F. Granero (1992). Álgebra y Geometría Analítica. McGraw-Hill
Luis Fuentes García (2005-). Apuntes y ejemplos (http://caminos.udc.es/info/asignaturas/grado_tecic/101/AL1/index.html). A Coruña
Anzola, Caruncho y Pérez-Canales (1981). Problemas de Álgebra (Tomos 1,3). Madrid
S. Lipschutz, M.L. Lipson (2000). Teoría y problemas de probabilidad. McGraw-Hill |
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| Complementary |
S.I. Grossman (1995). Álgebra lineal. McGraw-Hill
J. Rojo (2001). Álgebra lineal. McGraw-Hill
J. Arvesú y otros (1999). Álgebra lineal y aplicaciones. Síntesis
M. Castellet e I. Llerena (1991). Álgebra lineal y geometría. Reverté
J. Flaquer y otros (1996). Curso de álgebra lineal. Ediciones Universidad de Navarra
J. Rojo e I. Martín (1994). Ejercicios y problemas de álgebra. McGraw-Hill
P. Sanz y otros (1998). Problemas de álgebra lineal. Prentice Hall
J. Pérez Vilaplana (1991). Problemas de cálculo de probabilidades. Paraninfo
F. Ayres Jr. (1991). Teoría y problemas de matrices. McGraw-Hill |
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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 | |