| Study programme competencies |
| Code | Study programme competences |
| A1 | Capacidade para a resolución dos problemas matemáticos que se poden presentar na enxeñaría. Aptitude para aplicar os coñecementos sobre: álxebra linear; cálculo diferencial e integral; métodos numéricos; algorítmica numérica; estatística e optimización. |
| A33 | Capacidade de analizar e avaliar arquitecturas de computadores, incluíndo plataformas paralelas e distribuídas, así como desenvolver e optimizar sóftware para elas |
| A41 | Capacidade para avaliar a complexidade computacional dun problema, coñecer estratexias algorítmicas que poidan conducir á súa resolución e recomendar, desenvolver e implementar aquela que garanta o mellor rendemento de acordo cos requisitos establecidos. |
| B3 | Capacidade de análise e síntese |
| Learning aims | |||
| Learning outcomes | Study programme competences | ||
| Knowledge of the most representative models in science and engineering, specially in computing, formulated by mathematical models and that need numerical methods | A1 |
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| Knowledge and comprehension of the numerical techniques better adapted for each one of the formulated models | A1 A33 A41 |
B3 |
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| Implementation of software that develops the numerical techniques, or the use of software tools that develop them | A1 A41 |
B3 |
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| Abord of problems that arise in the fields of computational science, covering from the understanding of the models to the practical and efficient implementation in computer | A1 A41 |
B3 |
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| Contents |
| Topic | Sub-topic |
| Matrix numerical methods and applications | - Numerical resolution of large linear systems. Direct and iterative methods. Sparse matrices. Applications - Least-square problems. Applications - Power method for eigenvalues. Google page rank algorithm |
| Numerical methods for computer graphics | - Interpolation and piecewise interpolation - Spline interpolation - Introduction to B-splines and Bezier curves - Applictions in computer graphics |
| Numerical resolution of partial differential equations. Applications | - Introduction to partial differential equations - Finite difference methods - Applications in image processing |
| Numerical methods implementation | - Some MatLab and Python commands |
| Planning | ||||
| Methodologies / tests | Competencies | Ordinary class hours | Student’s personal work hours | Total hours |
| Laboratory practice | A1 A33 A41 B3 | 14 | 28 | 42 |
| Problem solving | A1 A41 B3 | 4 | 14 | 18 |
| Mixed objective/subjective test | A1 B3 | 3 | 0 | 3 |
| Guest lecture / keynote speech | A1 B3 | 21 | 60 | 81 |
| Personalized attention | 6 | 0 | 6 | |
| (*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students. | ||||
| Methodologies |
| Methodologies | Description |
| Laboratory practice | Some applied problems will be posed, different techniques will be discussed and the chosen one will be implemented. |
| Problem solving | Applied problems will be posed and solved by the teacher in order to understand the different methods and techniques explained in the theoretical courses. |
| Mixed objective/subjective test | The student will have to solve some theoretical questions and applied problems. |
| Guest lecture / keynote speech | In the session magistral the professor will expose the theoretical and practical contents. The contents will be issued from real problems, the concepts and methods will be developed and some applied examples and exercises will be presented. |
| Personalized attention |
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| Assessment | |||
| Methodologies | Competencies | Description | Qualification |
| Laboratory practice | A1 A33 A41 B3 | The student will implement the adequate numerical methods in order to solve some proposed applied problems. | 50 |
| Mixed objective/subjective test | A1 B3 | Theoretical-practical control about the contents of the subject. | 50 |
| Assessment comments | |||
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To surpass the matter, the student will have to: - do at leat the 75% of the proposed laboratory practices - obtain at least a qualification of 4 in the mixed objective/subjective proof. In the case of presencial activities, facilities will be given to part-time students. |
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| Sources of information |
| Basic |
R.L. Burden, J.D. Faires (2011). Análisis Numérico. Cengage Learning
D. Kincaid, W. Cheney (1994). Análisis numérico: las matemáticas del cálculo científico. Addison Wesley
(1996). Matlab, Partial differential equations toolbox. Mathworks
(1996). Matlab, the language of scientific computing. Mathworks
J.H. Mathews, K.D. Fink. (2000). Métodos numéricos con MATLAB. Prentice-Hall
J. Kiusalaas (2005). Numerical Methods in Engineering with Python. Cambridge U.P. |
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| Complementary | |
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| Recommendations | ||||
| Subjects that it is recommended to have taken before | ||||
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| Subjects that are recommended to be taken simultaneously |
| Subjects that continue the syllabus |
| Other comments | |