Degree | Type | Year | Semester |
---|---|---|---|
2503740 Computational Mathematics and Data Analytics | FB | 1 | 2 |
A first course on calculus in one variable, and a first course on linear algebra.
Modeling turns problems in science and engineering into mathematical problems. The complexity of the real world often gives rise to mathematical problems that cannot be addressed from an analytic approach. Or perhaps they can, but the analytic approach may be too complex in the context in which the solution of the problem is required. For instance, solving the problem could be part of a contract, for which limited time is available.
Numerical methods are techniques from which algorithms can be deduced in order to obtain approximate solutions of mathematical problems. Many times, especially when high precision is required, these algorithms demand a large amount of computations. The use of a computer is then mandatory. Computers are most efficient when using finite precision arithmetic (this is, working with a finite number of digits). This means that each operation introduces error, known as round-off. This is not usually a problem, in particular because we are looking for approximate solutions. Nevertheless, it is necessary to know how to avoid situations in which the propagation of round-off error could completely invalidate our computations.
This course is devoted to the analysis of basic numerical methods, related to the solution of the kind of mathematical problems studied in first-year courses. This analysis has as a goal being able to predict both the quality of the approximations produced by the different methods and the computational effort they involve. This course is also an introduction to scientific computing, this is, the set of techniques and skills needed for the implementation in a computer of the numerical solution of a problem.
The numerical methods studied in this course are building stones of numerical methods for the solution of more sophisticated problems, studied from the second year on, like ordinary and partial differential equations.
Error propagation
Numerical linear algebra
Numerical solution of non-linear equations
Interpolation, differentiation, integration
In the theoretical sessions, the lecturer will explain the different methods and their analysis. The explanation of the different methods will be accompanied by computer examples of their behavior, both for a better understanding of the methods and in order to introduce their analysis.
The problem sessions will be devoted to the solution of both theoretical and computational problems. Some of the computational ones will require the use of a calculator, whereas other problems will require the use of a computer. In this last case, the problems will not be computationally intensive, so the algorithms needed for their solution will be of a fast implementation in an interpreted Octave-type language. Problems will be solved by either the lecturer, a student for all the class, or all the students for themselves with the support of the lecturer.
The computer sessions are designed as an introduction to scientific computing. In these sessions, students will work in more computationally intensive problems, by implementing their solution in a compiled language. In doing this, students will progressively develop their personal library of routines for basic numerical methods.
The gender perspective goes beyond the contents of courses, since it implies also a revision of teaching methodologies and interactions between students and lecturers, both inside and outside the classroom. In this sense, participative teaching methodologies that give rise to an equality environment, less hierarchical in the classroom, avoiding examples stereotyped in gender and sexist vocabulary, are usually more favorable to the full integration and participation of female students in the classroom. Because of this, their effective implementation will be attempted in this course.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Problem sessions | 15 | 0.6 | 2, 19, 9, 3, 4, 18, 6, 7, 8, 10, 17, 16, 11, 14, 20, 12 |
Theoretical sessions | 30 | 1.2 | 2, 19, 9, 3, 4, 18, 6, 7, 8, 1, 10, 13, 17, 16, 15, 14, 12 |
Type: Supervised | |||
Computer sessions | 8 | 0.32 | 2, 19, 9, 3, 4, 18, 6, 7, 8, 1, 13, 17, 16, 15, 11, 14, 20, 12 |
Type: Autonomous | |||
Computer work | 16 | 0.64 | 2, 9, 6, 7, 8, 1, 13, 17, 16, 15, 11, 12 |
Personal study | 76 | 3.04 | 2, 19, 9, 3, 4, 5, 18, 6, 7, 8, 10, 13, 17, 16, 15, 14, 12 |
The course will be evaluated from three activities:
Students will be given the option of taking an additional recovery exam (RE), of the same format of the FE exam. The practical work (PR) will not be recoverable.
In order to suceed, it is mandatory that max(0.35*PE*0.65*FE,FE,RE)>=4 and PR>=4.
The final grade of the course will be
0.6*max(0.35*PE+0.65*FE,FE,RE)+0.4*PR
Honor grades will be granted at the first complete evaluation. They will not be withdrawn even if another student obtains a larger grade after consideration of the RE exam.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Computer work | 0.4 | 0 | 0 | 2, 19, 9, 6, 7, 1, 13, 17, 16, 15, 11, 20, 12 |
Final exam | 0.39 | 3 | 0.12 | 2, 19, 9, 3, 4, 5, 18, 6, 7, 8, 1, 10, 17, 16, 15, 11, 14 |
Partial exam | 0.21 | 2 | 0.08 | 2, 19, 9, 4, 6, 7, 8, 1, 10, 17, 16, 15, 11, 14 |
Basic references:
Advanced references: