Degree | Type | Year | Semester |
---|---|---|---|
2500149 Mathematics | OB | 2 | 2 |
As previous knowledge the students must know the basic results on continuity, derivability and integrability of real functions in one and several variables, on linear algebra and matrix calculation, and basic notions about algorithms and programming language C. These knowledges are the contents of linear algebra, real variable functions, computer tools for mathematics of the first year of the studies in mathematics, and the calculus in several variables, from the first semester of the second year.
Science and technology are supported by mathematical models of real phenomena, developed for predictive purposes. A minimum of realism gives rise to difficult resolvable models in a totally analytical way. One of the ways to study them is by calculating approximate solutions. The study of techniques (numerical methods) to obtain these approaches is the goal of the numerical analysis, this subject is an introduction. Numerical methods require a calculation effort depending on the complexity of the model and the desired precision. In accordance with the standards of today, this calculation effort forces the use of computers.
The subject's objective is double. On the one hand it has purely mathematical aspects that it shares with the other subjects of the degree. In addition, he wants to prepare the students to solve the numerical problems that they can find in their professional practice. This implies both the precise knowledge of several methods and their suitability in various situations as the dexterity in their application to the resolution of specific problems with the help of a computer.
1.- Errors: Representation of real numbers. Arithmetic of floating point and formula of error propagation. Stable and unstable algorithms. Well and badly conditioned problems.
2.- Zeros of functions: Methods of bisection, Newton and secant. Fixed point methods. Order of convergence and efficiency. Methods of Newton and Chebyshev. Acceleration of convergence. Localization of roots for polynomials: Rule of Descartes, Sturm method, complex roots.
3.- Polynomial interpolation: Existence and uniqueness of the interpolation polynomial. Lagrange polynomials, Neville algorithm, Newton's divided differences. Generalized Hermite Interpolation. Error formulas. Interpolation by splines.
4.- Differentiation and numerical integration: Numerical derivation. Extrapolation of Richardson. Interpolation integration formulas, Newton-Cotes closed formulas, composite rules. Romberg method.
5.- Linear systems:Triangular systems Gauss method. Pivoting strategies. Factorization. Calculation of determinants and inverse of matrices. Bad conditioned systems. Classic iterative methods. Power method.
The problem classes will consist in solving problems on the board with active participation of students.
Several practices will be proposed during the course. Each practice will contain a script, according to which a report must be submitted, which will be the basis for the score of the practice, together with the code developed in C. The delivery period will be announced for each practice. The practical sessions will take place in a computer room of the faculty, and will be devoted to the resolution of doubts related to the realization of each practice. It is not expected that the students finish the practices during the practical sessions, but they will have to devote time to personal study.
Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|
Type: Directed | |||
Exercise classes | 30 | 1.2 | |
Theoretical classes | 45 | 1.8 | |
Type: Supervised | |||
Practical classes with computer | 28 | 1.12 | |
Type: Autonomous | |||
Personal work | 187 | 7.48 |
There will be four qualifications to evaluate the course:
First partial exam (EP1). Problems similar to those worked during problem classes and some theoretical questions must be solved.
Second partial (EP2). Problems similar to those worked during problem classes and some theoretical questions must be solved.
Practices note (Prac). The practices will have to be delivered throughout the course, with deadlines that will be announced in a timely manner. It is an indispensable requirement to pass the subject that the qualification of practices is equal to or greater than 3.5 out of 10.
Recovery test. The two partial examinations will be recovered together with a single exam.
The final grade in June (QFJ) will be obtained using the formula,
QFJ: = (35EP1 + 35EP2 + 30Prac) / 100
Students who obtain Prac> = 3.5, EP1>=3.5, EP2>=3.5 and QFJ> = 5 will have passed the subject.
For students who do not pass by course qualification, there will be a recovery test in July on all the subject matter of the course. Starting with your qualification, about 10, let's say EF, recalculate the course qualification changing 35EP1 + 35EP2 for 70EF. To pass it is also nedded to have EF>=3.5.
The criterion for obtaining the "no avaluable" qualification is: all students that deliver 2 practices or submit to one of the partial exams (EP1) or (EP2) will be considered presented.
MH will be awarded once the EP1 and EP2 examinations have been evaluated.
Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|
Delivery of practices | 0.3 | 0 | 0 | 2, 3, 4, 5, 7, 9, 10 |
First test | 0.35 | 3 | 0.12 | 2, 3, 1, 8, 6 |
Recovery exam | 0.7 | 4 | 0.16 | 3, 8, 6 |
Second Test | 0.35 | 3 | 0.12 | 2, 3, 1, 8, 6 |
Basic bibliography:
Other bibliography:
Programming: