Academic management

The course is part of the matter called "Fundamentals of Mathematics" which includes, in addition to Numerical Computation, the following subjects in the first year of the Degree: Linear Algebra, Calculus and Statistics.

It is advisable to have basic knowledge of linear algebra and calculus.

The general and specific skills of the subject, described in the memoria Verifica del Grado are detailed in the following table:

Learning outcomes

RRA.FM-15: Identify the different types of errors that can occur in the use of numerical methods. Compare algorithm efficiency by precision degree and computational cost.
RA.FM-16: Choose appropriate methods to find the roots of nonlinear equations.
RA.FM-17: Describe, analyze and use numerical methods for solving systems of linear and nonlinear equations.
RA.FM-18: Solve numerically interpolation, data fitting and approximation problems.
RA.FM-19: Use formulas to approximate definite integrals.
RA.FM-20: Describe, use and evaluate basic numerical methods for solving optimization problems.

Chapter 1. Finite arithmetic and error analysis
Representation and arithmetic of numbers in computers
Types of errors

Chapter 2. Roots of nonlinear equations
Interval methods
Methods of calculating roots with sequences

Chapter 3. Approximation of functions
Function interpolation
Function approximation

Chapter 4. Derivation and numerical integration
Numerical derivation
Numerical Integration

Chapter 5. Systems of linear equations
Direct methods
Iterative methods

Chapter 6. Optimization
Unconstrained function optimization methods
Function optimization methods with constraints

Lectures

Teachers present the theoretical contents of the program, using the usual tools of teaching methodology. Students will be encouraged to reflection, participation and debate, as well as the use of the Campus Virtual or email to raise issues or concerns.

Seminars

Dedicated to the resolution of exercises. Active student participation will be encouraged.

Laboratories

Students, with guidance from the teacher, will solve mathematical problems related to the theoretical material of the course by implementing computer codes.

Evaluation session

Will be conducted as described in the section on evaluation.

Distribution of learning activity

Exceptionally, if it is required due to sanitary conditions, non-classroom teaching activities may be included. In this case, the students will be informed of the changes.

Ordinary evaluation

The final grade will be produced as follows: 70% of the evaluation will correspond to the lectures and seminars and 30% of the evaluation will correspond to the laboratory evaluation.

Evaluation of the lectures and seminars: they will be evaluated with written exams. The course will be divided into three partial exams of two units each one that will weight equally in the final mark. The first two partial exams will be done during the course and the third one on the day of the final exam. The marks obtained in each partial exam are only kept for the extraordinary evaluation of the current year. A necessary condition to pass the course is to obtain a mark of at least five out of ten in the joint global mark of the lectures and seminars. If this condition is not met, the final grade of this course will be the joint global mark of the lectures and seminars.

Evaluation of the labs: they will be evaluated only in the continuous evaluation modality. Attendance at laboratory practices is mandatory to pass this part. A maximum of two absences is allowed over the total number of lab sessions. The teacher can propose exercises, which will be compulsory to preserve the right to continuous evaluation. Two lab exams will be done during class hours and each one will weight 50% on the laboratory mark, as long as the necessary requirements have been fulfilled to qualify for continuous evaluation.

The laboratory marks will be kept only for the extraordinary evaluation of the present year.

Extraordinary evaluation

Extraordinary evaluation: There will be a written exam whose content corresponds to the lecture and seminar content. The final grade will be produced as follows: 70% of the written exam mark plus 30% of the mark obtained previously in the labs since there will be no lab exam in this evaluation. A necessary condition to pass the subject is to obtain a mark of at least five out of ten in the written exam. If this condition is not met, the mark of the subject will be the written exam mark.

Extraordinary early evaluation: There will be a written exam whose content corresponds to the lecture and seminar content and a lab exam. The final grade will be produced as follows: 70% of the written exam mark plus 30% of the lab exam mark. A necessary condition to pass the subject is to obtain a mark of at least five out of ten in the written exam. If this condition is not met, the mark of the subject will be the written exam mark.

Differentiated evaluation

There will be a written exam whose content will correspond to the lecture and seminar content and  a lab exam. The final grade will be produced as follows: 70% of the written exam mark plus 30% of the lab exam mark. A necessary condition to pass the subject is to obtain a mark of at least five out of ten in the written exam. If this condition is not met, the grade of the subject will be the written exam mark.

The marks obtained in the lab exam will be kept only for the extraordinary evaluation of the present year. The written exam grades are not kept.

Evaluation of the teaching process

During the course the activities carried out to detect strong and weak points will be reviewed and modifications will be introduced to improve the process.

Exceptionally, if it is required by sanitary conditions, on-line evaluation methods may be included. In this case, the students will be informed of the changes.

Resources

On the web page of the course (http://www.unioviedo.es/compnum) the students may find materials for the course, as well as links to many free resources available on the Web.

Bibliography

Bibliography in Spanish
[1] Burden, R., Faires, J.D., Análisis Numérico, Paraninfo (2004).
[2] Chapra.S.C., Canale,R.P., Métodos numéricos para ingenieros,  McGraw Hill (2011).
[3] Quarteroni, A., Saleri, F., Cálculo Científico con MATLAB y Octave, Springer-Verlag (2007).
[4] Sánchez Lasheras, F., García Gonzalo, E., Curso de Computación Numérica, Hifer (2021) (Web access)
[4] Sánchez Lasheras, F., García Gonzalo, E., Problemas de Computación Numérica, Hifer (2019) (Web access)

Bibliography in English
[1] Burden, R., Faires, J. D., Numerical Analysis, Cengage Learning (2011).
[2] Chapra.S.C., Canale,R.P., Numerical Methods for Engineers,  McGraw Hill (2014).
[3] Quarteroni, A., Saleri, F., Scientific Computing with MATLAB and Octave, Springer-Verlag (2014).
[4] Sánchez Lasheras, F., García Gonzalo, E., Course of Numerical Computing, HiFer (2021) (Web access)
[4] Sánchez Lasheras, F., García Gonzalo, E., Problems of Numerical Computing, HiFer (2019) (Web access)