• Description

Numerical methods play an important role in modern science. The approximation of the surface of an airplane and the aerodynamic simulation of the behavior of the air around it require the use of numerical methods. Many graphics in the world of computer animation are the result of applying these methods in solving a physical model. Interpolation allows to fix the intermediate positions between an initial and a final state of a body, and the movement of its clothing is given as a numerical solution of differential equations. The treatment of the error of the solutions that are generated allows us to differentiate the error of the algorithm, from the error caused by the finite precision of computers. This course introduces the basic numerical methods applied to engineering and science, as well as the analysis of the approach that their solutions imply.

• The subject within the syllabus as a whole

Any subject in the study plan that requires simulation or approximation of mathematical elements may be based on the ideas developed in this subject.

• Professional fields to which it applies

The simulation and numerical approximation required by any research and development activity has its first steps in the methods covered in this subject

• Prior knowledge

Adequate level of English in order to read technical and scientific documentation in this language. Engineering level in mathematics and programming.

• Information prior to enrolment

Prior knowledge: Adequate level of English in order to read technical and scientific documentation in this language. Engineering level in mathematics and programming.

Planned software: matlab, octave o scilab

• Learning objectives and results

- Know the concepts of error, stability and convergence of an algorithm

- Knows how to choose the appropriate algorithm for each situation.

- Knows how to apply the basic numerical techniques that appear in problems

scientific and engineering.

- Knows how to correctly interpret the results obtained with a numerical algorithm.

- Extracts the general meaning of texts that contain non-routine information

within a known scope.

- Use software for online communication: interactive tools (web, moodle,

blogs ..), email, forums, chat, video-conferences, tools

collaborative work

• Content

Computer errors and error propagation

Systems of linear equations

Interpolation by polynomials

Numerical differentiation

Numerical integration

Nonlinear equations

Ordinary differential equations

• Additional information on bibliography and information sources

Applied Numerical Methods Using MATLAB.  Won Y. Yang y otros . Editorial Wiley (2005).

• Methodology

Most topics will be worked for two weeks. In the first week, the student should study the theoretical part from the notes that will be provided, complemented with the bibliography. The second week will be of practical work, where you will have to solve some exercises or a practice using Matlab or Octave.

• Guidelines on assessment at the UOC

The assessment process is based on the student's personal work and presupposes authenticity of authorship and originality of the exercises completed.

Lack of authenticity of authorship or originality of assessment tests, copying or plagiarism, the fraudulent attempt to obtain a better academic result, collusion to copy or concealing or abetting copying, use of unauthorized material or devices during assessment, inter alia, are offences that may lead to serious academic or other sanctions.

Firstly, you will fail the course (D/0) if you commit any of these offences when completing activities defined as assessable in the course plan, including the final tests. Offences considered to be misconduct include, among others, the use of unauthorized material or devices during the tests, such as social media or internet search engines, or the copying of text from external sources (internet, class notes, books, articles, other students' essays or tests, etc.) without including the corresponding reference.

And secondly, the UOC's academic regulations state that any misconduct during assessment, in addition to leading to the student failing the course, may also lead to disciplinary procedures and sanctions.

The UOC reserves the right to request that students identify themselves and/or provide evidence of the authorship of their work, throughout the assessment process, and by the means the UOC specifies (synchronous or asynchronous). For this purpose, the UOC may require students to use a microphone, webcam or other devices during the assessment process, and to make sure that they are working correctly.

The checking of students' knowledge to verify authorship of their work will under no circumstances constitute a second assessment.

• View assessment model

• Continuous assessment

Continuous assessment consists of three practices (30% + 40% + 30%) to have the final mark of continuous assessment (CA). Each of these activities concludes the topics discussed.

• Final assessment

On this subject, the final assessment is  the result of weighing the Continuous Assessment (CA) and a Final Practice (Pr), according to the weighting indicated above.