Linear algebra, Calculus I and II

1. Basic numerical skills to solve problems in Engineering. 2. The use of MATLAB to solve numerical problems. 3. Basic solving skills to solve counting problems. 4. Be able to model, pose and solve problems of communication, sound and image technologies.

CB1: Students have demonstrated possession and understanding of knowledge in an area of study that builds on the foundation of general secondary education, and is usually at a level that, while relying on advanced textbooks, also includes some aspects that involve knowledge from the cutting edge of their field of study. CB2: Students are able to apply their knowledge to their work or vocation in a professional manner and possess the competences usually demonstrated through the development and defence of arguments and problem solving within their field of study. CG3: Knowledge of basic and technological subject areas which enable acquisition of new methods and technologies, as well as endowing the technical engineer with the versatility necessary to adapt to any new situation. CG10: Ability to solve mathematical problems arising in engineering. Aptitude for applied knowledge in: linear algebra, geometry; differential geometry; differential and integral calculus; differential equations and partial derivatives; numerical methods; numerical algorithms; statistics and optimization. RA1: To acquire the knowledge and understanding of the general basic fundamentals of engineering, as well as, in particular, of multimedia communications networks and services, audio and video signal processing, room acoustic control, distributed multimedia systems and interactive multimedia applications specific to Sound and Image Engineering within the telecommunications family. RA5: Be competent to apply the knowledge acquired to solve problems and design audiovisual networks and services, to configure their devices, as well as to deploy adaptive, personal audiovisual applications and services on them, bringing network intelligence to the value for the user, maximising the potential of multimedia networks and services in the different social and economic spheres, knowing the environmental, commercial and industrial implications of the practice of engineering in accordance with professional ethics.

1. Introduction to Matlab and floating point arithmetic. Polynomial interpolation. Fourier series and trigonometric polynomial. Representation and approximation of signals. 2. Numerical integration methods. Simple and composite rules. Adaptive quadrature. 3. Initial value problems. The Euler, Taylor and Runge-Kutta methods. Prediction and correction methods. 4. Boundary value problems. Method of finite differences. Resolution of the wave equation. Finite element method and its applications.

There will be weakly sessions: - Theory sessions: the teacher will explain the fundamental concepts and results of the theory. - Exercise/Lab sessions: the students will work in solving exercises or writing codes to solve problems proposed by the professor.