Calculus I Linear Algebra

The aim of this course is to make the student familiar with the basic concepts of probability, random variables and stochastic processes. In order to achieve this goal, the student should acquire knowledge and skills. With respect to the knowledge, at the end of the course, the student should be able to: -Know and use the basic concepts and properties of probability. -Understand the concept of density and probability function of random variables and vectors. -Identify and understand transformations of random variables and vectors. -Understand the concept of signals and knoise as stochastic processes. The student will gain specific and general skills: Specific skills: -Calculate the reliability of a system -Manage the concept of random variables in the context of telecommunications -Work with transformations of random variables and their properties -Identify and classify stochastic process, and calculate their statistics. General skills: -Capacity to identify and apply theoretical concepts to real problems. This skill will be acquired by solving problems proposed in class -Hability to analyze data and interpret results. This skill will be developed in class and in computel labs -Effective communication of knowledge and statistical results. This skill will be acquired by solving problems in class and in computer labs -Capacity to work in groups, in an effective, responsible and creative manner. This skill will be acquired by solving computer labs exercises in groups and solving problems in class

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. 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.

In this course, the students study the foundations of probability and random variables. The programm is divided in 5 blocks: * Probability -Events -Properties of probability -Laplace rule -Conditional probability and independence of events -Bayes Theorem *Random Variables -Definition of random variable -Dicrete random variables: probability and distribution functions -Continuous random variables: density and distribution functions -Moments of a random variable -Transformation of random variables *Probability models -Bernouilli and Binomial -Poisson -Exponencial -Normal -Central Limit Theorem: Approximation of random variables *Random Vectors -Joint distribution -Discrete and continupus random vectors: Joint probability, density and distribution functions -Marginal distributions -Conditional distributions, independence of events -Moments of a random vector -Transformations of renaom vectors *Stochastic Processes -Definition and classification of processes -Distribution function -Characteristic measures: Mean, Variance, Autocovariance, Autocorrelation -Correlation between processes, independence, orthogonality -Stationarity -Ergodicity

-Theory classes: Presentation of basic concepts and examples. In order to help the student to acquire the relevant knowledge, a basic textbook will be available, as well as slides and problem sheets 2.5 ECTS -Problem solving classes: Solving exercises in small groups 2.2 ECTS -Computer Laboratories: Work in groups and presentation of reports 0.3 ECTS -Evaluation: 1 ECTS