Calculus I

The student will be able to formulate, solve and understand mathematically the problems arising in engineering. To do so it is necessary, in this second course of Calculus, to be familiar with the n-dimensional euclidean space, in particular in dimension 3, and with its more usual subsets. He/she must be able to manage (scalar and vectorial) several variables functions and its continuity, differentiability and integrability properties. The student must solve optimization problems with and without restrictions and will apply the main integration theorems to compute areas and volumes, inertial moments and heat flow.

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. 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.

1- Differential calculus in several variables a Functions of several variables. Limits and continuity b Derivatives. Differentiability c Differential operators d Chain rule. Directional derivatives 2- Local study of functiopns of several variables a Higher order derivatives b Extrema c Conditional optimization 3- Integration of functions of several variables a Iterated integration b Change of variables in the integral c Aplications 4- Trajectory integrals. Surface integrals. a Integrals along curves. Conservative vector fields b Integrales on surfaces c Computation of areas and volumes d Vectorial integral Theorems: Green, Stokes and Gauss

The docent methodology will include: - Master classes, where the knowledge that the students must acquire will be presented. To make easier the development of the class, the students will have written notes and also will have the basic texts of reference that will facilitate their subsequent work. - Resolution of exercises by the student that will serve as self-evaluation and to acquire the necessary skills. - Problem classes, in which problems proposed to the students are discussed and developed. - Partial controls. - Final control. - Tutorials.