Calculus I.

By the end of this content area, students will be able to have: 1.- Knowledge and understanding of the mathematical principles of calculus of several variables underlying automation and industrial electronics engineering. 2.- The ability to apply their knowledge and understanding to identify, formulate and solve mathematical problems of calculus of several using established methods. 3.- The ability to choose and apply relevant analytical and modelling methods in calculus of several variables. 4.- The ability to select and use appropriate tools and methods to solve mathematical problems in terms of calculus of several variables. 5.- The ability to combine theory and practice to solve mathematical problems of calculus of several variables. 6.- Understanding of the applicable methods and techniques applicable to calculus of several variables and their limitations.

RA1.1: Knowledge and understanding of the scientific and mathematical principles underlying their branch of industrial engineering. RA2.1: The ability to apply their knowledge and understanding to identify, formulate and solve engineering problems using established methods. RA5.1: The ability to select and use appropriate equipment, tools and methods. RA5.2: The ability to combine theory and practice to solve engineering problems. 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. CG1: Ability to resolve problems with initiative, creativity decision-making and critical reasoning skills, and to communicate and transmit knowledge, skills and abilities in the Industrial Engineering area. CG11: Capacity to solve mathematic problems arising in engineering. Aptitude for applying knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; differential equations and partial derivatives: numerical methods; numerical algorithms; statistics and optimization.

The Euclidean space. Several variables Functions. Continuity and differentiability. Polar, spherical and cylindrical coordinates. Free and conditional optimization. Iterated integration. Changes of variables. Integration along trajectories. Integration on surfaces. Computation of areas and volumes. Other applications of the integral. Green, Stokes and Gauss theorems. Laplace transform. Introduction to differential equations.

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.