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 and of the basic theory of linear differential equations underlying mechanical engineering. 2.- The ability to apply their knowledge and understanding to identify, formulate and solve mathematical problems of calculus of several variables and basic linear differential equations using established methods. 3.- The ability to choose and apply relevant analytical and modelling methods in calculus of several variables as well as in basic linear differential equations. 4.- The ability to select and use appropriate tools and methods to solve mathematical problems in terms of calculus of several variables as well as in basic linear differential equations. 5.- The ability to combine theory and practice to solve mathematical problems of calculus of several variables and of the basic theory of linear differential equations. 6.- Understanding of the applicable methods and techniques applicable to calculus of several variables and to basic linear differential equations and their limitations.

RA1.1 Knowledge and understanding of the scientific and mathematical principles underlying their branch of 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. 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, that previously have worked on. - Partial controls. - Final control. - Tutorials.