The student must be able to state, solve and understand, from a mathematical point of view, problems related to Engineering and of Energy Engineering. First of all, a comprehensive approach to Euclidean spaces with a special emphasis in the two-dimensional and three-dimensional cases as well as their most relevant subsets will be done. He must handle the main properties of functions in several variables related to continuity, differentiability and integrability both in the scalar and vector cases. The study of problems related to optimisation, with and without constraints, constitutes a nice application of Taylor formula and local extrema.
Iterated integrals on domains as well as the integration on lines and surfaces will provide the basic background for the analysis of areas and volumes as well as the computation of some characteristics of rigid solids. The computation of such integrals will be used as applications of the most important theorems of integral Calculus.
By the end of this subject, students will be able to have:
1.- Knowledge and understanding of the mathematical principles underlying the branch of energy engineering;
2.- The ability to a ly their knowledge and understanding to identify, formulate and solve mathematical problems using established methods;
3.- The ability to choose and apply relevant analytical and modelling methods;
4.- The ability to select and use appropriate tools and methods to solve mathematical problems;
5.- The ability to combine theory and practice to solve mathematical problems;
6.- Understanding of the applicable methods and techniques and their limitations.