Continuum Mathematics

The aim of the course is to provide the basic mathematical tools, both from a conceptual and from a calculus point of view, which are essential to successfully attend a university undregraduate program in a scientific area. The course should also provide the required mathematics prerequisites for the other courses of the program.

At the end of the course, students should prove to have a sufficient knowledge of basic mathematics, that includes the main properties of sets, of the main number sets, in particular of real numbers, of functions between sets, of elementary functions, of combinatorics and of complex numbers. Also, she/he should know the basic results in the theory of differential and integral calculus for functions of one real variable. Finally, at the end of the course students should be able to apply the theoretical results to solve elementary problems and exercises and in
particular they should be able to tackle the following kinds of problems: computation of limits of sequences or functions, analysis of the continuity of a function, computation of derivates, study of the qualitative graph of a function, computation of the Taylor polynomial and expansion, computation of definite and indefinite integrals.