This text is aimed at students enrolling at university and taking their first course in Mathematics. The book was born from the experience gained over the years of teaching in university courses in Mathematics, as a support for solving applicative exercises, and for deepening and complementing the actual theory lessons. Keeping aware of the main difficulties encountered by students, we have decided to provide a useful compendium in order to build and consolidate the necessary skills and gain the degree of self-assurance required to face the examinations in university mathematics courses with confidence.
In the text, the fundamental topics proposed in many university courses involving a first course in Mathematics are analyzed: functions, limits, continuity, derivatives and differentiability, general study of functions, integrals, linear algebra, vectors and matrices, linear systems, functions with several variables and constrained optimisation.
The focus of the text is on the exercises, which are carried out in detail and with clarification of the adopted solution strategies, approached with progressive difficulty so as to make the applications of the theory explicit and favouring the inductive method. The theory recalls are concise, schematic and aimed at solving the exercises themselves. For each topic, various examination topics, assigned in previous academic years’ examinations, are included, which are carried out in their entirety. In order to encourage personal and autonomous work, ample space is given to testing the knowledge and skills acquired, with sets of exercises to be completed (with solutions in the online extensions of the text) and exit tests for each chapter.
MARCO PAPI is an Associate Professor of Mathematical Methods of Economics and Actuarial and Financial Sciences at the Departmental Faculty of Engineering of the University Campus Bio-Medico of Rome and contract lecturer at the Department of Economics and Management of the Luiss - Guido Carli University of Rome.
MARCO BUSCEMA, FRANCESCA LATTANZI, LAURA MAZZOLI, ANTONIO VEREDICE
are high school professors of Mathematics and Physics and, since A.A. 2004-2005, lecturers of the Mathematics courses at the Faculty of Economics at Luiss - Guido Carli University in Rome.