Mathematical Analysis

Mathematical Analysis is a very broad discipline, which seems to have no boundary. It is the only discipline to give certainty to the human mind, but it demands from those who wish to use it an absolute logical rigor. Mathematical Analysis meets needs of mathematicians, of scientists and of engineers who are working at frontiers of their fields. They often have to use the modern Mathematical Analysis to formulate their particular problem. They often have to also modify some result of the modern Mathematical Analysis to be able to solve their particular problem. This work is an introduction to Mathematical Analysis, written for individual study. Don't need prerequisites for reading it. This work concerns classical real Mathematical Analysis, i.e. the study of real number field and the study (continuity, differentiation, integration) of real functions of one or several real variables. The theoretical analysis is complete and is accompanied by a wide range of detailed calculation examples. The strict autonomy, the rigour of exposure, the modern and sufficiently general conception make this book a useful basis as well for the challenging study of the modern Mathematical Analysis. However, it ranks at the elementary level because of the abundance, perhaps excessive, of explanations, clarifications and details. The treatise “Mathematical Analysis” written by Aldo Maceri, consists of the following 10 chapters: It analyzes the set theory, the set of real numbers, the set of complex numbers. It analyzes matrices, determinants, systems of linear equations, eigenvalue problem. It analyzes metric spaces and the particular case Rn. It analyzes numerical sequences, numerical series, sequences of k-tuples of real numbers. It analyzes limits of real functions of one real variable, limits of real functions of several real variables, continuity of real functions of one real variable, continuity of real functions of several real variables. It analyzes the differentiation of real functions of one real variable and the differentiation of real functions of several real variables. It analyzes definite integral, regular curves of Rn , curvilinear integral, differential forms, multiple integral, regular surfaces of Rn , surface integral. It analyzes sequences of functions, series of functions and in particular power series and trigonometric series. It lists all properties of all elementary functions and performs numerous detailed examples of calculations. It analyzes the ordinary differential equations.