Analisi complexa

The theory of complex variable functions is a central topic of mathematical analysis with links to several branches of mathematics. A knowledge of the foundations of this theory is necessary for anyone who wants to have a general mathematical background or who wants to use mathematics in the applied sciences or in technology. The book presents the basic aspects of the theory of analytic functions of complex variables while seeking points of contact with other parts of analysis. This approach means that the book brings several novelties with respect to the current literature on the subject. Some of the issues addressed are: the real version of the Cauchy-Goursat theorem, the theorems of vector calculus with weak hypotheses of regularity, an approach to the concept of holomorphy for functions of real variables, Green's formula with multiplicities, Cauchy's theorem for locally exact forms, the parallel study of the Poisson equation and the Cauchy-Riemannian inhomogènies equations, the relation between the Green's function and the conformal representation, the connection between the solutions of the Poisson equation and the zeros of holomorphic functions, and the Shannon-Whittaker theorem of information theory. To read the book, which can be used as a textbook for multilevel complex variable courses and as a reference book, it is sufficient to know the topology of the plan and differential calculus in order to be able to read it.