This superb and self-contained work is an introductory presentation of basic ideas, structures, and results of differential and integral calculus for functions of several variables. The wide range of topics covered include the differential calculus of several variables, including differential calculus of Banach spaces, the relevant results of Lebesgue integration theory, and systems and stability of ordinary differential equations. An appendix highlights important mathematicians and other scientists whose contributions have made a great impact on the development of theories in analysis. This text motivates the study of the analysis of several variables with examples, observations, exercises, and illustrations. It may be used in the classroom setting or for self-study by advanced undergraduate and graduate students and as a valuable reference for researchers in mathematics, physics, and engineering.

The impact of optimization methods in electromagnetism has been much less than in mechanical engineering and particularly the solution of inverse problems in structural mechanics. This book addresses this omission: it will serve as a guide to the theory as well as the computer implementation of solutions. It is self-contained covering all the mathematical theory necessary.

The formulation of Maxwell’s equations completely defines the connection between the electric field and the magnetic field, definitively unifying electricity and magnetism and at the same time providing a theoretical synthesis of all the experimental phenomena connected to these areas. In his revolutionary 1864 memoir where J.C. Maxwell presented his equations, he cites a handful of scientists, which were at the basis of his Theory. This book, in its first part, presents an insight on all these latter scientists, reconstructing the scientific network behind Maxwell’s unification and, in the second part, focuses on the Italians in such a network: Ottaviano Fabrizio Mossotti and Riccardo Felici, with a further insight on the connections between Maxwell and Italy and, in particular, Tuscany.