This book shows hundreds of guided problems, with very detailed explanation on how to go about finding the right argument. This is the second of a 3-book project, the first book being already published (Calculus Problems, UNITEXT 101). The style, therefore, follows closely that of the aforementioned volume, with improvements in the graphic packaging, due to updating of the used software and the inclusion of further graphical packages. Each chapter contains a summary of the relevant definitions and theorems, a section with worked problems and a section on suggested exercises with solutions. This second book includes an elementary but thorough introduction to basic topology of Euclidean spaces and then focusses on of functions of several variables and on multiple integrals, sequences and series of functions. It is addressed to UG students based both in EU and USA.

Autorentext

Marco Baronti was born and grew up in Genova (Italy) where he got his Laurea in Mathematics in 1979. He won a scholarship from the C.N.R. in Genoa and subsequently a research grant from I.N.D.A.M. at the University of Bologna. In 1984 he became a researcher at the University of Parma and then associate professor in 1987 at the University of Ancona. In 1991 he returned to Genova, where he presently holds a position as associate professor in Mathematical Analysis. Enrico Calcagno was born and grew up in Genova (Italy) where he got his Laurea in Mathematics. He started his tenured position at the University of Genova in 1981. His scientific interests are mainly in Differential Geometry and Algebraic Topology. He has been involved for about forty years in a wide teaching activity for mathematicians, physicists, chemists, biologists, computer scientists, geologists and engineers. Filippo De Mari was born and grew up in Genova (Italy) where he got his Laurea in Mathematics in 1983. He obtained his Ph.D. in 1987 from Washington University in St. Louis (USA) and then held two post-doctoral positions in Bremen (Germany) 1988-89 and Torino (Italy) 1990-92. In 1992 he returned to Genova, where he presently holds a position as full professor in Mathematical Analysis. Robertus van der Putten was born and grew up in Sanremo (Italy). He got his Laurea in Mathematics in 1984 at the University of Genova. He obtained his Ph.D. in 1989 from the University of Milan. Since 1990, he is a researcher in Mathematical Analysis at the University of Genoa. His scientific interests are mainly in the Calculus of Variations. His main scientific interests may be grouped into following main areas. The first concerns the properties of energy functional integrals in the setting of nonlinear elasticity and the existence of the minimum in Sobolev spaces.