¿Nicola Fusco is Full Professor of Mathematical Analysis at University of Naples "Federico II" and member of Accademia dei Lincei. He was awarded the 1994 Caccioppoli Prize of the Italian Mathematical Union (UMI). His research revolves around calculus of variations, regularity theory for partial differential equations, symmetrization problems and isoperimetric inequalities. He was visiting professor at Australian National University, Canberra; Carnegie Mellon University, Pittsburgh; Heriot-Watt University, Edinburgh; University of Oxford; Technische Universität, München and University of Jyväskylä.Paolo Marcellini is Emeritus Professor of Mathematical Analysis at University of Florence. His research interests are in calculus of variations and regularity theory for partial differential equations. He was Dean of the Faculty of Sciences at University of Florence and President of GNAMPA (National Group for Mathematical Analysis, Probability and their Applications). He was visiting professor at University of California, Berkeley; Collège de France, Paris; Institute for Advanced Study, Princeton; Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh; Mathematical Institute, University of Oxford; University of Texas, Austin and Institut Mittag-Leffler, Stockholm.

Carlo Sbordone is Emeritus Professor of Mathematical Analysis at University of Naples "Federico II", member of Accademia dei Lincei and was President of the Italian Mathematical Union (UMI). His research interests regard calculus of variations, Sobolev maps and function spaces. He was visiting professor at Scuola Normale Superiore in Pisa; Collège de France, Paris; Institut für Mathematik, Universität Zürich; Center for Nonlinear Analysis, Carnegie Mellon University, Pittsburgh; University of California, Berkeley; Mathematical Institute, University of Oxford and University of Helsinki.

Offers teachers the possibility to choose two different approaches a more basic and a more sofisticated one

Covers a wide variety of examples and applications

Addressed to students at a university level

1 Sequences and Series of Functions.- 2 Metric Spaces and Banach Spaces.- 3 Functions of Several Variables.- 4 Ordinary Differential Equations.- 5 Linear Differential Equations.- 6 Curves and Integrals Along Curves.- 7 Differential One-Forms.- 8 Multiple Integrals.- 9 The Lebesgue Integral.- 10 Surfaces and Surface Integrals.- 11 Implicit Functions.- 12 Manifold in Rn and k-Forms.