Chaire d'analyse mathématique et applications CAA

"The Pullback Equation for Differential Forms"

An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem under considersation is therefore to find a map so that it satisfies the pullback equation

The Pullback Equation for Differential forms is a self contained and concise monograph intended for both geometers and analysts. The book can serve as a valuable reference for researchers or a supplemental text for graduate students.

"Direct Methods in the calculus of Variations" (2ème édition)

This book studies vectorial problems in the calculus of variations and quasiconvex analysis. It is a new edition of the earlier book published in 1989 and has been updated with some new material and examples added. This monograph will appeal to researchers and graduate students in mathematics and engineering.

"Direct Methods in the Calculus of Variations" (1ère édition épuisée)

"Analyse avancée pour ingénieurs" (2ème édition)

La matière traitée dans cet ouvrage comprend l’analyse vectorielle (théorèmes de Green, de la divergence, de Stokes), l'analyse complexe (fonctions holomorphes, équations de Cauchy-Riemann, séries de Laurent, théorème des résidus, applications conformes) ainsi que l'analyse de Fourier (séries de Fourier, transformées de Fourier, transformées de Laplace, applications aux équations différentielles). Les définitions et les théorèmes principaux sont présentés sous forme d’aide-mémoire, énoncés avec clarté et précision sans commentaires. De très nombreux exemples significatifs sont ensuite discutés en détail. Enfin, de nombreux exercices corrigés sont proposés intégralement.

"Mathematical Analysis for Engineers" (version anglaise)

This book follows an advanced course in analysis (vector analysis, complex analysis and Fourier analysis) for engineering students, but can also be useful, as a complement to a more theoretical course, to mathematics and physics students.

The first three parts of the book represent the theoretical aspect and are independent of each other. The fourth part gives detailed solutions to all exercises that are proposed in the first three parts.

"Introduction to the Calculus of Variations" (2ème édition - version anglaise)

The calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.
In this new edition, the chapter on regularity has been significantly expanded and 27 new exercises have been added. The book, containing a total of 103 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.

"Introduction to the Calculus of Variations" (version anglaise)

This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist — mathematicians, physicists, engineers, students or researchers — in discovering the subjects most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.
The book, containing more than seventy exercises with detailed solutions, is well designed for a course both at the undergraduate and graduate levels.

"Introduction au Calcul des Variations " (version française - épuisée)

"Implicit Partial Differential Equations"

Provides a self-contained development of the new kind of differential equations… Includes many examples helpful in understanding the theory and is well [and] clearly written.

"Weak Continuity and Weak Lower Semicontinuity of Non-Linear Functionals"

This book is concerned with the theory of compensated compactness with applications to partial differential equations and the calculus of variations.

E-book only available.

"Calculus of Variations and Non-Linear Partial Differential Equations "

This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo.
Edited by B. Dacorogna and P. Marcellini.