A brief guide to differential calculus for the preparation of la licence and l'agrégation (Q2753152)

This book is directed to students preparing for certain university examinations (\textit{la licence} and \textit{l'agrégation}) in France. The subject matter is the differential calculus of functions from \({\mathbb R}^m\) to \({\mathbb R}^n\) at a rather sophisticated level. The seven chapter titles are \textit{Normes; Différentielles; Inégalité de la moyenne; Point fixe; Fonctions inverses, implicites, et sous-variétés; Différentielles secondes}; and \textit{Problèmes d'extremum}. Each chapter opens with a brief section on the goals (\textit{objectifs}) of the chapter, followed by a \textit{panorama du cours} stating the principal definitions and theorems (without proofs, but with references) covering typically several pages. The remainder (and the bulk) of the chapter is then devoted to examples and exercises with solutions. There is a table of contents, a table of notations used, a bibliography of 50 items, and an index.