A brief guide to differential calculus for the preparation of la licence and l’agrégation. (Petit guide de calcul différentiel à l’usage de la licence et de l’agrégation.) (French) Zbl 0983.26001

Enseignement des Mathématiques (Cassini). 4. Paris: Cassini. xvi, 399 p. (1999).
This book is directed to students preparing for certain university examinations (la licence and 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 Normes; Différentielles; Inégalité de la moyenne; Point fixe; Fonctions inverses, implicites, et sous-variétés; Différentielles secondes; and Problèmes d’extremum. Each chapter opens with a brief section on the goals (objectifs) of the chapter, followed by a 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.


26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
00A05 Mathematics in general
26Bxx Functions of several variables