\input zb-basic \input zb-matheduc \iteman{ZMATH 2014b.00704} \itemau{Sondaz, Daniel} \itemti{Differentiable functions. L3, Masters, CAPES, Agregation. (Fonctions diff\'erentiables. L3, Masters, CAPES, Agr\'egation.)} \itemso{Bien Ma{\^\i}triser les Math\'ematiques. Toulouse: C\'epadu\`es-\'Editions (ISBN 978-2-36493-075-9/pbk). iv, 146~p. (2013).} \itemab This work is an introductory course on differential calculus in vector spaces. The following subjects are presented: 1. Introduction: Normed spaces, linear (multilinear) continuous applications, canonic isomorphisms, series in Banach algebras; 2. Differentiable applications: linearity, composition of differentiable applications, Leibniz formula, partial derivatives, derivatives of higher order. 3. Mean value theorems: Rolle's theorem, the fundamental theorem of integral calculus. 4. Sequences and series of differentiable applications, Schwarz' theorem. There is a set of exercises at the end of each chapter. \itemrv{Cristinel Mortici (T\^argovi\c{s}te)} \itemcc{I45 I65 I55} \itemut{vector spaces; normed spaces; linear applications; Banach spaces; series; differentials; mean theorems} \itemli{} \end