\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