
06213222
b
2014b.00704
Sondaz, Daniel
Differentiable functions. L3, Masters, CAPES, Agregation. (Fonctions diff\'erentiables. L3, Masters, CAPES, Agr\'egation.)
Bien Ma{\^\i}triser les Math\'ematiques. Toulouse: C\'epadu\`es\'Editions (ISBN 9782364930759/pbk). iv, 146~p. (2013).
2013
Toulouse: C\'epadu\`es\'Editions
FR
I45
I65
I55
vector spaces
normed spaces
linear applications
Banach spaces
series
differentials
mean theorems
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.
Cristinel Mortici (T\^argovi\c{s}te)