The theory of differentiation in linear topological spaces

CONTENTSIntroductionChapter I. Differentiation along a subspace § 1. Definition of the first derivative § 2. Formal rules of differentiation § 3. The mean value theorem. Partial derivatives § 4. Applications to functionals defined on function spacesChapter II. Derivatives of higher order § 1. Derivatives, variations and differences of higher orders § 2. Some theorems of the differential calculus § 3. Polynomials. Taylor's formula § 4. Applications to functionals defined on function spacesChapter III. Primitives and integrals along curves in linear topological spaces § 1. Integration along curves in linear topological spaces § 2. Some theorems of the integral calculus § 3. The connection between differentiation and integration along curves in linear topological spaces § 4. Applications to functionals defined on function spacesReferences