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Analysis. Foundations, techniques, evolution. (Analyse. Fondements, techniques, évolution.) (French) Zbl 0759.26004
Bruxelles: De Boeck Université. iv, 808 p. (1992).
The book is a continuation of author’s “Introduction à l’analyse” (1979; Zbl 0444.26002). It is designed for students in mathematics and physics of the Catholic University in Louvain. The material presented in this book covers the basics of: continuity and differentiation of functions \(f: \mathbb{R}^ n\to \mathbb{R}^ m\) and of complex functions \(f: \mathbb{C}\to \mathbb{C}\), the integration theory, the general theory of sequences and series, the theory of trigonometric and power series, vector analysis including Stokes’ theorem on chains, an introduction to the theory of Banach spaces, and the theory of differential equations. The integration described in this book is the Denjoy-Perron integration introduced by the Henstock-Kurzweil method. Each of the 17 chapters contains some exercises and very interesting bibliographical hints. At the end of the book there is a valuable Historical Index containing a lot of biographical informations.

MSC:
26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
30-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable
34-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations
28-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to measure and integration
46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
Keywords:
textbook; analysis
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