Mathematical analysis II: Differential calculus, Fourier series, holomorphic functions. (Analyse mathématique II: Calcul différentiel et intégral, séries de Fourier, fonctions holomorphes.) (French) Zbl 0908.26002

Godement, Roger

Berlin: Springer. viii, 474 p. (1998).

[See also the review of the first volume above.]
This second volume of Godement’s Analyse mathématique is devoted to integral calculus (Riemann integral with glimpses on Lebesgue integral, Radon measure and Schwartz distributions), asymptotic expansions, harmonic analysis and holomorphic functions. The style is similar to that of volume I, and the book concludes with a polemic postface of almost one hundred pages on Science, technology and weapons, a mixture of generous ideas and local French politics, built around the famous discussion of Fourier and Jacobi about applied and pure mathematics. In contrast to the always appreciated scientific quotations, some of them occurring in this postface and throughout the book may be less appreciated.
The reading of this book is recommended to mathematicians both for the inspiring style and taste of the presentation of the topics and for the unusual character of the comments: we learn, among deeper things, that Marshall Stone not only gave a new proof of Weierstrass, but had a definite taste for French gastronomy, and that Marcel Riesz was not only Frederic’s brother, but had a strong taste for aquavit.
This book, a definitive testimony of fact that mathematics is before all a human science, is an excellent antidote to the industrial character of a large part of the production of mathematical monographs.

Reviewer: J.Mawhin (Louvain-La-Neuve)

MSC:

26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
00A05	Mathematics in general
42-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to harmonic analysis on Euclidean spaces
30-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functions of a complex variable

Keywords:

mathematical analysis

Citations:

Zbl 0908.26001