Analyse mathématique II. Calcul différentiel et intégral, séries de Fourier, fonctions holomorphes: Differential and Integral Calculus, Fourier Series by Roger GodementAnalyse mathématique II. Calcul différentiel et intégral, séries de Fourier, fonctions holomorphes: Differential and Integral Calculus, Fourier Series by Roger Godement

Analyse mathématique II. Calcul différentiel et intégral, séries de Fourier, fonctions holomorphes…

byRoger GodementTranslated byP. Spain

Paperback | October 19, 2005

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Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major...
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Title:Analyse mathématique II. Calcul différentiel et intégral, séries de Fourier, fonctions holomorphes…Format:PaperbackDimensions:455 pagesPublished:October 19, 2005Publisher:Springer Berlin HeidelbergLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3540209212

ISBN - 13:9783540209218

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Table of Contents

Differential and Integral Calculus.- The Riemann Integral.- Integrability Conditions.- The "Fundamental Theorem" (FT).- Integration by parts.- Taylor's Formula.- The change of variable formula.- Generalised Riemann integrals.- Approximation Theorems.- Radon measures in ? or ?.- Schwartz distributions.- Asymptotic Analysis.- Truncated expansions.- Summation formulae.- Harmonic Analysis and Holomorphic Functions.- Analysis on the unit circle.- Elementary theorems on Fourier series.- Dirichlet's method.- Analytic and holomorphic functions.- Harmonic functions and Fourier series.- From Fourier series to integrals.

Editorial Reviews

From the reviews of the original French edition:"... The content is quite classical ... [...] The treatment is less classical: precise although unpedantic (rather far from the definition-theorem-corollary-style), it contains many interesting commentaries of epistemological, pedagogical, historical and even political nature. [...] The author gives frequent interesting hints on recent developments of mathematics connected to the concepts which are introduced. The Introduction also contains comments that are very unusual in a book on mathematical analysis, going from pedagogy to critique of the French scientific-military-industrial complex, but the sequence of ideas is introduced in such a way that readers are less surprised than they might be.J. Mawhin in Zentralblatt Mathematik (1999)