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Analysis I: Convergence, Elementary Functions

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Analysis I: Convergence, Elementary Functions Cover

 

Synopses & Reviews

Publisher Comments:

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.

Table of Contents

Preface.- Sets and Functions: Set Theory; The Logic of Logicians.- Convergence: Discrete variables: Convergent sequences and series; Absolutely convergent series; First concepts of analytic functions.- Convergence: Continuous variables: The intermediate value theorem; Uniform convergence; Bolzano-Weierstrass and Cauchy's criterion; Differentiable functions; Differentiable functions of several variables.- Powers, Exponentials, Logarithms, Trigonometric Functions: Direct construction; Series expansion; Infinite products; The topology of the functions arg(z) and Log z.- Index.

Product Details

ISBN:
9783540059233
Translator:
Spain, P.
Publisher:
Springer
Translator:
Spain, P.
Author:
Spain, P.
Author:
Godement, Roger
Location:
Berlin
Subject:
Functions
Subject:
Functional Analysis
Subject:
Infinity
Subject:
Convergence
Subject:
Variables
Subject:
Mathematics : Functional Analysis
Subject:
Mathematical Analysis
Subject:
Fourier
Subject:
Analytic functions
Subject:
derivations
Subject:
Integrals
Subject:
Real functions
Copyright:
Edition Description:
Softcover reprint of the original 1st ed. 2004
Series:
Universitext
Series Volume:
no. 95
Publication Date:
20040122
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
451
Dimensions:
235 x 155 mm 1410 gr

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Related Subjects

History and Social Science » Economics » General
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