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AuthorGodement, Roger. author
TitleAnalysis I [electronic resource] : Convergence, Elementary functions / by Roger Godement
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004
Connect tohttp://dx.doi.org/10.1007/978-3-642-18491-8
Descript XXI, 430 p. 1 illus. online resource

SUMMARY

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


CONTENT

I Sets and Functions -- ยง1. Set Theory -- ยง2. The logic of logicians -- II - Convergence: Discrete variables -- ยง1. Convergent sequences and series -- ยง2. Absolutely convergent series -- ยง3. First concepts of analytic functions -- III - Convergence: Continuous variables -- ยง1. The intermediate value theorem -- ยง2. Uniform convergence -- ยง3. Bolzano-Weierstrass and Cauchyโ{128}{153}s criterion -- ยง4. Differentiable functions -- ยง5. Differentiable functions of several variables -- Appendix to Chapter III -- 1 - Cartesian spaces and general metric spaces -- 2 - Open and closed sets -- 3 - Limits and Cauchyโ{128}{153}s criterion in a metric space; complete spaces -- 4 - Continuous functions -- 5 - Absolutely convergent series in a Banach space -- 6 - Continuous linear maps -- 7 - Compact spaces -- 8 - Topological spaces -- IV Powers, Exponentials, Logarithms, Trigonometric Functions -- ยง1. Direct construction -- ยง2. Series expansions -- ยง3. Infinite products -- ยง4. The topology of the functions Arg(z) and Log z


Mathematics Mathematical analysis Analysis (Mathematics) Functions of real variables Mathematics Analysis Real Functions



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