Analysis I : Convergence, Elementary functions /
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 nonl...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg :
Springer Berlin Heidelberg,
2004.
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| Series: | Universitext,
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| Online Access: | Connect to the full text of this electronic book |
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.