| 书目名称 | Functions of a Real Variable | | 副标题 | Elementary Theory | | 编辑 | Nicolas Bourbaki,Philip Spain | | 视频video | | | 概述 | Includes supplementary material: | | 图书封面 |  | | 描述 | .This book is an English translation of the last French edition of Bourbaki’s .Fonctions d‘une Variable Réelle...The first chapter is devoted to derivatives, Taylor expansions, the finite increments theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to thestudy of the Gamma function on the real line as well as on the complex plane...Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanc | | 出版日期 | Book 2004 | | 关键词 | MSC (2000): 26xx; YellowSale2006; calculus; derivatives; gamma function; integrals; real functions; Convexi | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-59315-4 | | isbn_softcover | 978-3-642-63932-6 | | isbn_ebook | 978-3-642-59315-4 | | copyright | Springer-Verlag Berlin Heidelberg 2004 |
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发表于 2025-3-21 16:39:24
