Functions of a Real Variable : Elementary Theory
Language: English
Published by Springer Berlin Heidelberg, 2014
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
AbeBooks seller since August 14, 2006
Condition: New
US$ 163.05
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Druck auf Anfrage Neuware - Printed after ordering - 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 advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc. …
Seller Inventory # 9783642639326
- Title
- Functions of a Real Variable : Elementary Theory
- Author
- N. Bourbaki
- Publisher
- Springer Berlin Heidelberg
- Publication year
- 2014
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 3642639321
- ISBN 13
- 9783642639326
- Item weight
- 540 grams
- Dimensions
- 235x155x20 mm
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 advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependence on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc.
"Synopsis" may belong to another edition of this title.
Review
From the reviews:
"Nicolas Bourbaki is the name given to a collaboration of mainly French mathematicians who wrote a series of textbooks that started from basics and aimed to present a complete picture of all essential mathematics. ... The Elements of Mathematics series is the result of this project. ... The translation is true to the original. ... should be part of any good library of mathematics books." (Partrick Quill, The Mathematical Gazette, March, 2005)
"The book under review is the latest installment in the translation into English of the voluminous Bourbaki exercise. ... Respectable mathematics libraries should have this book on their shelves. ... the book may be judged as an unqualified intellectual success and the publisher and the translator are to be congratulated on making it available in English." (Barry D.Hughes, The Australian Mathematical Society Gazette, Vol. 43 (1), 2005)
"About the title" may belong to another edition of this title.
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