Don’t miss it: Get 40% off Education & Linguistics books! Save through November 30, 2018.

Elements of Mathematics

Functions of a Real Variable

Elementary Theory

Authors: Bourbaki, N.

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-642-59315-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA in USD
  • ISBN 978-3-540-65340-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-3-642-63932-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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 the study 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.

Reviews

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)


Table of contents (8 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-642-59315-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA in USD
  • ISBN 978-3-540-65340-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.99
price for USA in USD
  • ISBN 978-3-642-63932-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Functions of a Real Variable
Book Subtitle
Elementary Theory
Authors
Translated by
Spain, P.
Copyright
2004
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-59315-4
DOI
10.1007/978-3-642-59315-4
Hardcover ISBN
978-3-540-65340-0
Softcover ISBN
978-3-642-63932-6
Edition Number
1
Number of Pages
XIV, 338
Additional Information
Original French edition published by Hermann, Paris, 1976 and Nicolas Bourbaki, 1982
Topics