#
Elements of mathematics functions of a real variable : elementary theory
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The work ** Elements of mathematics functions of a real variable : elementary theory** represents a distinct intellectual or artistic creation found in **University of Oklahoma Libraries**. This resource is a combination of several types including: Work, Language Material, Books.

The Resource
Elements of mathematics functions of a real variable : elementary theory
Resource Information

The work

**Elements of mathematics functions of a real variable : elementary theory**represents a distinct intellectual or artistic creation found in**University of Oklahoma Libraries**. This resource is a combination of several types including: Work, Language Material, Books.- Label
- Elements of mathematics functions of a real variable : elementary theory

- Title remainder
- elementary theory

- Statement of responsibility
- by Nicolas Bourbaki ; translator, Philip Spain

- Language
- eng

- Summary
- This book is an English translation of the last French edition of Bourbaki?s Fonctions d'une Variable R?elle. 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

- Cataloging source
- GW5XE

- Dewey number
- 515/.8

- Index
- no index present

- LC call number
- QA331.5

- Literary form
- non fiction

- Nature of contents
- dictionaries

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