Functions of a Real Variable Elementary Theory
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)...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2004, 2004
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| Edition: | 1st ed. 2004 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I Derivatives
- § 1. First Derivative
- § 2. The Mean Value Theorem
- § 3. Derivatives of Higher Order
- § 4. Convex Functions of a Real Variable
- Exercises on §1
- Exercises on §2
- Exercises on §3
- Exercises on §4
- II Primitives and Integrals
- § 1. Primitives and Integrals
- § 2. Integrals Over Non-Compact Intervals
- § 3. Derivatives and Integrals of Functions Depending on a Parameter
- Exercises on §1
- Exercises on §2
- Exercises on §3
- III Elementary Functions
- § 1. Derivatives of the Exponential and Circular Functions
- § 2. Expansions of the Exponential and Circular Functions, and of the Functions Associated with Them
- Exercises on §1
- Exercises on §2
- Historical Note (Chapters I-II-III)
- IV Differential Equations
- § 1. Existence Theorems
- § 2. Linear Differential Equations
- Exercises on §1
- Exercises on §2
- Historical Note
- V Local Study of Functions
- § 1. Comparison of Functions on a Filtered Set
- § 2. Asymptotic Expansions
- § 3. Asymptotic Expansions of Functions of a Real Variable
- § 4. Application to Series with Positive Terms
- Exercises on §1
- Exercises on §3
- Exercises on §4
- Exercises on Appendix
- VI Generalized Taylor Expansions. Euler-Maclaurin Summation Formula
- § 1. Generalized Taylor Expansions
- § 2. Eulerian Expansions of the Trigonometric Functions and Bernoulli Numbers
- § 3. Bounds for the Remainder in the Euler-Maclaurin Summation Formula
- Exercises on §1
- Exercises on §2
- Exercises on §3
- Historical Note (Chapters V and VI)
- VII The Gamma Function
- § 1. The Gamma Function in the Real Domain
- § 2. The Gamma Function in the Complex Domain
- Exercises on §1
- Exercises on §2
- Historical Note
- Index of Notation