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Real Analysis

Foundations and Functions of One Variable

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Publisher:

Springer

Pages: 483
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Recommend to library


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Paperback - 9781493942220

23 August 2016

€46.79

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Hardcover - 9781493927654

09 October 2015

€62.39

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Ebook - 9781493927661

08 October 2015

€35.69

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Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples...

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Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated.

In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.

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Includes insightful historical remarks regarding real analysis

Presents core ideas of analysis "as a way of thinking" as opposed to "a body of facts"

Explains how and why ideas arise, then how they evolve to the mature notions of real analysis

A Short Historical Introduction
Basic Concepts
Real Numbers
Infinite Sequences I
Infinite Sequences II
Infinite Sequences III
Rudiments of Infinite Series
Countable Sets
Real Valued Functions of One Variable
Continuity and Limits of Functions
Various Important Classes of Functions (Elementary Functions)
Differentiation
Applications of Differentiation
The Definite Integral
Integration
Applications of Integration
Functions of Bounded Variation
The Stieltjes Integral
The Improper Integral.

“This book is written to be accessible to the competent university student. … The book is consistent in addressing the classical analysis of real functions of one real variable, and it can serve as an introduction to monographs of complex functions, functional analysis and differential equations, upon which it touches occasionally. It can also serve as an introduction to Lebesgue integration or to generalized functions, which are not mentioned.” (Luis Manuel Braga de Costa Campos, Mathematical Reviews, December, 2016)
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Miklós Laczkovich is Professor of Mathematics at Eötvös Loránd University and the University College London, and was awarded the Ostrowski Prize in 1993 and the Széchenyi Prize in 1998. Vera T. Sós is a Research Fellow at the Alfréd Rényi Institute of Mathematics, and was awarded the Széchenyi Prize in 1997.

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Miklós Laczkovich is Professor of Mathematics at Eötvös Loránd University and the University College London, and was awarded the Ostrowski Prize in 1993 and the Széchenyi Prize in 1998. Vera T. Sós is a Research Fellow at the Alfréd Rényi Institute of Mathematics, and was awarded the Széchenyi Prize in 1997.

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