Real Analysis : Foundations and Functions of One Variable / by Miklós Laczkovich, Vera T. Sós.

Format:

Book

Author/Creator:

Laczkovich, Miklós, Author.

Sós, Vera T., Author.

Series:

Undergraduate Texts in Mathematics, 0172-6056

Language:

English

Subjects (All):

Mathematical analysis.

Analysis (Mathematics).

Analysis.

Local Subjects:

Analysis.

Physical Description:

1 online resource (X, 483 p. 94 illus.)

Edition:

1st ed. 2015.

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 2015.

Language Note:

English

Summary:

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 students' mathematical intuition. The modular organization of the book makes it adaptable for either semester or year-long introductory courses, while the wealth of material allows for it to be used at various levels of student sophistication in all programs where analysis is a part of the curriculum, including teachers' education. 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. There are frequent hints and occasional complete solutions provided for the more challenging exercises making it an ideal choice for independent study. The book includes a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a rigorous study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous historical notes and applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of mathematical analysis.

Contents:

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

Description based on publisher supplied metadata and other sources.

ISBN:

1-4939-2766-3

OCLC:

1076262794