Miklós Laczkovich, Vera T. Sós

Real Analysis (eBook, PDF)

Foundations and Functions of One Variable

• Format: PDF

Produktbeschreibung

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 groundingin 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.

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Produktdetails

• Verlag: Springer-Verlag GmbH
• Seitenzahl: 483
• Erscheinungstermin: 8. Oktober 2015
• Englisch
• ISBN-13: 9781493927661
• Artikelnr.: 44617831

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

"This book develops a thorough treatment of multivariate derivatives, viewing them both as linear transformations and as partial derivatives. ... The book is consistent in addressing the classical analysis of real functions of several variables. This volume will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis." (Teodora-Liliana Radulescu, zbMATH 1407.26001, 2019)

"The explicit intent of the authors is to present material gradually, and to develop precision based on intuition with the help of well-designed examples. The book contains 600 exercises. In my opinion this interesting book represents an alternative viewpoint in real analysis." (Zbigniew Grande, Mathematical Reviews, August, 2018)