Real Analysis: Foundations and Functions of One Variable (Undergraduate Texts in Mathematics) by Miklós Laczkovich | (PDF) Free Download

Description

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.

User’s Reviews

Editorial Reviews: Review “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) From the Back Cover 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. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐E’ evidente la estrema chiarezza degli argomenti, in particolare delle dimostrazioni. Non vi sono ecessivi voli pindarici o esibizioni di sap3ere, per cui è didatticamente suggeribile.Il livello potrebbe essere leggermente innalzato, ma dipende dall’uso a cui è destinato. Per un primo corso di Analisi è adattissimo.L’Autore ha mediato, cosa non sempre riscontrabile in altri trattati, fra semplicità e rigore.The book is a fairly comprehensive introduction to real analysis.

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