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An Introduction to Modern Analysis de Vicente Montesinos

An Introduction to Modern Analysis

Autor Vicente Montesinos, Peter Zizler, Václav Zizler
en Limba Engleză Hardback – 13 mai 2015
Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.   
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Specificații

ISBN-13: 9783319124803
ISBN-10: 3319124803
Pagini: 861
Ilustrații: XXXI, 863 p. 339 illus., 5 illus. in color.
Dimensiuni: 155 x 235 x 53 mm
Greutate: 1.42 kg
Ediția:2015
Editura: Springer International Publishing
Colecția Springer
Locul publicării:Cham, Switzerland

Public țintă

Graduate

Cuprins

Real​​ ​Numbers: The Basics.- Sequences and Series.- Measure.- Functions.- Function Convergence.- Metric Spaces.- Integration.- Convex Functions.- Fourier Series.- Basics on Descriptive Statistics.- Excursion to Functional Analysis.- Appendices.  

Recenzii

“The book under review … published as a 21st century introduction to modern analysis, is closer in spirit to Dieudonné’s text, but there are substantial differences. … Instructors and students will no doubt relish this treasure trove of problems – the exercises and hints account for a quarter of the book’s 863 pages! … When all has been said and done, the authors must be congratulated on writing a useful textbook that includes plenty of bonuses for both students and instructors.” (Tushar Das, MAA Reviews, maa.org, June, 2016)
“This book presents a widely treated approach to the foundations of modern analysis. … recommended to teachers and researchers, who will find here a new view of interrelations between various phenomena in analysis where topological facts and powerful methods of functional analysis play an essential role. … comments by the authors describing the exact meaning of notions and ideas, together with a host of exercises showing the power of theory applicable in‘practical’ problems, make this book useful and modern.” (Marek Balcerzak, Mathematical Reviews, January, 2016)
“This monograph presents a combined introduction to both elementary mathematical analysis and real analysis. … this monograph covers a wide range of topics and can be warmly recommended to everyone in need of a text- and reference book in real analysis.” (Dirk Werner, zbMATH 1321.26001, 2015)

Notă biografică

Vincente Montesinos is a Corresponding Member of the Spanish Royal Academy of Sciences, and is a Professor at the Universidad Politécnica de Valencia, Spain.
Peter Zizler is an Associate Professor at Mount Royal University in Calgary, Canada.

Václav Zizler is the former Head of Research at the Mathematical Institute of the Czech Academy of Sciences, and previously served as Faculty Lecturer at the University of Alberta, and Professor of Mathematics at the University of Alberta, Edmonton. In 2001, his book Functional Analysis and Infinite Dimensional Geometry was named university textbook of the year by the Czech Minister of Education.   

Textul de pe ultima copertă

Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.

Caracteristici

Carefully examines the main principles, results and techniques in advanced undergraduate real analysis courses Fully self-contained, it presents proofs and an ample amount of nontrivial exercises with hints to help to master the subject Provides links to several areas of modern analysis like Functional analysis, Fourier analysis and Nonlinear analysis at the graduate level Individual chapters may be downloaded separately for professors interested in teaching a particular topic in-depth Includes supplementary material: sn.pub/extras