An Introduction to Modern Analysis

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.

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

Autorentext

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.

Klappentext
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.

Zusammenfassung
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.

Inhalt
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.