An Introduction to Modern 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 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.