(Ebook) Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals by Andrei Bourchtein, Ludmila Bourchtein ISBN 9781119303381, 9781661331337, 9781119303404, 9781119303428, 1119303389, 1661331335, 1119303400, 1119303427

(Ebook) Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals by Andrei Bourchtein, Ludmila Bourchtein ISBN 9781119303381, 9781661331337, 9781119303404, 9781119303428, 1119303389, 1661331335, 1119303400, 1119303427

Main subject categories: • Mathematical analysis • Mathematical analysis ‒ Problems, exercises • Calculus ‒ Problems, exercises • Sequences (Mathematics) • Functions • IntegralsA comprehensive and thorough analysis of concepts and results on uniform convergenceCounterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals presents counterexamples to false statements typically found within the study of mathematical analysis and calculus, all of which are related to uniform convergence. The book includes the convergence of sequences, series and families of functions, and proper and improper integrals depending on a parameter. The exposition is restricted to the main definitions and theorems in order to explore different versions (wrong and correct) of the fundamental concepts and results.The goal of the book is threefold. First, the authors provide a brief survey and discussion of principal results of the theory of uniform convergence in real analysis. Second, the book aims to help readers master the presented concepts and theorems, which are traditionally challenging and are sources of misunderstanding and confusion. Finally, this book illustrates how important mathematical tools such as counterexamples can be used in different situations.The features of the book include: An overview of important concepts and theorems on uniform convergenceWell-organized coverage of the majority of the topics on uniform convergence studied in analysis coursesAn original approach to the analysis of important results on uniform convergence based\ on counterexamplesAdditional exercises at varying levels of complexity for each topic covered in the bookA supplementary Instructor’s Solutions Manual containing complete solutions to all exercises, which is available via a companion website Counterexamples on Uniform Convergence: Sequences, Series, Functions, and Integrals is an appropriate reference and/or supplementary reading for upper-undergraduate and …