An Introduction to Real Analysis presents the concepts of real analysis and highlights the problems which necessitate the introduction of these concepts. Topics range from sets, relations, and functions to numbers, sequences, series, derivatives, and the Riemann integral.
This volume begins with an introduction to some of the problems which are met in the use of numbers for measuring, and which provide motivation for the creation of real analysis. Attention then turns to real numbers that are built up from natural numbers, with emphasis on integers, rationals, and irrationals. The chapters that follow explore the conditions under which sequences have limits and derive the limits of many important sequences, along with functions of a real variable, Rolle's theorem and the nature of the derivative, and the theory of infinite series and how the concepts may be applied to decimal representation. The book also discusses some important functions and expansions before concluding with a chapter on the Riemann integral and the problem of area and its measurement. Throughout the text the stress has been upon concepts and interesting results rather than upon techniques. Each chapter contains exercises meant to facilitate understanding of the subject matter.
This book is intended for students in colleges of education and others with similar needs.
To view this DRM protected ebook on your desktop or laptop you will need to have Adobe Digital Editions installed. It is a free software. We also strongly recommend that you sign up for an AdobeID at the Adobe website. For more details please see FAQ 1&2. To view this ebook on an iPhone, iPad or Android mobile device you will need the Adobe Digital Editions app, or BlueFire Reader or Txtr app. These are free, too. For more details see this article.
|Size: ||19.6 MB|
|Date published: || 2014|
|ISBN: ||9781483158969 (DRM-PDF)|
|Read Aloud: ||not allowed|