Welcome to Real Analysis: Continuity and Calculus, Distance and Dynamics (AMS/MAA Textbooks) - Softcover

Benjamin B. Kennedy (author)

Softcover

ISBN 10: 1470464543 ISBN 13: 9781470464547

Publisher: American Mathematical Society, 2022

Synopsis

Welcome to Real Analysis is designed for use in an introductory undergraduate course in real analysis. Much of the development is in the setting of the general metric space. The book makes substantial use not only of the real line and $n$-dimensional Euclidean space, but also sequence and function spaces. Proving and extending results from single-variable calculus provides motivation throughout. The more abstract ideas come to life in meaningful and accessible applications. For example, the contraction mapping principle is used to prove an existence and uniqueness theorem for solutions of ordinary differential equations and the existence of certain fractals; the continuity of the integration operator on the space of continuous functions on a compact interval paves the way for some results about power series.

The exposition is exceedingly clear and well-motivated. There are a wide variety of exercises and many pedagogical innovations. For example, each chapter includes Reading Questions so that students can check their understanding. In addition to the standard material in a first real analysis course, the book contains two concluding chapters on dynamical systems and fractals as an illustration of the power of the theory developed.

About this title

About the Author

Benjamin B. Kennedy, Gettysburg College, PA.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2022
• Language: English
• ISBN 10: 1470464543
• ISBN 13: 9781470464547
• Binding: Paperback
• Number of pages: 370