A Course in Real Analysis (Textbooks in Mathematics) - Hardcover

Junghenn, Hugo D.

Hardcover

ISBN 10: 1041045638 ISBN 13: 9781041045632

Publisher: Chapman and Hall/CRC, 2026

Synopsis

Now in its second editon, A Course in Real Analysis provides a rigorous treatment of the foundations of differential and integral calculus. It proceeds gradually from an axiomatic characterization of the real number system to the study of differentiation and integration on m-dimensional surfaces. Proofs of theorems are given in detail, and many examples are provided to illustrate the concepts expressed in the theorems.

The book consists of three parts. Part I treats the calculus of functions of one variable. Traditional topics such as sequences, continuity, differentiability, Riemann integrability, numerical series, and the convergence of sequences and series of functions are covered. Optional sections on Stirling’s formula, Riemann–Stieltjes integration, and other topics are also included.

The second part focuses on functions of several variables. It introduces the topological ideas (such as compact and connected sets) needed to describe analytical properties of multivariable functions. This part also discusses differentiability and integrability of multivariable functions, and it develops the theory of differential forms on surfaces in Rn.

Many proofs and explanations in the first edition have been revised, and details have been added to clarify the exposition. Part III contains the Appendices on set theory and linear algebra, as well as solutions to some of the exercises are offered, while a full Solutions Manual contains complete solutions to all exercises for qualifying instructors.

About this title

About the Author

Hugo D. Junghenn is emeritus professor of mathematics at The George Washington University. He has published numerous journal articles and is the author of several books, including Option Valuation: A First Course in Financial Mathematics; Principles of Analysis; and Discrete Mathematics with Coding. His research interests include functional analysis, semigroups, and probability.

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2026
• Language: English
• ISBN 10: 1041045638
• ISBN 13: 9781041045632
• Binding: Hardcover
• Edition number: 2
• Number of pages: 591