Synopses & Reviews
This self-contained text, suitable for advanced undergraduates, provides an extensive introduction to mathematical analysis, from the fundamentals to more advanced material. It begins with the properties of the real numbers and continues with a rigorous treatment of sequences, series, metric spaces, and calculus in one variable. Further subjects include Lebesgue measure and integration on the line, Fourier analysis, and differential equations. In addition to this core material, the book includes a number of interesting applications of the subject matter to areas both within and outside the field of mathematics. The aim throughout is to strike a balance between being too austere or too sketchy, and being so detailed as to obscure the essential ideas. A large number of examples and 500 exercises allow the reader to test understanding, practise mathematical exposition and provide a window into further topics.
Review
"Analysis: An Introduction is most appropriate for a undergraduate who has already grappled with the main ideas from real analysis, and who is looking for a succinct, well-written treatise that connects these concepts to some of their most powerful applications. Beals' book has the potential to serve this audience very well indeed."
MAA Reviews, Christopher Hammond, Connecticut College
Synopsis
Consisting of an extensive introduction to proof and mathematical logic based on the author's considerable teaching experience, this book covers the basic core topics and explores a number of other interesting applications within mathematics as well. Many remarks, examples and nearly 500 exercises are included to provide motivation, test understanding, help practice mathematical writing and uncover additional topics.
Synopsis
This book is a text on mathematical analysis suitable for graduate students and advanced undergraduates. It provides an extensive introduction to proof and to rigorous mathematical thinking. It contains many remarks and examples and 500 exercises designed to provide motivation, test understanding, help practice mathematical writing and explore additional topics.
Synopsis
This book is an extensive introductory text to mathematical analysis for graduate students and advanced undergraduates, complete with 500 exercises and numerous examples.
About the Author
Richard Beals is James E. English Professor of Mathematics at Yale University. He has also served as Professor at the University of Chicago and visiting Professor at the University of Paris, Orsay. He is the author of over 100 research papers and monographs in partial differential equations, differential equations, functional analysis, inverse problems, mathematical physics, mathematical psychology and mathematical economics.