Overview
- Unique owing to its conciseness and brevity of the subject matter
- Contains topics unusual in other texts at this level, such as the proof of the prime number theorem
- Covers polar coordinates and the divergence theorem, applying these to derivation of Cauchy's integral formula
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Table of contents (6 chapters)
Keywords
About this book
Among the unusual features of this book is the treatment of analytic function theory as an application of ideas and results in real analysis. For instance, Cauchy's integral formula for analytic functions is derived as an application of the divergence theorem. The last section of each chapter is devoted to exercises that should be viewed as an integral part of the text.
A Concise Introduction to Analysis should appeal to upper level undergraduate mathematics students, graduate students in fields where mathematics is used, as well as to those wishing to supplement their mathematical education on their own. Wherever possible, an attempt has been made to give interesting examples that demonstrate how the ideas are used and why it is important to have a rigorous grasp of them.
Reviews
“The uniqueness of the order and choice of topics makes the book an excellent resource and/or supplement to an introductory analysis course. Summing Up: Highly recommended. Upper-division undergraduates, graduate students, and researchers/faculty.” (J. T. Zerger, Choice, Vol. 54 (1), September, 2016)
“Goal of this book is to establish the principles of mathematical analysis both for functions of real variables and for functions of a complex variable in the shortest possible way. … book can be read and understood without resorting to any external reference since the author provides detailed proofs of all results. … in each chapter one can find several examples of the theory discussed as well as a list of working exercises that will be useful to the reader.” (Julià Cufí, zbMATH 1337.26001, 2016)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: A Concise Introduction to Analysis
Authors: Daniel W. Stroock
DOI: https://doi.org/10.1007/978-3-319-24469-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2015
Softcover ISBN: 978-3-319-24467-9Published: 10 November 2015
eBook ISBN: 978-3-319-24469-3Published: 31 October 2015
Edition Number: 1
Number of Pages: XII, 218
Topics: Functional Analysis, Real Functions, Functions of a Complex Variable, Sequences, Series, Summability, Integral Equations