Overview
- Recognises and addresses student difficulties
- A selection of special topics (“nuggets”) sets it apart from existing texts
- Includes a large number of exercises with hints
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers, and the Gamma function.
Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.
Reviews
“Fundamental Mathematical Analysis is a complete and wide-ranging text that offers a rigorous introduction to the analysis of real-valued, single-variable functions. This text is well organized and peppered with insight and mathematical nuggets. … I found it an enjoyable read and am confident that a well-prepared student would gain a tremendous deal from this text.” (John Ross, MAA Reviews, May 29, 2021)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Fundamental Mathematical Analysis
Authors: Robert Magnus
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-3-030-46321-2
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 2020
Softcover ISBN: 978-3-030-46320-5Published: 15 July 2020
eBook ISBN: 978-3-030-46321-2Published: 14 July 2020
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XX, 433
Number of Illustrations: 24 b/w illustrations, 11 illustrations in colour
Topics: Real Functions, Sequences, Series, Summability, Analysis