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Springer Undergraduate Mathematics Series

Fundamental Mathematical Analysis

Authors: Magnus, Robert

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  • 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
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  • ISBN 978-3-030-46321-2
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Softcover $44.99
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  • ISBN 978-3-030-46320-5
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About this Textbook

This textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout.

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.

About the authors

Robert Magnus was born in the UK and studied mathematics at the Universities of Cambridge and Sussex. He has taught nearly all subjects associated with analysis and has published papers in the areas of bifurcation theory, catastrophe theory, analytic operator functions and non-linear partial differential equations. Since 1977 he has lived and worked in Iceland.

Table of contents (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook $34.99
price for USA
  • ISBN 978-3-030-46321-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $44.99
price for USA
  • ISBN 978-3-030-46320-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.

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Bibliographic Information

Bibliographic Information
Book Title
Fundamental Mathematical Analysis
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2020
Publisher
Springer International Publishing
Copyright Holder
The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-46321-2
DOI
10.1007/978-3-030-46321-2
Softcover ISBN
978-3-030-46320-5
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XX, 433
Number of Illustrations
24 b/w illustrations, 11 illustrations in colour
Topics

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