Springer Undergraduate Mathematics Series

Essential Real Analysis

Authors: Field, Michael

  • Contains more than 570 exercises of varying difficulty
  • Provides proofs of basic results on existence and regularity of solutions of ordinary differential equations
  • Includes a full treatment of the inverse function theorem in several variables
  • Emphasizes the importance of estimates and computation in analysis
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eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-67546-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-67545-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses.

Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals.

Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.

About the authors

Michael Field has held appointments in the UK (Warwick University and Imperial College London), Australia (Sydney University) and the US (the University of Houston and Rice University) and has taught a wide range of courses at undergraduate and graduate level, including real analysis, partial differential equations, dynamical systems, differential manifolds, Lie groups, complex manifolds and sheaf cohomology. His publications in the areas of equivariant dynamical systems and network dynamics include nine books and research monographs as well as many research articles. His computer graphic art work, based on symmetric dynamics, has been widely exhibited and is on display at a number of universities around the world.

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Table of contents (9 chapters)

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-67546-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA
  • ISBN 978-3-319-67545-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Essential Real Analysis
Authors
Series Title
Springer Undergraduate Mathematics Series
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-67546-6
DOI
10.1007/978-3-319-67546-6
Softcover ISBN
978-3-319-67545-9
Series ISSN
1615-2085
Edition Number
1
Number of Pages
XVII, 450
Number of Illustrations and Tables
29 b/w illustrations, 1 illustrations in colour
Topics