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  • Textbook
  • © 2015

Mathematical Analysis I

  • Thoroughness of coverage, from elementary to very advanced

  • Clarity of exposition

  • Originality and variety of exercises and examples

  • Complete logical rigor of discussion

  • Various new appendices

  • Useful not only to mathematicians, but also to physicists and engineers

  • Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-XX
  2. Some General Mathematical Concepts and Notation

    • Vladimir A. Zorich
    Pages 1-34
  3. The Real Numbers

    • Vladimir A. Zorich
    Pages 35-78
  4. Limits

    • Vladimir A. Zorich
    Pages 79-148
  5. Continuous Functions

    • Vladimir A. Zorich
    Pages 149-170
  6. Differential Calculus

    • Vladimir A. Zorich
    Pages 171-329
  7. Integration

    • Vladimir A. Zorich
    Pages 331-408
  8. Back Matter

    Pages 545-616

About this book

This second edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis.

The main difference between the second and first editions is the addition of a series of appendices to each volume. There are six of them in the first volume and five in the second. The subjects of these appendices are diverse. They are meant to be useful to both students (in mathematics and physics) and teachers, who may be motivated by different goals. Some of the appendices are surveys, both prospective and retrospective. The final survey establishes important conceptual connections between analysis and other parts of mathematics.

The first volume constitutes a complete course in one-variable calculus along with the multivariable differential calculus elucidated in an up-to-date, clear manner, with a pleasant geometric and natural sciences flavor.

Reviews

“This is a thorough and easy-to-follow text for a beginning course in real analysis … . In coverage the book is slanted towards physics (mostly mechanics), and in particular there is a lot about line and surface integrals. … Will be popular with students because of the detailed explanations and the worked examples.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)

Authors and Affiliations

  • Dept of Mathematical Analysis, Moscow State University, Moskva, Russia

    Vladimir A. Zorich

About the author

VLADIMIR A. ZORICH is professor of mathematics at Moscow State University. His areas of specialization are analysis, conformal geometry, quasiconformal mappings, and mathematical aspects of thermodynamics. He solved the problem of global homeomorphism for space quasiconformal mappings. He holds a patent in the technology of mechanical engineering, and he is also known by his book “Mathematical Analysis of Problems in the Natural Sciences”.

Bibliographic Information

  • Book Title: Mathematical Analysis I

  • Authors: Vladimir A. Zorich

  • Translated by: Roger Cooke, Octavio Paniagua Taboada

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-662-48792-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag GmbH Germany, part of Springer Nature 2015

  • Hardcover ISBN: 978-3-662-48790-7Published: 11 March 2016

  • Softcover ISBN: 978-3-662-56955-9Published: 25 April 2018

  • eBook ISBN: 978-3-662-48792-1Published: 29 February 2016

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 2

  • Number of Pages: XX, 616

  • Number of Illustrations: 66 illustrations in colour

  • Additional Information: Original Russian edition (6th edition) published by MCCME, Moscow, Russia, 2012

  • Topics: Analysis, Theoretical, Mathematical and Computational Physics

Buy it now

Buying options

eBook USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 79.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access