Universitext

Mathematical Analysis II

Authors: Zorich, Vladimir A.

  • 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 
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eBook $59.99
price for USA (gross)
  • ISBN 978-3-662-48993-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-662-48991-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This second English 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 English 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.

This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

About the authors

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.

Table of contents (11 chapters)

  • *Continuous Mappings (General Theory)

    Zorich, Vladimir A.

    Pages 1-40

  • *Differential Calculus from a More General Point of View

    Zorich, Vladimir A.

    Pages 41-108

  • Multiple Integrals

    Zorich, Vladimir A.

    Pages 109-161

  • Surfaces and Differential Forms in $\mathbb{R}^{n}$

    Zorich, Vladimir A.

    Pages 163-211

  • Line and Surface Integrals

    Zorich, Vladimir A.

    Pages 213-255

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-3-662-48993-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-3-662-48991-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Mathematical Analysis II
Authors
Translated by
Cooke, R., Paniagua, O.
Series Title
Universitext
Copyright
2016
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-48993-2
DOI
10.1007/978-3-662-48993-2
Hardcover ISBN
978-3-662-48991-8
Series ISSN
0172-5939
Edition Number
2
Number of Pages
XX, 720
Number of Illustrations and Tables
42 illustrations in colour
Additional Information
Original Russian edition (6th edition) published by MCCME, Moscow, Russia, 2012
Topics