Authors:
- 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)
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Front Matter
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Back Matter
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
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Dept of Mathematical Analysis, Moscow State University, Moskva, Russia
Vladimir A. Zorich
About the author
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