Introduction to Mathematical Analysis

Authors: Kriz, Igor, Pultr, Ales

  • In a single text, the student gets a glimpse of a  big picture
  • The treatment of mathematical analysis is rigorous and self-contained
  • Can be used not only as a textbook for a course but also as a reference book for lecturers in analysis or mathematicians and scientists in general ​
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  • ISBN 978-3-0348-0636-7
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Softcover $89.99
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  • ISBN 978-3-0348-0635-0
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About this Textbook

The book begins at the level of an undergraduate student assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, Lebesgue integral, vector calculus and differential equations. After having built on a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis, as understood by a mathematician today.​  

About the authors

Igor Kriz studied in Prague, Czech Republic. He has lived in the United States since 1988 and been teaching at the University of Michigan since 1994. His main interests are geometry and algebraic topology. Aleš Pultr studied in Prague and has been teaching at the Charles University since 1961. His main interests are point-free topology, category theory and combinatorics. Both authors have taught numerous courses of mathematical analysis.

Reviews

From the reviews:

“The book is intended as a second-year course of mathematical analysis for advanced undergraduate students. … The volume is addressed to undergraduate students seriously interested in mathematics and is accessible to students before they start taking graduate classes. Researchers in pure and applied nonlinear analysis will find interesting material in this volume.” (Teodora-Liliana Rădulescu, zbMATH, Vol. 1279, 2014)

“The authors included in their book some topics from topology, calculus of real functions of one and several real variables … elements of functional analysis, as well as some applications. … the present well written book is a valuable addition to the existing ones on similar topics. It can be used by graduate students in mathematics and researchers in mathematics and other areas … . The instructors can recommend the book as a supplementary material for their courses.” (S. Cobzaş, Studia Universitatis Babes-Bolyai, Math, Vol. 58 (4), 2013)


Table of contents (17 chapters)

  • Preliminaries

    Kriz, Igor (et al.)

    Pages 3-31

  • Metric and Topological Spaces I

    Kriz, Igor (et al.)

    Pages 33-63

  • Multivariable Differential Calculus

    Kriz, Igor (et al.)

    Pages 65-95

  • Integration I: Multivariable Riemann Integral and Basic Ideas Toward the Lebesgue Integral

    Kriz, Igor (et al.)

    Pages 97-116

  • Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration

    Kriz, Igor (et al.)

    Pages 117-143

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-0636-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-0348-0635-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Mathematical Analysis
Authors
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-3-0348-0636-7
DOI
10.1007/978-3-0348-0636-7
Softcover ISBN
978-3-0348-0635-0
Edition Number
1
Number of Pages
XX, 510
Number of Illustrations and Tables
1 illustrations in colour
Topics