Overview
- 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 ?
- Includes supplementary material: sn.pub/extras
Access this book
Tax calculation will be finalised at checkout
Other ways to access
About this book
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.
Similar content being viewed by others
Keywords
Table of contents (17 chapters)
-
Front Matter
-
A Rigorous Approach to Advanced Calculus
-
Front Matter
-
-
Analysis and Geometry
-
Front Matter
-
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)
Authors and Affiliations
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.
Bibliographic Information
Book Title: Introduction to Mathematical Analysis
Authors: Igor Kriz, Aleš Pultr
DOI: https://doi.org/10.1007/978-3-0348-0636-7
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2013
Softcover ISBN: 978-3-0348-0635-0Published: 02 August 2013
eBook ISBN: 978-3-0348-0636-7Published: 25 July 2013
Edition Number: 1
Number of Pages: XX, 510
Number of Illustrations: 1 illustrations in colour
Topics: Real Functions, Linear and Multilinear Algebras, Matrix Theory, Measure and Integration, Functions of a Complex Variable, Ordinary Differential Equations, Sequences, Series, Summability