Overview
- Includes the theory of nets to study arbitrary topological spaces
- Illustrates the insufficiency of sequences with simple but rarely presented examples
- Elaborates on the historical background of most notions and results treated in this volume
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Undergraduate Mathematics Series (SUMS)
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Table of contents (12 chapters)
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Front Matter
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Topology
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Front Matter
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Differential Calculus
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Front Matter
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Approximation Methods
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Front Matter
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Back Matter
Keywords
About this book
The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations.
Students of both pure and applied mathematics, as well as physics and engineering should find this textbook useful. Only basic results of one-variable calculus and linear algebra are used, and simple yet pertinent examples and exercises illustrate the usefulness of most theorems. Many of these examples are new or difficult to locate in the literature, and so the original sources of most notions and results are given to help readers understand the development of the field.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Topology, Calculus and Approximation
Authors: Vilmos Komornik
Series Title: Springer Undergraduate Mathematics Series
DOI: https://doi.org/10.1007/978-1-4471-7316-8
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Ltd. 2017
Softcover ISBN: 978-1-4471-7315-1Published: 10 April 2017
eBook ISBN: 978-1-4471-7316-8Published: 04 April 2017
Series ISSN: 1615-2085
Series E-ISSN: 2197-4144
Edition Number: 1
Number of Pages: XIV, 382
Number of Illustrations: 63 b/w illustrations, 1 illustrations in colour
Additional Information: Original French edition published by Ellipses, Paris, 2001
Topics: Ordinary Differential Equations, Numerical Analysis, Approximations and Expansions