Topology, calculus, and approximation
 Responsibility
 Vilmos Komornik.
 Publication
 London, United Kingdom : Springer, [2017]
 Physical description
 xiv, 379 pages ; 24 cm.
 Series
 Springer undergraduate mathematics series
At the library
Science Library (Li and Ma)
Stacks
Call number  Status 

QA611 .K66 2017  Unknown 
More options
Description
Creators/Contributors
 Author/Creator
 Komornik, V., author.
Contents/Summary
 Contents

 Part 1. Topology.
 Chapter 1. Metric spaces.
 Chapter 2. Topological spaces.
 Chapter 3. Normed spaces.
 Part 2. Differential calculus.
 Chapter 4. The Derivative.
 Chapter 5. Higherorder derivatives.
 Chapter 6. Ordinary differential equations.
 Chapter 7. Implicit functions and their applications.
 Part 3. Approximation methods.
 Chapter 8. Interpolation.
 Chapter 9. Orthogonal polynomials.
 Chapter 10. Numerical integration.
 Chapter 11. Finding roots.
 Chapter 12. Numerical solution of differential equations.
 (source: Nielsen Book Data)
 Publisher's Summary
 ["Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdos, Fejer, Stieltjes, and Turan. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdos 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 Caratheodory'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 onevariable 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.", {"source"=>"(source: Nielsen Book Data)"}, "9781447173151", "20170717"]
Bibliographic information
 Publication date
 2017
 Series
 Springer undergraduate mathematics series, 16152085
 ISBN
 9781447173151 paperback
 1447173155 paperback