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a 9781447173168

100 
1 

a Komornik, Vilmos

245 
0 
0 
a Topology, Calculus and Approximation
h Elektronische Ressource
c by Vilmos Komornik

250 


a 1st ed. 2017

260 


a London
b Springer London
c 2017, 2017

300 


a XIV, 382 p. 64 illus., 1 illus. in color
b online resource

505 
0 

a 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

653 


a Numerical Analysis

653 


a Approximations and Expansions

653 


a Numerical analysis

653 


a Approximation theory

653 


a Differential Equations

653 


a Differential equations

041 
0 
7 
a eng
2 ISO 6392

989 


b Springer
a Springer eBooks 2005

490 
0 

a Springer Undergraduate Mathematics Series

028 
5 
0 
a 10.1007/9781447173168

856 
4 
0 
u https://doi.org/10.1007/9781447173168?nosfx=y
x Verlag
3 Volltext

082 
0 

a 515.35

520 


a 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, Erdős, Fejér, Stieltjes, and Turán. 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 algebraicand 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
