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020 _a9781447173168
_9978-1-4471-7316-8
024 7 _a10.1007/978-1-4471-7316-8
_2doi
040 _cCUS
050 4 _aQA372
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
082 0 4 _a515.352
_223
100 1 _aKomornik, Vilmos.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aTopology, Calculus and Approximation
_h[electronic resource] /
_cby Vilmos Komornik.
250 _a1st ed. 2017.
264 1 _aLondon :
_bSpringer London :
_bImprint: Springer,
_c2017.
300 _aXIV, 382 p. 64 illus., 1 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Undergraduate Mathematics Series,
_x1615-2085
505 0 _aPart 1. Topology -- Chapter 1. Metric spaces -- Chapter 2. Topological spaces -- Chapter 3. Normed spaces -- Part 2. Differential calculus -- Chapter 4. The Derivative -- Chapter 5. Higher-order 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.
520 _aPresenting 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 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.
650 0 _aDifferential equations.
650 0 _aNumerical analysis.
650 0 _aApproximation theory.
650 1 4 _aOrdinary Differential Equations.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12147
650 2 4 _aNumerical Analysis.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M14050
650 2 4 _aApproximations and Expansions.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M12023
830 0 _aSpringer Undergraduate Mathematics Series,
_x1615-2085
856 4 0 _uhttps://doi.org/10.1007/978-1-4471-7316-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
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999 _c206204
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