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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Analysis Topology, Calculus and Approximation
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Topology, Calculus and Approximation
Vilmos Komornik (Taschenbuch, Englisch)
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Beschreibung
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 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. 37,44 €
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Technische Daten
Erscheinungsdatum
10.04.2017
Sprache
Englisch
EAN
9781447173151
Herausgeber
Springer London
Serien- oder Bandtitel
Springer Undergraduate Mathematics Series
Sonderedition
Nein
Autor
Vilmos Komornik
Seitenanzahl
382
Einbandart
Taschenbuch
Autorenporträt
Vilmos Komornik has studied in Budapest, Hungary, and has taught in Hungary and France for nearly 40 years. His main research fields are control theory of partial differential equations and combinatorial number theory. He has made a number of contributions to the theory of J.L. Lions on exact controllability and stabilization and has co-authored several papers on expansions in noninteger bases with P. Erdős. He is an external member of the Hungarian Academy of Sciences.
Schlagwörter
metric space, normed space, topology, calculus, differential equations, implicit functions, interpolation, orthogonal polynomials, numerical integration, Sturm sequences, Newton's method, Runge-Kutta method, ordinary differential equations
Thema-Inhalt
PBKJ - Differentialrechnung und -gleichungen
PBKS - Numerische Mathematik
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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