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Topology, Calculus and Approximation

Topology, Calculus and Approximation

Wydawnictwo Springer Nature Customer Service Center GmbH
Data wydania 01/04/2017
Wydanie Pierwsze
Liczba stron 382
Forma publikacji książka w miękkiej oprawie
Poziom zaawansowania Dla szkół wyższych i kształcenia podyplomowego
Język angielski
ISBN 9781447173151
Kategorie Rachunek różniczkowy i formuły, Analiza numeryczna
230.12 PLN (z VAT)
$51.76 / £42.83 / €49.34 /
Produkt na zamówienie
Dostawa 5-6 tygodni
Do schowka

Opis książki

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 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.

Topology, Calculus and Approximation

Spis treści

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. 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.

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