Komornik, Vilmos Topology, calculus and approximation 9781447173151

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Автор: Komornik, Vilmos
Название: Topology, calculus and approximation
Перевод названия: Вилмос Коморник: Топология, математический анализ и прогнозирование
ISBN: 9781447173151
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

Дифференциальное исчисление и дифференциальные уравнения

Вычислительная математика

ISBN-10: 1447173155
Обложка/Формат: Paperback
Страницы: 382
Вес: 0.59 кг.
Дата издания: 10.04.2017
Серия: Springer undergraduate mathematics series
Язык: English
Издание: 1st ed. 2017
Иллюстрации: 63 black & white illustrations, 1 colour illustrations, 9 colour tables, biography
Размер: 157 x 239 x 25
Читательская аудитория: Professional & vocational
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: 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, Fejer, Stieltjes, and Turan.

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 Caratheodorys 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, Komornik, Vilmos