Mathematics of the 19th Century: Function Theory According to Chebyshev Ordinary Differential Equations Calculus of Variations Theory of Finite Differences - Hardcover

Hardcover

ISBN 10: 3764358459 ISBN 13: 9783764358457

Publisher: Birkhäuser, 1998

Synopsis

The editors of the present series had originally intended to publish an integrated work on the history of mathematics in the nineteenth century, passing systemati­ cally from one discipline to another in some natural order. Circumstances beyond their control, mainly difficulties in choosing authors, led to the abandonment of this plan by the time the second volume appeared. Instead of a unified mono­ graph we now present to the reader a series of books intended to encompass all the mathematics of the nineteenth century, but not in the order of the accepted classification of the component disciplines. In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication. 1 We recall that the first book contained essays on the history of mathemati­ 2 cal logic, algebra, number theory, and probability, while the second covered the history of geometry and analytic function theory. In the present third volume the reader will find: 1. An essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory" by S. N. Bernshtein. This highly original essay is due to the late N. I. Akhiezer (1901-1980), the author of fundamental discoveries in this area. Akhiezer's text will no doubt attract attention not only from historians of mathematics, but also from many specialists in constructive function theory.

About this title

Synopsis

This text concludes the series of historical studies of the mathematics of the 19th century. Previous volumes have studied logic, algebra, number theory, probability, geometry, and analytic functions. The third volume encompasses: an essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory"; a systematic analysis of the history of the theory of ordinary differential equations from Cauchy and certain of his predecessors up to Poincare and A.M. Lyapunov; an essay of the development of the calculus of variations; and a study of the history of finite differences, in whose development Soviet mathematicians have played a prominent role. This book should be a valuable source for understanding the development of these areas. It provides the general reader, as well as historians of science, not only with the descriptive history but also with a good perception of the outer and inner motivations and the results and effects of the presented concepts and methods.

Edition details

• Publisher: Birkhäuser
• Publication date: 1998
• Language: English
• ISBN 10: 3764358459
• ISBN 13: 9783764358457
• Binding: Hardcover
• Number of pages: 363
• Editor: Kolmogorov A.N., Yushkevich A.P.