Analysis by Its History

Name: Analysis by Its History
Author: Gerhard Wanner

Auteur: Ernst Hairer

Taal: Engels

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Auteur: Ernst Hairer Gerhard Wanner

Co-auteur: E. Hairer

Engels
Hardcover
9780387945514
26 oktober 1995
379 pagina's

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Samenvatting

. Emphasis upon its relation to neighboring fields, such as calculus of dif ferences and interpolation . mappings functions On the other hand, the historical development of these subjects occurred in reverse order: Archimedes Cantor 1875 Cauchy 1821 Newton 1665 . ;::: Kepler 1615 Dedekind . ;::: Weierstrass .

This book presents first-year calculus roughly in the order in which it first was discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating and enjoyable reading for students, teachers, as well as researchers.

From the reviews:

The aim of this interesting new contribution to the series Readings in Mathematics is an attempt to restore the historical order in the presentation of basic mathematical analysis...such a historical approach can provide a very fruitful and interesting approach to mathematical analysis.

- Jean Mawhin, Zentralblatt

The authors include a large number of once-traditional subjects which have now vanished from the analysis curriculum, at least in the standard American courses. Thus we find continued fractions, elliptic integrals, the Euler-MacLaurin summation formula, etc., most of which are found only in more compendious works. Many of the exercises are inspired by original papers, with the bibliographic references sometimes given. The work is very well illustrated. The book is definitely an analysis text, rather than a history, but a great deal of reliable historical material is included. For those seeking an alternative to the traditional approach, it seems to me to be of great interest.

- Thomas Archibald, Mathematical Reviews

The authors...have assembled an impressive array of annotated results, quotations, tables, charts, figures and drawings, many copied from original documents....they write with great enthusiasm and with evident affection for both analysis and history.

- John Troutman, American Mathematical Monthly

. . . that departed from the traditional dry-as-dust mathematics textbook. (M. Kline, from the Preface to the paperback edition of Kline 1972) Also for this reason, I have taken the trouble to make a great number of drawings. (Brieskom & Knorrer, Plane algebraic curves, p. ii) . . . I should like to bring up again for emphasis . . . points, in which my exposition differs especially from the customary presentation in the text books: 1. Illustration of abstract considerations by means of figures. 2. Emphasis upon its relation to neighboring fields, such as calculus of dif ferences and interpolation . . . 3. Emphasis upon historical growth. It seems to me extremely important that precisely the prospective teacher should take account of all of these. (F. Klein 1908, Eng\. ed. p. 236) Traditionally, a rigorous first course in Analysis progresses (more or less) in the following order: limits, sets, '* continuous '* derivatives '* integration. mappings functions On the other hand, the historical development of these subjects occurred in reverse order: Archimedes Cantor 1875 Cauchy 1821 Newton 1665 . ;::: Kepler 1615 Dedekind . ;::: Weierstrass . ;::: Leibniz 1675 Fermat 1638 In this book, with the four chapters Chapter I. Introduction to Analysis of the Infinite Chapter II. Differential and Integral Calculus Chapter III. Foundations of Classical Analysis Chapter IV. Calculus in Several Variables, we attempt to restore the historical order, and begin in Chapter I with Cardano, Descartes, Newton, and Euler's famous Introductio.

Productspecificaties

Inhoud

Taal: en
Bindwijze: Hardcover
Oorspronkelijke releasedatum: 26 oktober 1995
Aantal pagina's: 379
Illustraties: Met illustraties

Betrokkenen

Hoofdauteur: Ernst Hairer
Tweede Auteur: Gerhard Wanner
Co Auteur: E. Hairer
Hoofduitgeverij: Springer-Verlag New York Inc.

Overige kenmerken

Editie: 1st Corrected ed. 1996. Corr. 3rd printing 2000
Extra groot lettertype: Nee
Product breedte: 161 mm
Product hoogte: 27 mm
Product lengte: 241 mm
Studieboek: Nee
Verpakking breedte: 155 mm
Verpakking hoogte: 235 mm
Verpakking lengte: 235 mm
Verpakkingsgewicht: 1610 g

EAN

EAN: 9780387945514

Je vindt dit artikel in

Categorieën: Wetenschap & Natuur

Wiskunde

Calculus & Wiskundige analyse

Boeken
Taal: Engels
Boek, ebook of luisterboek?: Boek
Beschikbaarheid: Leverbaar
Studieboek of algemeen: Studieboeken

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