Tweddle James Stirling’s Methodus Differentialis

An Annotated Translation of Stirling’s Text
Erscheinungsjahr 2012
ISBN: 978-1-4471-0021-8
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 296 Seiten, eBook

Reihe: Sources and Studies in the History of Mathematics and Physical Sciences

James Stirling's "Methodus Differentialis" is one of the early classics of numerical analysis. It contains not only the results and ideas for which Stirling is chiefly remembered, for example, Stirling numbers and Stirling's asymptotic formula for factorials, but also a wealth of material on transformations of series and limiting processes. An impressive collection of examples illustrates the efficacy of Stirling's methods by means of numerical calculations, and some germs of later ideas, notably the Gamma function and asymptotic series, are also to be found. This volume presents a new translation of Stirling's text that features an extensive series of notes in which Stirling's results and calculations are analysed and historical background is provided. Ian Tweddle places the text in its contemporary context, but also relates the material to the interests of practising mathematicians today. Clear and accessible, this book will be of interest to mathematical historians, researchers and numerical analysts.

Zielgruppe

Research

Autoren/Hrsg.

Tweddle, Ian

Inhaltsverzeichnis

Introduction.- Background.- Some Mathematical Points.- Summary of the Contents of Stirling's Text.- Stirling's Principal Calculations.- Stirling's Text in Translation: Preface; Introduction; Part I: On the Summation of Series; Part II: On the Interpolation of Series.- Notes.- Appendix: Stirling's Letter to De Moivre Dated 17th June 1729.- References.- Index.