James Stirling's Methodus Differentialis
Subtitle: an Annotated Translation of Stirling's Text
By: by Ian Tweddle
Series: Sources and Studies in the History of Mathematics and Physical Sciences; Sources and studies in the history of mathematics and physical sciences
Publisher: Springer London
Published: 2003
Place of publication: London
Language: eng
Format: [electronic resource] :
Number of pages: 295
ISBN-13: 9781447100218
Subjects: Mathematics; Numerical analysis; Global analysis (Mathematics)
Description: 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.
Table of contents: title: Introduction; title: Background; title: Some Mathematical Points; title: Summary of the Contents of Stirling's Text; title: Stirling's Principal Calculations; title: <STRONG>Stirling's Text in Translation:</STRONG> Preface; Introduction; Part I: On the Summation of Series; Part II: On the Interpolation of Series; title: Notes; title: Appendix: Stirling's Letter to De Moivre Dated 17th June 1729; title: References; title: Index.