James Stirling’s Methodus Differentialis: An Annotated Translation of Stirling’s Text (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. Front Matter....Pages I-VIII Introduction....Pages 1-13 Front Matter....Pages 15-18 A Treatise on Summation & Interpolation of Infinite Series ....Pages 19-32 Part One On the Summation of Series....Pages 33-100 Part Two On the Interpolation of Series....Pages 101-283 Appendix Stirling’s Letter to De Moivre Dated 19 June 1729....Pages 285-287 References....Pages 289-292 Back Matter....Pages 284-296 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. A new translation makes this classic and important text more generally accessible. The text is placed in its contemporary context, but also related to the interests of practising mathematicians today. This book will be of interest to mathematical historians, researchers, and numerical analysts.