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AuthorTweddle, Ian. author
TitleJames Stirling's Methodus Differentialis [electronic resource] : An Annotated Translation of Stirling's Text / by Ian Tweddle
ImprintLondon : Springer London : Imprint: Springer, 2003
Connect tohttp://dx.doi.org/10.1007/978-1-4471-0021-8
Descript VIII, 296 p. online resource

SUMMARY

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


CONTENT

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


Mathematics Mathematical analysis Analysis (Mathematics) Numerical analysis History Mathematics History of Mathematical Sciences Analysis Numerical Analysis



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