G. Petit Boi的不定积分表 Tables of Indefinite Integrals

文件名称: G. Petit Boi的不定积分表 Tables of Indefinite Integrals by G. Petit Boi

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详细说明：G. Petit Boi的不定积分表 Tables of Indefinite Integrals by G. Petit Boi s,lITHSONIAN MISCELLANEOUS COLLECTIONS VOLUME 74. NUMBER 1 SMITHSONIAN MATHEMATICAL FORMULAE AND TABLES OF ELLIPTIC FUNCTIONS MATHIELMATICAL FORMULAE PREPARED BY EDWIN P. ADAMS, PH D PRDFESSOR DF PHYSICS, PRINCETON WNIVERSITY TABLES OF ELLIPTIC FU NCTIONS PREPARED UNDER THE DIRECTION OF SIR GEORGE GREENHILL, BAHT. B° COL. R. L. HIPPISLEY, C B THE, INCA AFFRiC EA YNGT。 PUBLICATION 2672 CITY OF WASHINGTON PUBLISHED BY THE SMITHSONIAN INSTTTUTION 1922 QA山 Sc6 1922 2 ce1千C ADVERTISEMENT The Smithsonian Institution has maintained for many years a group of publications in the nature of handy books of information on geographical meteorological, physical, and mathermatical subjects. These include the Smithsonian Geographical Tables(third edition, reprint, 1o18): the Smithsonian Meteorological Tables (fourth revised edition, 1918); the Smithsonian Physical Tables (seventh revised edition, 1q21): and the Smithsonian Mathematical Tables: Hyperbolic Functions (second reprint, 1921). The present volume comprises the most important formulae of many branches of applied mathematics, an illustrated discussion of the methods of mechanical integration, and tables of elliptic functions. The volume has been compiled by Dr E. P. Adams, of Princeton [niversity prof f. r moulton of the univer. sity of Chicago, contributed the section on numerical solution of difierential equations. The tables of elliptic functions were prepared by Col. R. L. Hippisley, C B, under the direction of Sir George Greenhill, Bart who has contributed the introduction to these tables The compiler, Dr. Adams, and the Smithsonian Institution are indebted to many physicists and mathematicians, especially to Dr. H. L. Curtis and col leagues of the Bureau of Standards, for advice, criticism, and cooperation in the preparation of this volume. CHARLES D. WALCOTT, Secretary of the Smithsonian Institution .ay, ro PREFACE The original object of this collection of mathematical formulae was to bring together, compactly, some of the more useful results of mathematical analysis for the benefit of those who regard mathematics as a tool, and not as an end in tself. There are many such results that are difficult to remember, for one who is not constantly using them, and to find them one is obliged to look through a number of books which may not immediately be accessible. A collection of formulae, to meet the object of the present one, must be largely a matter of individual selection; for this reason this volume is issued in an interleaved edition, so that additions, meeting individual needs, may be made, and be readily available for reference It was not originally intended to include any tables of functions in this volume, but merely to give references to such tables. An exception was made however, in favor of the tables of elliptic functions, calculated, on Sir George Greenhills new plan, by Colonel Hippisley, which were fortunately secured for this volume, inasmuch as these tables are not otherwise available. In order to keep the volume within reasonable bounds, no tables of indefinite and definite integrals have been included. For a brief collection, that of the late Professor B. O. Peirce can hardly be improved upon; and the elaborate collection of definite integrals by Bierens de Haan show how inadequate.any brief tables of definite integrals would be. A short list of useful tables of this kind, as well as of other volumes, having an object similar to this one, is appended. Should the plan of this collection meet with iavor, it is hoped that suggestions for improving it and making it more generally useful may be received To Professor Moulton, for contributing the chapter on the Numerical Integration of Differential Equations, and to Sir George greenhill, for his Intro- duction to the Tables of Elliptic Functions, I wish to express my gratitude. And I wish also to record my obligations to the Secretary of the Smithsonian In- stitution, and to Dr C G, Abbot, Assistant Secretary of the Institution, for the way in which they have met all my suggestions with regard to this volume E. P. ADAM PRINCETON, NTW JERSEY COLLECTIONS OF MATHEMATICAL FORMULAE, ETC. B O. PEtRCE: .A Short Table of Integrals, Boston, I8gg G. PETIT BoIS: Tables d'Integrales Indefinies, Paris, Iooo T.J. IA. BRoMwIcIL: Elementary Integrals, Cambridge, roll D. BIERENS DE HAAN: Nouvelles Tables d'Integrales Definies, Leiden, 1867. E. JAHNKE and F. EMDE: Funktionentafeln mit Formeln und Kurven, Leipzig, Ioo. G. S. CARR: A Synopsis of Elementary Results in Pure and Applied Mathe matIcs, London,t88°. W. LASKA: Sammlung von Formeln der reinen und angewandten Mathematik Braunschweig, :888-18o4 W. LIGOWSKI: Taschenbuch der Mathematik, Berlin, I893 O. TH. BURKLEN: Formelsammlung und Repetitorium der Mathematik Berlin,1o22 F. AUERBACH: Taschenbuch fur Mathematiker und Physiker, I. jahrgang, Agog. Leipzig, too

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