BESIDUAL CALCULUS. A branch of integral calculus due to Cauchy, in which the integration takes place around a contour inclosing points for which the function is infinite. The integral is called the residual, and in case the contour con tains all tile critical points. the integral is called the total or principal residual.
BIBLIOGRAPHY. The literature on the subject Bibliography. The literature on the subject of calculus is so extensive that any limited selec tion of references must be unsatisfactory. The hest :election of important works will be found iu Neyer. Ene!,klopd fir der mathentatisehen Iris senschuf ten. Vol. It. ( Leipzig. 1900). Of the older works the most important are: Leibnitz. Matheniatisehe Schriften, ed. by Gerhardt (Ber lin and Halle, 1849-63) Newton, Opusevla (Lausanne. 1714) : Euler, Introduetio in analy sin infinitorum, new ed. (Lausanne, 1848) ; id..
Institutiones calculi differentia/is, new ed.
(Saint Petersburg, 1835) id., Instit utiones cal culi integralis, 3d ed. (Vienna, 1830). Of the later works may he mentioned those of Cauchy (Paris. 1821-47) ; Bertrand. de ealeul differentia et de Meld integral (Paris, 1864 70) : Serret, emirs de cairn! differentia of in tegral. -nth ed. (Paris, 1894) ; Hermite. Lours d'analyse de reeole polyteehnique (Paris, 1873) : Laurent. Traite. d'analysc (Paris, 1885-91) ; and •Jordan. Court( d'analyse. 2d ed. (Paris, 1893-911), which may be taken as typical of the best French works. In Germany and Austria,
('onmpendiumn der hiiheren Analysis, 4th ed. I Brunswiek, ISA) : Scbharrilch, rehungs ltch :um Studium tier hoheren Analysis, •Ith ed. (Leipzig. 1888) ; Lipschitz, Lehrbuch der Ana lysis ( Bonn, 1877-80) ; Stolz. Drundziiye tier Dif ferential- and Integralrcehnunq (Leipzig, 1893 99 ) and Rietnnmt, Oesammelle Werke, edited by Weber and Detlekind. 2d ed. (Leipzig, 1892). In England, Prime. Trrnt isr on Infinitesimal Calculus, 2•1 ed. (4 N'HIA.. oxford, 1855-89) Todhunter, Differential Calculus (Cambridge, 18651: and Todhunter. Integral Calculus (Cam bridge. 1861). are widely known. Italy' has recently produced a work of merit, viz.. Pascal. Lezioni di «Iodise infinilesitnale (3 vols., Milan. 1895). Of the American works covering the general field, Byerly, Elements of Differential Calculus and Elements of Integral Calculus I Boston, Hsl ). are representative. For the history of the subject. eonsult the Eneyklopadie mentioned above; also: Cantor. Deschichte der ilathematik, Vols. H. and Ill. (Leipzig, 1892 98) : Ball, 7i/story of 31 les, 3d ed. (New York, 1901) : Fink, History of Mathematics. translated by Bernal' and Smith (('hicago, 1900). The Calculus of Varklii0IIR is treated historieally.• as well as mathematically, by Carl! (New York.