KARL GUSTAV

JACOB

See also:

• JACOBI, FRIEDRICH HEINRICH (1743-1819)
• JACOBI, JOHANN GEORG (1740-1814)
• KARL GUSTAV JACOB JACOBI (1804-1851)

JACOBI (1804-1851)  , German mathematician, was born at Potsdam, of Jewish parentage, on the loth of December 1804 . He studied at Berlin University, where he obtained the degree of doctor of philosophy in 1825, his thesis being an analytical discussion of the theory of fractions . In 1827 he became extraordinary and in 1829 ordinary professor of mathematics at Konigsberg, and this chair he filled till 1842, when he visited Italy for a few months to recruit his health . On his return he removed to Berlin, where he lived as a royal pensioner till his death, which occurred on the 18th of February 1851 . His investigations in elliptic functions, the theory of which he established upon quite a new basis, and more particularly his development of the theta-function, as given in his great treatise Fundamenta nova theoriae functionum ellipticarum (Konigsberg, 1829), and in later papers in Crelle's Journal, constitute his grandest analytical discoveries . Second in importance only to these are his researches in differential equations, notably the theory of the last multiplier, which is fully treated in his Vorlesungen fiber Dynamik, edited by R . F . A . Clebsch (Berlin, 1866) . It was in analytical development that Jacobi's peculiar power mainly lay, and he made many important contributions of this kind to other departments of mathematics, as a glance at the long list of papers that were published by him in Crelle's Journal and elsewhere from 1826 onwards will sufficiently indicate . He was one of the early founders of the theory of determinants; in particular, he invented the functional determinant formed of the n' differential coefficients of n given functions of n independent variables, which now bears his name (Jacobian), and which has played an important part in many analytical investigations (see ALGEBRAIC FORMS) . Valuable also are his papers on Abelian transcendents, and his investigations in the theory of numbers, in which latter department he mainly supplements the labours of K .

F .

Gauss . The planetary theory and other particular dynamical problems likewise occupied his attention from time to time . He left a vast store of manuscript, portions of which have been published at intervals in Crelle's Journal . His other works include Commentatio de transformatione integralis duplicis indefiniti in formam simpliciorem (1832), Canon arithmeticus (1839), and Opuscula mathematica (1846–1857) . His Gesammelte Werke (1881–1891) were published by the Berlin Academy . See Lejeune-Dirichiet, Gedachtnisrede auf Jacobi " in the Abhandlungen der Berliner Akademie (1852) .