The reduction to normal form of a non-normal system of differential equations. De aequationum differentialium systemate non normali ad formam normalem revocando

English translation of a posthumous manuscript in Latin first published in Vorlesungen über Dynamik von C.G.J. Jacobi nebstes fünf hinterlassenen Abhandlungen desselben, A. Clesch ed., Berlin, Georg Reimer, 1866.International audienceThis paper was edited by Sigismund Cohn, C.W. Borchardt and A. Clebsch from posthumous manuscripts of C.G.J. Jacobi. The solution of the following problem: "to transform a square table of m^2 numbers by adding minimal numbers l_i to each horizontal row, in such a way that it possess m transversal maxima", determines the order and the shortest normal form reduction of he system: the equations u_i = 0 must be respectively diff erentiated l_i times. One also determines the number of di fferentiations of each equation of the given system needed to produce the differential equations necessary to reduce the proposed system to a single equation

Looking for the order of a system of arbitrary ordinary differential equations. De investigando ordine systematis aequationum differentialium vulgarium cujuscunque

English translation of a posthumous paper in Latin of C.G.J. Jacobi: Journal für die reine und angewandte Mathematik, 64 , 4, 297-320, Berlin, Georg Reimer, 1865.International audienceThis paper was edited by S. Cohn and C.W. Borchardt from posthumous manuscripts of C.G.J. Jacobi. The various canonical forms that a given system ordinary differential equations may take are considered. Looking for the order of the system, without using a normal form, is reduced to a problem of inequalities: the affectation problem. A new type of formulas, the truncated determinants, is introduced. The non vanishing of this quantity means that the order will be equal to the value H , solution of this in- equalities problem, which is obtained by an algorithm similar to Harold Kuhn's Hungarian metho

Vorlesungen über Dynamik : nebst fünf hinterlassenen Abhandlungen desselben

von C. G. J. Jacobi ; hrsg. von A. Clebsch

Canon arithmeticus sive tabulae quibus exhibentur pro singulis numeris primis vel primorum potestatibus infra 1000 numeri ad datos indices et indices ad datos numeros pertinentes

edidit C. G. J. Jacob