Title:
CAUCHY'S FURTHER CONTRIBUTIONS TO MATHEMATICS: THE EXISTENCE THEOREMS IN ORDINARY DIFFERENTIAL EQUATIONS

Authors:
Boniello Carmine, Italy

Abstract:

Cauchy was a mathematician who gave pure mathematics a great and important impetus; for fecundity and variety of production, he can be compared only to Euler: his writings, published during forty-seven years of continuous work, in separate volumes or in scientific collections, are about 789. To prevent this immense work from being lost, the Académie des Sciences in Paris began publishing the “Oeuvres complétes” as early as 1882, which is not yet finished. In this paper, we will examine one interesting innovations Cauchy made to mathematics of all time, the existence theorems in ordinary differential equations.