The Cauchy kovalevskaya theorem tells us about solutions to
systems of differential equations. If we look at m equations in n
dimension, with coefficient that are analytic function, we can know
about the existence of solutions using this theorem.
View page
There is a theorem called the Cauchy-Kowalevski theoremwhich deals with the existence of solutions to a system of mdifferential equation in n dimensions when the coefficients are analytic functions. I am guessing this is what you are asking about. A special case of this theorem was proved by Cauchy alone.
The theorem talks about the local existence of a solution.
Since this is a complicated topic, I will provide a link.
View page
Cauchy was the first mathematician who developed definitions and
rules for mathematics. He introduced the definitions of the
integral and rules for series convergence. There are sixteen
concepts and theorems named after him.
View page
We need more information. Is there a limit or integral? The
theorem states that the deivitive of an integral of a function is
the function