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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.
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What math equation did sonya kovalskaya figure out?
She did not figure out a particular equation but found the set of conditions under which solutions to a class of partial differential equations would exist. This is now known as the Cauchy-Kovalevskaya Theorem.
What is cauchy riemen equation?
partial of u with respect to x = partial of v with respect to y partial of u with respect to y = -1*partial of v with respect to x
What are the applications of cauchy-riemann equations in engineering?
Well, cauchy-riemann differential equation is a part of complex variables and in real-life applications such as engineering, it can be used in determining the flow of fluids, such as the flow around the pipe. In fluid mechanics, the cauchy-riemann equations are decribed by two complex variables, i.e. u and v, and if these two variables satisfy the equations in an open subset of R2, then the vector field can be asserted from the two cauchy-riemann equations, ux = vy (1) uy = - vx (2) This I think can help interpreting the potential flow (Wikipedia) in two dimensions using the cauchy-riemann equations. In fluid mechanics, the potential flow can be analyzed using the cauchy-riemann equations.
What did Sofia kovalevskaya did in math?
She is probably best known for her work on partial differential equations. Her paper on the subject contains what is now known as the Cauchy–Kovalevskaya theorem, which gives conditions under which a certain class of those equations does have solutions.For her doctorate she also presented papers, at the University of Göttingen, on the dynamics of Saturn's rings and on elliptic integrals.
What is a cauchy sequence?
(xn) is Cauchy when abs(xn-xm) tends to 0 as m,n tend to infinity.
