Qualitative Behavior Of Dynamical Vector Fields

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dc.contributor Kirby , Roger Dale en_US
dc.date.accessioned 2007 -09 -17T17 :07 :34Z
dc.date.accessioned 2011 -08 -24T21 :41 :01Z
dc.date.available 2007 -09 -17T17 :07 :34Z
dc.date.available 2011 -08 -24T21 :41 :01Z
dc.date.issued 2007 -09 -17T17 :07 :34Z
dc.date.submitted August 2007 en_US
dc.identifier.uri http : / /hdl .handle .net /10106 /617
dc.description.abstract Differential Equations come in two classes , deterministic and stochastic . The first part of this analysis establishes the stable properties of the set of all trajectories converging on a critical point in the real plane defined by two distinct negative eigenvalues . Also in the deterministic class I offer a method for finding closed -form primitives for a great variety of differential forms , through a reduction process facilitated by a Lyapunov -type Energy function . Many of these forms lie in classes which heretofore have not been shown to be solvable in closed form . The last part of this work outlines the appropriate procedures for calculating differentials and solutions for fields perturbed by random processes . In the final chapter a new theory of Laplace Transforms for stochastic calculations has been developed . The introduction of a Table of Transforms has been initiated , and shall eventually be enlarged . Applications are offered to demonstrate its utility . en_US
dc.language.iso EN en_US
dc.publisher Mathematics en_US
dc.title Qualitative Behavior Of Dynamical Vector Fields en_US
dc.type Ph .D . en_US

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Qualitative Behavior Of Dynamical Vector Fields. Available electronically from http : / /hdl .handle .net /10106 /617 .

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