Symmetry group solutions to differential equations

dc.contributor.advisor Wilkens, George en_US Burkman, Jacob Harry en_US 2013-02-06T20:13:07Z 2013-02-06T20:13:07Z 2007 en_US
dc.description Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2007 en_US
dc.description.abstract In this project we will be looking at Sophus Lie’s desire (his so called idee fixe) to apply Contact Transformations (what would eventually develop into the modern idea of a Lie Algebra) in order to arrive at symmetries of differential equations, and thus certain solutions. Our goal—as well as Lie’s—is to develop a more universal method for solving differential equations than the familiar cook-book methods we learn in an introductory ordinary or partial differential equations class. We answer three questions. What was the historical underpinning of Sophus Lie’s theory? How do we find the symmetry Lie algebras? How do we use the symmetry Lie algebras to find solutions to the differential equation? (In order to answer these questions we will need to fill in some background material and our answers will also result in a novel derivation of the “Fundamental Source Solution.”) Our second objective will be to establish a connection between solvability in Galois Theory and in Differential Equations. We will assume a familiarity with certain concepts from Abstract Algebra. en_US
dc.format.extent 69 pages en_US
dc.language en-US en_US
dc.publisher University of Hawaii at Manoa en_US
dc.rights All UHM dissertations and theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission from the copyright owner. en_US
dc.title Symmetry group solutions to differential equations en_US
dc.type Master's project en_US
dc.type.dcmi Text en_US
local.thesis.degreelevel Masters en_US
local.thesis.department Mathematics en_US
local.thesis.mastertype Plan B en_US
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