Show simple item record

Transforming ordinary linear differential equations to constant coefficient differential equations

dc.contributor.advisorAllaway, W. R.
dc.contributor.authorRanta, Martin
dc.date.accessioned2017-06-06T13:08:44Z
dc.date.available2017-06-06T13:08:44Z
dc.date.created1978
dc.date.issued1978
dc.identifier.urihttp://knowledgecommons.lakeheadu.ca/handle/2453/2264
dc.description.abstractThe main purpose of this thesis is to give a characterization of nth order linear homogeneous differential equations that can be transformed into constant coefficient differential equations. The characterization given makes use of invariance theory originated by G. H. Halphen around 1880. Chapter 1 gives an introduction to the problem of transforming ordinary linear homogeneous differential equations into constant coefficient differential equations. Chapter 1 includes an example as well as enough of the theory of invariants to give a proof of the main theorem of this thesis. Chapter 3 is a development of the transform equations that we make use of throughout this thesis. That is, we make changes of the dependent variable and/or independent variable of a given differential equation. The transformed equation is expressed in terms of the coefficients of the original differential equation and the functions used to define the changes of variables that we have made. In the last section of Chapter 4, we prove an important invariance relation that is used in Chapter 5. The rest of Chapter 4 contains invariance results that are of historical interest as well as being a prelude to the results of Chapter 5. Chapter 5, the most important chapter of this thesis, concerns the invariance theory of Halphen. This invariance theory is needed to give the characterization of nth order differential equations that can be transformed into constant coefficient differential equations. Chapter 6 is devoted to applying the preceding theory to the solution of differential equations that can be transformed into constant coefficient differential equations. The appendix contains some interchange of summation formulas that we use throughout the thesis.
dc.language.isoen_US
dc.subjectDifferential equations, Linear
dc.subjectDifferential invariants
dc.titleTransforming ordinary linear differential equations to constant coefficient differential equations
dc.typeThesis
etd.degree.nameMaster of Science
etd.degree.levelMaster
etd.degree.disciplineMathematical Sciences
etd.degree.grantorLakehead University


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record