Degree Type

Dissertation

Date of Award

1988

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Rajbir S. Dahiya

Abstract

In this dissertation important theoretical results on n-dimensional Laplace transform, for n ≥ 2, are developed. It starts with a brief review on literature of Laplace transformation. The definitions and the concept of the region of convergence in n-dimensional Laplace transform are successfully extended from those of two dimensional Laplace transform. A number of new and useful theorems on multidimensional Laplace transforms and inverse multidimensional Laplace transform are presented. Proofs of these theorems are explicitly shown. Furthermore, in order to justify the validity of these results, several examples corresponding to each of these theorems are discussed in some detail;In certain non-linear system analysis it becomes necessary to find the inverse of n-dimensional Laplace transform and specify the inverse image at a single variable. A commonly used technique to obtain the inverse of the multidimensional Laplace transform is known as the association of variable. Several new and useful theorems on the association of variables are also developed with illustrative examples. With the concept of association of variables, a transformed function in n-dimensions is first evaluated at a single transformed variable and is then taken single dimensional inverse Laplace transform. This notion shows a technique of evaluating complicated integrals in a straight-forward manner;As a direct application of multidimensional Laplace transform, several boundary value problems characterized by partial differential equation are solved. These boundary value problems include the flow of electricity in a transmission line, semi-infinite string problem, heat transfer for a thin semi-infinite plate, electrostatic potential and a temperature distribution for the semi-infinite slab problem;Finally, a summary of the major contributions of this dissertation together with several possible directions for future research are included.

DOI

https://doi.org/10.31274/rtd-180813-11250

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Joyati C. Debnath

Language

en

Proquest ID

AAI8825386

File Format

application/pdf

File Size

134 pages

Included in

Mathematics Commons

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