THIS SEMINAR WAS SUBMITTED TO
DEPARTMENT OF INDUSTRIAL MATHEMATICS AND APPLIED
STATISTICS, FACULTY OF APPLIED PHYSICAL SCIENCE EBONYI STATE UNIVERSITY,
ABAKALIKI
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
AWARD OF BACHELOR OF SCIENCE (B.SC) DEGREE IN INDUSTRIAL MATHEMATICS AND
COMPUTER SCIENCE
Table of contents
Title page
Certification
Approval
Dedication
Acknowledgement
Abstract
Table of contents
Chapter one
Introduction
Chapter two
Literature review
Chapter three
Research
methodology
APPLICATIONS OF INTEGRAL TRANSFORMS
Abstract
In this seminar work we study the
properties of integral transforms, and their application to the solution of differential equations. In
particular we consider Laplace and
Fourier Transform.
1.0 Introduction
Integral transforms are
fundamental to the solution of differential (ordinary and partial) as well as integral
equations. They sometimes provide a means of obtaining closed form solutions to
some nonlinear equations. In this seminar work we examine the properties of
Laplace and Fourier transforms and their applications to the solution of differential equations.
1.1 Definition (Integral Transform)
Given a known function K(a,x)
of two variables a and x such that the integral
(1)
is convergent, then the
integral (1) is termed as the integral transform of the function
/(x) denoted /(:e)or T{f(x)}, i.e.
f(x) =
T{f(x)}=[K(a,x)f(x)dx (2)
The function K(a,x) is known as
the Kernel of the transformation and a is a parameter (real or complex)
independent of x.
1.2 Example: Suppose we take the Kernel,
K(a,x) = K(s,t) = 0 for t<0
= e-st for
t>0 Then the transform
is known as the Laplace Transform.
1.3 Definition (Laplace Transform)..................................READ MORE