LINEAR VOLTERRA INTEGRAL EQUATIONS AND LAPLACE TRANSFORMS

by Sudhanshu Aggarwal, Ms. Nidhi Sharma

Many advance problems of engineering and sciences like electric circuit problem, the problem of determining the blood glucose concentration of patient during intravenous injection and growth problem of cells can be easily solved by building their mathematical models using Volterra integral equation or system of Volterra integral equations. Laplace transform is widely used integral transform and can be used for determining the solution of Volterra integral equations and their systems. This book is to explore the basic concepts of Volterra integral equations and their systems in a simple, systematic and easy-to-understand manner. The present book is divided into seven chapters which cover all the important topics like introduction of Volterra integral equations, Laplace transforms, inverse Laplace transforms, applications of Laplace transforms for solving convolution type linear Volterra integral equation (first and second kind) and their systems.Chapter 1 presents introduction of Volterra integral equations. The definition and examples of integral equation, Volterra integral equation, primitive of Volterra integral equation, different types of Volterra integral equations, linear and non-linear Volterra integral equations, convolution type Volterra integral equations and their system are presented in a brief manner.Chapter 2 deals with Laplace transforms with its fundamental properties. Chapter 3 discusses the inverse Laplace transforms with partial fraction method and convolution theorem of inverse Laplace transforms for determining the inverse Laplace transforms of functions.Chapter 4 discusses the application of Laplace transform for solving convolution type linear Volterra integral equation of second kind.Chapter 5 discusses the application of Laplace transform for solving convolution type linear Volterra integral equation of first kind.Chapter 6 deals with the application of Laplace transform for solving system of convolution type linear Volterra integral equations of second kind.Chapter 7 discusses the application of Laplace transform for solving system of convolution type linear Volterra integral equations of first kind.

Paperback

Published August 2, 2020