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Richa Nandra, Lovely Professional University Unit 24: Integral Equations and Algebraic System of Linear Equations

Unit 24: Integral Equations and Algebraic Notes
System of Linear Equations

CONTENTS
Objectives
Introduction
24.1 Connection between a First Order Differential Equation and Integral Equation

24.2 Conversion of a Differential Equation of Second Order to an Integral Equation
24.3 Fredholm Integral Equations and Boundary Value Problem
24.4 Relation between Integral Equations and Algebraic System of Linear Equations
24.5 Summary
24.6 Keywords

24.7 Review Questions
24.8 Further Readings

Objectives

After studying this unit, you should be able to:
 Remind ourselves that in unit six we studied Picard s method of showing the existence of
the solution of first order differential equations which let us to integral equations.
 Study how to express a differential equation with boundary conditions or initial conditions
into an integral equation.

 See the connection between an integral equation and an algebraic system of linear equations.
Introduction

In the next few units we are interested in studying various types of integral equations and see
how to solve them.
You will learn how to express a differential equation with initial conditions into an integral
equation.
In the case of boundary value problem of a differential equation we are let to Fredholm type of
integral equations.
By dividing the interval into segments we will see how the solution of an integral equation
reduced to an algebraic system to equations.
24.1 Connection between a First Order Differential Equation and
Integral Equation

In unit 6 we studied the existence and uniqueness of the solution of the first order differential
equation of the type

dy
= f(x, y) ...(1)
dx

LOVELY PROFESSIONAL UNIVERSITY 411