Integral Equation
Subject Name  Code  Type of course  TPPj  Prerequisite 
Integral Equation  CUNT2481 
Theory & Project

301  NIL 
Objective

Course outcomes
Upon successful completion of this course, students will be able to:

COs  Course outcomes  Mapping Cos with POs (High3, Medium2, Low1) 
CO1  · Solve wave equation and understand significance of transverse waves.

PO1(3), PO2(2) 
CO2  · Identify classes of nonlinear ordinary differential equations.

PO2(2), PO4(2) 
CO3  · Apply an appropriate method for the solution of nonlinear ordinary differential equations.

PO9(3) 
CO5  · Competence in solving applied problems which are linear and nonlinear form, Solve Laplace equation, Diffusion equation, heat equation.

PO2(2), PO1(3) 
Course outline
ModuleI
Introduction, Definitions of Integral Equation ,Linear, Non Linear Equations ,Fredholm Integral Equation, Volterra Integral Equation, Singular Integral Equation, Special Kinds of Kernels , Integral equations of Convolution type, Iterated Kernel sand Resolvent Kernel.
Project 1: Prepare a detail report of different kind of Integral Equations.
ModuleII
Eigen values, Leibnitz’s rule of differentiation under integral sign, Formula for converting multiple integral into single ordinary integral, Regularity conditions, Inner product of two functions, Definition and some simple examples of Solution of Integral Equations.
Project 2: Prepare a report on Leibnitz’s rule of differentiation under integral sign and
Formula for converting multiple integral into single ordinary integral.
ModuleIII
Conversion of Ordinary differential equations into integral equations.
Project 3: Prepare a report on advantages of Conversion of Ordinary differential equations
into integral equations
ModuleIV
Homogeneous Fredholm Integral Equations of the Second kind with Separable Kernels.
Project4 : Prepare a report on advantages of Fredholm Integral Equations of the Second kind.
ModuleV
Fredholm Integral Equations of the Second kind with Separable Kernels.
ModuleVI
Method of Successive approximations: Concepts, Solution of Fredholm Integral Equation of the Second Kind by Successive Substitutions.
Project 5: Prepare a report on Solution of Fredholm Integral Equation of the Second Kind by Successive Substitutions.
ModuleVII
Solution of Volterra Integral Equation of the Second Kind by Successive Substitutions.
Project6: Prepare a report on Solution of Volterra Integral Equation of the Second Kind by
Successive Substitutions
BOOK PRESCRIBED
 Integral Equations and Boundary Value Problems by M.D. Raisinghania, S.Chand & Company pvt Ltd. Ch1, Ch2, Ch3, Ch4 Ch5 (5.15.7)
BOOK FOR REFERENCE
 Introduction to Integral Equations with Applications , A.J. Jerri, WileyInterscience Publication,1999
 Linear Integral Equations, W.V Lovitt, , McGraw Hill, New York