# CUNT2481 Integral Equation

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Integral Equation

 Subject Name Code Type of course T-P-Pj Prerequisite Integral Equation CUNT2481 Theory  & Project 3-0-1 NIL

Objective

 This course unit aims to identify different type of Integral equations  To Solve different type of Boundary value problems of Integral Equations in nature To Covert differential equations into Integral equations.

Course outcomes

 Upon successful completion of this course, students will be able to: Solve Integral equations of different types. Solve Boundary Value  Problems of Integral type
 COs Course outcomes Mapping Cos with POs (High-3, Medium-2, Low-1) CO1 ·         Solve wave equation and understand significance of transverse waves. PO1(3), PO2(2) CO2 ·         Identify classes of non-linear ordinary differential equations. PO2(2), PO4(2) CO3 ·         Apply an appropriate method for the solution of non-linear 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

### Module-I

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.

### Module-II

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.

### Module-III

Conversion of Ordinary differential equations into integral equations.

Project 3: Prepare a report on advantages of  Conversion of Ordinary differential equations
into integral equations

### Module-IV

Homogeneous Fredholm Integral Equations of the Second kind with Separable Kernels.
Project-4 : Prepare a report on advantages of  Fredholm Integral Equations of the Second kind.

### Module-V

Fredholm Integral Equations of the Second kind with Separable Kernels.

### Module-VI

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.

### Module-VII

Solution of Volterra Integral Equation of the Second Kind  by Successive Substitutions.

Project-6: Prepare a report on Solution of Volterra Integral Equation of the Second Kind  by
Successive Substitutions

BOOK PRESCRIBED

1. Integral Equations and Boundary Value Problems by M.D. Raisinghania, S.Chand & Company pvt Ltd.  Ch-1, Ch-2, Ch-3, Ch-4 Ch-5 (5.1-5.7)

BOOK FOR REFERENCE

1. Introduction to Integral Equations with Applications , A.J. Jerri, Wiley-Interscience Publication,1999
2. Linear Integral Equations, W.V  Lovitt, , McGraw Hill, New York

Session-1:

Introduction, Definitions of Integral Equation, Linear, Non Linear Equation ,

Session-2

Fredholm Integral Equation, Volterra Integral Equation, Singular Integral Equation

Session-3

Special Kinds of Kernels , Integral equations of Convolution type

Session-4

Iterated Kernels and Resolvent Kernel.

Session-5 & 6:

Project 1: Prepare a detail report of different kind of Integral Equations

Session-7

Eigen values, Leibnitz’s rule of differentiation under integral sign

Session-8

Formula for converting multiple integral into single ordinary integral

Session-9

Regularity conditions, Inner product of two functions

Session-10

Definition and some simple examples of Solution of Integral Equations.

Session-11 &12

Project 2: Prepare a report on Leibnitz’s rule of differentiation under integral sign and Formula for converting multiple integral into single ordinary integral.

Session-13

Conversion of Ordinary differential equations into integral equations.

Session-14

Conversion of Ordinary differential equations into integral equations.

Session-15

Conversion of Ordinary differential equations into integral equations.

Session-16

Conversion of Ordinary differential equations into integral equations.

Session- 17 & 18

Project 3: Prepare a report on advantages of Conversion of Ordinary differential equations

Session-19
Homogeneous Fredholm Integral Equations of the Second kind

Session-20
Homogeneous Fredholm Integral Equations of the Second kind with Separable Kernels.

Session-21
Homogeneous Fredholm Integral Equations of the Second kind with Separable Kernels

Session-22
More problems on Homogeneous Fredholm Integral Equations of the Second kind with Separable Kernels

Session- 23 & 24
Project-4: Discuss some examples Fredholm Integral Equations of the Second      kind  with Separable  Kernels

Session-25
Fredholm Integral Equations of the Second kind with Separable Kernels

Session-26
Fredholm Integral Equations of the Second kind with Separable Kernels

Session-27
Fredholm Integral Equations of the Second kind with Separable Kernels

Session-28
Fredholm Integral Equations of the Second kind with Separable Kernels

Session-29
Method of Successive approximations: Concepts

Session-30
Solution of Fredholm Integral Equation of the Second Kind  by Successive Substitutions.

Session -31
Solution of Volterra Integral Equation of the Second Kind  by Successive Substitutions

Session -32

Solution of Volterra Integral Equation of the Second Kind  by Successive Substitutions

Session -33 & 34

Project-5:Discuss  Volterra Integral Equation of the Second Kind  and it’s Solutions.

Session-35
Method of Successive approximations: Solution of Fredholm Integral Equation of the Second Kind

Session-36
Solution of Fredholm Integral Equation of the Second Kind  by Successive Approximations

Session -37
Some Important Theorems

Session- 38
Solved examples of Method of Successive approximations

Session-39
Doubt clearing Class

Session -40 & 41
Project-6: Discuss Some Important Theorems of successive approximation

Session -42
Doubt Clearing Class

Session Plan:

Session Plan:

Session Plan:

### Dr Tumbanath Samantara

##### Teaching
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Dr. Tumbanath  Samantara currently works as Associate Professor & HoD, Department of Applied Mathematics, , School of Applied Sciences, Centurion University of Technology and Management, (Bhubaneswar Campus) Odisha. He has completed his Ph.D. in the field of Fluid Dynamics. He has more than 10 years of research experience and 19 years of teaching experience. During […]