CUNT2481 Integral Equation

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Dr Tumbanath Samantara

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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 ,

https://www.youtube.com/watch?v=krGSlWnM-4k

Session-2

Fredholm Integral Equation, Volterra Integral Equation, Singular Integral Equation
https://www.youtube.com/watch?v=sZ9H72v21pQ

Session-3

Special Kinds of Kernels , Integral equations of Convolution type

Session-4

Iterated Kernels and Resolvent Kernel.

https://www.youtube.com/watch?v=hsTW7H3bztc

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

https://www.youtube.com/watch?v=8R2Oj3WhvUk

Session-8

Formula for converting multiple integral into single ordinary integral

https://www.youtube.com/watch?v=tZZ_bYqD1XU

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.

https://www.youtube.com/watch?v=jFa81XkK5i0

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

https://www.youtube.com/watch?v=iRoaujIE4yM

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

https://www.youtube.com/watch?v=IBUWWqEQAfs

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

https://www.youtube.com/watch?v=K0t53t7RLWY

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

https://www.youtube.com/watch?v=Qo9riz9NZ64

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

https://www.youtube.com/watch?v=Qo9riz9NZ64

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

https://www.youtube.com/watch?v=yR-Ct6eNDrg

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

https://www.youtube.com/watch?v=9zUitWinDZI

 

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

https://www.youtube.com/watch?v=xsFgoxikXS4

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:

Our Main Teachers

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 […]