Integral Equation
| Subject Name | Code | Type of course | T-P-Pj | Prerequisite |
| Integral Equation | CUNT2481 |
Theory & Project
|
3-0-1 | NIL |
Objective
|
Course outcomes
Upon successful completion of this course, students will be able to:
|
| 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
- 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
- Introduction to Integral Equations with Applications , A.J. Jerri, Wiley-Interscience Publication,1999
- Linear Integral Equations, W.V Lovitt, , McGraw Hill, New York