Lect. 03 M.Sc. I Sem. II Integral Equations

2MTH3 : INTEGRAL EQUATIONS
Unit I : Definition of integral equations, Types of integral equations: Fredholm integral equations of the first and second kind, homogeneous Fredholm integral equations of the second kind,Volterra integral equations of first and second kind, Homogeneous Volterra integral equations of the second kind, special kinds of kernels, symmetric kernels, separable and degenerate kernels, Leibnitz rule, solution of integral equations, solved examples, Method
of converting an initial value problem into integral equations, solved examples, method of
converting a boundary value problems into a Fredholm integral equations. Solved examples.
Unit II : Eigen values and Eigen functions: (a) Solution of homogeneous Fredholm integral equations
of the second kind with separable kernels, solved examples based on (a).
(b) Solution of Fredholm integral equation of the second kind with separable kernels,
Solved examples based on (b).
Unit III : Definition of iterated kernels or functions, definition of resolvent kernels or reciprocal kernel, solution of Fredholm integral equation of the second kind by successive substitutions, solution of Volterra integral equation of the second kind by successive substitutions, Neumann’s series, some important theorems, determination of iterated kernels, determination of resolvent kernels for Fredholm integral equations, solution of Fredholm integral equation with the help of resolvent kernels, solution of Fredholm integral equations by method of successive approximation to find solutions up to third order. Solve examples.
Unit IV : Solution of Volterra integral equations of second kind, determination of resolvent kernels for Volterra integral equations, solution of Volterra integral equations with the help of the resolvent kernels, solved examples, Neumann’s series, Method of successive approximation for solving Volterra integral equations of second kind, Volterra integral equations of first kind , solution of Volterra integral equations of the first kind, solved examples, some fundamental properties of Eigen values and Eigen functions for symmetric kernels.
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Unit V : Applications of integral equations and Green’s function to ordinary differential equations, definition of Green’s functions, Important theorems, constructions of Green’s functions, solved examples, solution of boundary value problems using Green’s functions, solved examples, solution of boundary value problems using Green’s functions, solved examples, the case of homogeneous and conditions of boundary value problems.
Reference books:
1) Integral equations by Shanti Swaroop, Shiv Raj Singh
2) Linear integral equation, Theory and techniques, Academic press, New York 1971
3) R.P. Kanwal, Linear Integral Equation, Theory and Techniques, Academic Press, N.Y. (1971).
4) S.G. Mikhlin, Linear Integral Equations, Hindustan Book Agency, (1960).
5) A.M. Viazwaz, A First Course in Integral Equations, World Scientific (1997).
6) L.I.G. Chambers, Integral Equation: A Short Course, International Text Book Company Ltd. (1976).
7) Larry Andrews, Bhimsen Shiramoggo, Integral Transform for Engineers, Prentice Hall of India (2003).
8) Integral equations and boundary value problems by M. D. Raisinghania, S. Chand publication
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#Solved examples

[movewithmaths]

Chaitali Jagdish Taori
Well explain 👍

[shivaniadsad]

Shivani Surendra Adsad
Easy to understand. Well explained

[shubhamadkine]

Shubham Martandrao Adkine
Thanks 🙏 for point to point explanation...!!

[kirandahake]

Kiran Madhukarrao Dahake
thanks sir basic concept understand easily

[akshaysonwane]

Akshay Madhukarrao Sonwane
Concept is explained very nicely.. 👍

[pallavigade]

Pallavi Babarao Gade
You explain so very well..Thanku so much for that🙏🙏👍

[poojakamble]

Pooja Gopichand Kamble good teaching sir

[maurinawaghare]

Mayuri Narayanrao Nawghare
Most helpful lecture sir..