NPTEL - Integral equations, calculus of variations and its applications 

offered by IIT Roorkee

Definition and classification of linear integral equations

Conversion of IVP into integral equations

Conversion of BVP into integral equations

Conversion of integral equationsinto differential equations

Integro-differential equations

Fredholm integral equation with separable kernel: Theory

Fredholm integral equation with separable kernel: Examples

Solution of integral equations by successive substitutions

Solution of integral equations by successive approximations

Solution of integral equations by successive approximations: Resolvent kernel

Fredholm integral equations with symmetric kernels:Properties of eigenvalues and eigen functions

Fredholm integral equations with symmetric kernels:Hilbert Schmidt theory

Fredholm integral equations with symmetric kernels:Examples

Construction of Green's function-I

Construction of Green's function-II

Green's function for self adjoint linear differential equations

Green's function for non- homogeneous boundary value problem

Fredholm alternative theorem-I

Fredholm alternative theorem-II

Fredholm method of solutions

Classical Fredholm theory: Fredholm first theorem-I

Classical Fredholm theory: Fredholm first theorem-II

Classical Fredholm theory: Fredholm second and third theorem

Method of successive approximations

Neumann Series and resolvent kernels-I

Neumann Series and resolvent kernels-II

Equations with convolution type kernels-I

Equations with convolution type kernels-II

Singular integral equations-I

Singular integral equations-II

Cauchy type integral equations-I

Cauchy type integral equations-II

Cauchy type integral equations-III

Cauchy type integral equations-IV

Cauchy type integral equations-V

Solution of integral equations using Fourier transform

Solution of integral equations using Hilbert- transform-I

Solution ofintegral equations using Hilbert- transform-II

Calculus of variations: Introduction

Calculus of variations: Basic concepts-I

Calculus of variations:Basic concepts-II

Calculus of variations: Basic concepts and Euler's equation

Euler's equation:Some particular cases

Euler's equation:A particular case and Geodesics

Brachistochrone problem and Euler's equation-I

Euler's equation-II

Functions of several independent variables

Variational problems in parametric form

Variational problems of general type

Variational derivative and invariance of Euler's equation

Week 11

Invariance of Euler's equation and isoperimetric problem-I

Isoperimetri c problem-II

Variational problem involving a conditional extremum-I

Variational problem involving a conditional extremum-II

Variational problems with moving boundaries- I

Variational problems with moving boundaries- II

Variational problems with moving boundaries- III

Variational problems with moving boundaries; One sided variation

Variational problem with a movable boundary for a functional dependent on two functions

Hamilton's principle;Variational principle of least action