Lecture 1 - Definition and classification of linear integral equations

Lecture 2 - Conversion of IVP into integral equations

Lecture 3 - Conversion of BVP into an integral equations

Lecture 4 - Conversion of integral equations into differential equations

Lecture 5 - Integro-differential equations

Lecture 6 - Fredholm integral equation with separable kernel: Theory

Lecture 7 - Fredholm integral equation with separable kernel: Examples

Lecture 8 - Solution of integral equations by successive substitutions

Lecture 9 - Solution of integral equations by successive approximations

Lecture 10 - Solution of integral equations by successive approximations: Resolvent kernel

Lecture 11 - Fredholm integral equations with symmetric kernels: Properties of eigenvalues and eigenfunctions

Lecture 12 - Fredholm integral equations with symmetric kernels: Hilbert Schmidt theory

Lecture 13 - Fredholm integral equations with symmetric kernels: Examples

Lecture 14 - Construction of Green function - I

Lecture 15 - Construction of Green function - II

Lecture 16 - Green function for self adjoint linear differential equations

Lecture 17 - Green function for non-homogeneous boundary value problem

Lecture 18 - Fredholm alternative theorem - I

Lecture 19 - Fredholm alternative theorem - II

Lecture 20 - Fredholm method of solutions

Lecture 21 - Classical Fredholm theory: Fredholm first theorem - I

Lecture 22 - Classical Fredholm theory: Fredholm first theorem - II

Lecture 23 - Classical Fredholm theory: Fredholm second theorem and third theorem

Lecture 24 - Method of successive approximations

Lecture 25 - Neumann series and resolvent kernels - I

Lecture 26 - Neumann series and resolvent kernels - II

Lecture 27 - Equations with convolution type kernels - I

Lecture 28 - Equations with convolution type kernels - II

Lecture 29 - Singular integral equations - I

Lecture 30 - Singular integral equations - II

Lecture 31 - Cauchy type integral equations - I

Lecture 32 - Cauchy type integral equations - II

Lecture 33 - Cauchy type integral equations - III

Lecture 34 - Cauchy type integral equations - IV

Lecture 35 - Cauchy type integral equations - V

Lecture 36 - Solution of integral equations using Fourier transform

Lecture 37 - Solution of integral equations using Hilbert transform - I

Lecture 38 - Solution of integral equations using Hilbert transform - II

Lecture 39 - Calculus of variations: Introduction

Lecture 40 - Calculus of variations: Basic concepts - I

Lecture 41 - Calculus of variations: Basic concepts - II

Lecture 42 - Calculus of variations: Basic concepts and Euler equation

Lecture 43 - Euler equation: Some particular cases

Lecture 44 - Euler equation : A particular case and Geodesics

Lecture 45 - Brachistochrone problem and Euler equation - I

Lecture 46 - Euler's equation - II

Lecture 47 - Functions of several independent variables

Lecture 48 - Variational problems in parametric form

Lecture 49 - Variational problems of general type

Lecture 50 - Variational derivative and invariance of Euler's equation

Lecture 51 - Invariance of Euler's equation and isoperimetric problem - I

Lecture 52 - Isoperimetric problem - II

Lecture 53 - Variational problem involving a conditional extremum - I

Lecture 54 - Variational problem involving a conditional extremum - II

Lecture 55 - Variational problems with moving boundaries - I

Lecture 56 - Variational problems with moving boundaries - II

Lecture 57 - Variational problems with moving boundaries - III

Lecture 58 - Variational problems with moving boundaries; One sided variation

Lecture 59 - Variational problem with a movable boundary for a functional dependent on two functions

Lecture 60 - Hamilton's principle: Variational principle of least action