NOC:Integral Equations, Calculus of Variations and its Applications


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