Learn · Integral Equations, Calculus of variations and its applications
Lecture 19 of 60Unit-4
Fredholm alternative theorem-II
Prof. P. N. Agrawal and Prof. D. N. Pandey · IIT Roorkee
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All the lectures
- Definition and classification of linear integral equations
- Conversion of IVP into integral equations
- Conversion of BVP into an integral equations
- Conversion of integral equations into 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 eigenfunctions
- Fredholm integral equations with symmetric kernels: Hilbert Schmidt theory
- Fredholm integral equations with symmetric kernels: Examples
- Construction of Green function-I
- Construction of Green function-II
- Green function for self adjoint linear differential equations
- Green 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 theorem 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 of integral 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 equation
- Euler equation: Some particular cases
- Euler equation : A particular case and Geodesics
- Brachistochrone problem and Euler 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
- Invariance of Euler's equation and isoperimetric problem-I
- Isoperimetric 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