Modules / Lectures

Sl.No | Chapter Name | English |
---|---|---|

1 | Definition and classification of linear integral equations | Download To be verified |

2 | Conversion of IVP into integral equations | Download To be verified |

3 | Conversion of BVP into an integral equations | Download To be verified |

4 | Conversion of integral equations into differential equations | Download To be verified |

5 | Integro-differential equations | Download To be verified |

6 | Fredholm integral equation with separable kernel: Theory | Download To be verified |

7 | Fredholm integral equation with separable kernel: Examples | Download To be verified |

8 | Solution of integral equations by successive substitutions | Download To be verified |

9 | Solution of integral equations by successive approximations | Download To be verified |

10 | Solution of integral equations by successive approximations: Resolvent kernel | Download To be verified |

11 | Fredholm integral equations with symmetric kernels: Properties of eigenvalues and eigenfunctions | Download To be verified |

12 | Fredholm integral equations with symmetric kernels: Hilbert Schmidt theory | Download To be verified |

13 | Fredholm integral equations with symmetric kernels: Examples | Download To be verified |

14 | Construction of Green function-I | Download To be verified |

15 | Construction of Green function-II | Download To be verified |

16 | Green function for self adjoint linear differential equations | Download To be verified |

17 | Green function for non-homogeneous boundary value problem | Download To be verified |

18 | Fredholm alternative theorem-I | Download To be verified |

19 | Fredholm alternative theorem-II | Download To be verified |

20 | Fredholm method of solutions | Download To be verified |

21 | Classical Fredholm theory: Fredholm first theorem-I | Download To be verified |

22 | Classical Fredholm theory: Fredholm first theorem-II | Download To be verified |

23 | Classical Fredholm theory: Fredholm second theorem and third theorem | Download To be verified |

24 | Method of successive approximations | Download To be verified |

25 | Neumann series and resolvent kernels-I | Download To be verified |

26 | Neumann series and resolvent kernels-II | Download To be verified |

27 | Equations with convolution type kernels-I | Download To be verified |

28 | Equations with convolution type kernels-II | Download To be verified |

29 | Singular integral equations-I | Download To be verified |

30 | Singular integral equations-II | Download To be verified |

31 | Cauchy type integral equations-I | Download To be verified |

32 | Cauchy type integral equations-II | Download To be verified |

33 | Cauchy type integral equations-III | Download To be verified |

34 | Cauchy type integral equations-IV | Download To be verified |

35 | Cauchy type integral equations-V | Download To be verified |

36 | Solution of integral equations using Fourier transform | Download To be verified |

37 | Solution of integral equations using Hilbert transform-I | Download To be verified |

38 | Solution of integral equations using Hilbert transform-II | Download To be verified |

39 | Calculus of variations: Introduction | Download To be verified |

40 | Calculus of variations: Basic concepts-I | Download To be verified |

41 | Calculus of variations: Basic concepts-II | Download To be verified |

42 | Calculus of variations: Basic concepts and Euler equation | Download To be verified |

43 | Euler equation: Some particular cases | Download To be verified |

44 | Euler equation : A particular case and Geodesics | Download To be verified |

45 | Brachistochrone problem and Euler equation-I | Download To be verified |

46 | Euler's equation-II | Download To be verified |

47 | Functions of several independent variables | Download To be verified |

48 | Variational problems in parametric form | Download To be verified |

49 | Variational problems of general type | Download To be verified |

50 | Variational derivative and invariance of Euler's equation | Download To be verified |

51 | Invariance of Euler's equation and isoperimetric problem-I | Download To be verified |

52 | Isoperimetric problem-II | Download To be verified |

53 | Variational problem involving a conditional extremum-I | Download To be verified |

54 | Variational problem involving a conditional extremum-II | Download To be verified |

55 | Variational problems with moving boundaries-I | Download To be verified |

56 | Variational problems with moving boundaries-II | Download To be verified |

57 | Variational problems with moving boundaries-III | Download To be verified |

58 | Variational problems with moving boundaries; One sided variation | Download To be verified |

59 | Variational problem with a movable boundary for a functional dependent on two functions | Download To be verified |

60 | Hamilton's principle: Variational principle of least action | Download To be verified |

Sl.No | Language | Book link |
---|---|---|

1 | English | Not Available |

2 | Bengali | Not Available |

3 | Gujarati | Not Available |

4 | Hindi | Not Available |

5 | Kannada | Not Available |

6 | Malayalam | Not Available |

7 | Marathi | Not Available |

8 | Tamil | Not Available |

9 | Telugu | Not Available |