# Integral Equations, Calculus of variations and its applications - Institution: IIT Roorkee - Department: Mathematics - Taught by: Prof. P. N. Agrawal, Prof. D. N. Pandey - Level: Undergraduate - Language: English - Subjects: Mathematics - Source: [NPTEL](https://nptel.ac.in/courses/111107103) - Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.) - Syllabus: [at the source](https://nptel.ac.in/courses/111107103) - Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words) ## Lectures 1. [Definition and classification of linear integral equations](https://invisiblenetwork.ai/learn/nptel/111107103/a3c5f18904c5) (Video) 2. [Conversion of IVP into integral equations](https://invisiblenetwork.ai/learn/nptel/111107103/8febebe57a7f) (Video) 3. [Conversion of BVP into an integral equations](https://invisiblenetwork.ai/learn/nptel/111107103/b9dd2119978a) (Video) 4. [Conversion of integral equations into differential equations](https://invisiblenetwork.ai/learn/nptel/111107103/a53212575854) (Video) 5. [Integro-differential equations](https://invisiblenetwork.ai/learn/nptel/111107103/3ef5f118ce5e) (Video) 6. [Fredholm integral equation with separable kernel: Theory](https://invisiblenetwork.ai/learn/nptel/111107103/01a65f378db7) (Video) 7. [Fredholm integral equation with separable kernel: Examples](https://invisiblenetwork.ai/learn/nptel/111107103/0bd0f839f274) (Video) 8. [Solution of integral equations by successive substitutions](https://invisiblenetwork.ai/learn/nptel/111107103/b50b2cffa11a) (Video) 9. [Solution of integral equations by successive approximations](https://invisiblenetwork.ai/learn/nptel/111107103/c951957c6436) (Video) 10. [Solution of integral equations by successive approximations: Resolvent kernel](https://invisiblenetwork.ai/learn/nptel/111107103/b8c5483b1970) (Video) 11. [Fredholm integral equations with symmetric kernels: Properties of eigenvalues and eigenfunctions](https://invisiblenetwork.ai/learn/nptel/111107103/8ae60af2fd09) (Video) 12. [Fredholm integral equations with symmetric kernels: Hilbert Schmidt theory](https://invisiblenetwork.ai/learn/nptel/111107103/47836a6a40fc) (Video) 13. [Fredholm integral equations with symmetric kernels: Examples](https://invisiblenetwork.ai/learn/nptel/111107103/ffdbd9e45b09) (Video) 14. [Construction of Green function-I](https://invisiblenetwork.ai/learn/nptel/111107103/ed3163526091) (Video) 15. [Construction of Green function-II](https://invisiblenetwork.ai/learn/nptel/111107103/7b668ec34810) (Video) 16. [Green function for self adjoint linear differential equations](https://invisiblenetwork.ai/learn/nptel/111107103/6aad07d86b48) (Video) 17. [Green function for non-homogeneous boundary value problem](https://invisiblenetwork.ai/learn/nptel/111107103/91acab102d18) (Video) 18. [Fredholm alternative theorem-I](https://invisiblenetwork.ai/learn/nptel/111107103/69b5c09a14c4) (Video) 19. [Fredholm alternative theorem-II](https://invisiblenetwork.ai/learn/nptel/111107103/b593da0ace2e) (Video) 20. [Fredholm method of solutions](https://invisiblenetwork.ai/learn/nptel/111107103/585f516b81f2) (Video) 21. [Classical Fredholm theory: Fredholm first theorem-I](https://invisiblenetwork.ai/learn/nptel/111107103/c253f942c971) (Video) 22. [Classical Fredholm theory: Fredholm first theorem-II](https://invisiblenetwork.ai/learn/nptel/111107103/289b3112d314) (Video) 23. [Classical Fredholm theory: Fredholm second theorem and third theorem](https://invisiblenetwork.ai/learn/nptel/111107103/067bc79de56b) (Video) 24. [Method of successive approximations](https://invisiblenetwork.ai/learn/nptel/111107103/f88cabb1307e) (Video) 25. [Neumann series and resolvent kernels-I](https://invisiblenetwork.ai/learn/nptel/111107103/fee08b023529) (Video) 26. [Neumann series and resolvent kernels-II](https://invisiblenetwork.ai/learn/nptel/111107103/2ed9db169ac9) (Video) 27. [Equations with convolution type kernels-I](https://invisiblenetwork.ai/learn/nptel/111107103/98a14d082fff) (Video) 28. [Equations with convolution type kernels-II](https://invisiblenetwork.ai/learn/nptel/111107103/711f9438df17) (Video) 29. [Singular integral equations-I](https://invisiblenetwork.ai/learn/nptel/111107103/8c2f1f61d1d8) (Video) 30. [Singular integral equations-II](https://invisiblenetwork.ai/learn/nptel/111107103/baf324df6143) (Video) 31. [Cauchy type integral equations-I](https://invisiblenetwork.ai/learn/nptel/111107103/22685e501afa) (Video) 32. [Cauchy type integral equations-II](https://invisiblenetwork.ai/learn/nptel/111107103/6c5e3de6cc31) (Video) 33. [Cauchy type integral equations-III](https://invisiblenetwork.ai/learn/nptel/111107103/0a22743dd3e6) (Video) 34. [Cauchy type integral equations-IV](https://invisiblenetwork.ai/learn/nptel/111107103/e6d6d1b7c91e) (Video) 35. [Cauchy type integral equations-V](https://invisiblenetwork.ai/learn/nptel/111107103/3f81a66bc291) (Video) 36. [Solution of integral equations using Fourier transform](https://invisiblenetwork.ai/learn/nptel/111107103/e2304e468d28) (Video) 37. [Solution of integral equations using Hilbert transform-I](https://invisiblenetwork.ai/learn/nptel/111107103/21076f6e015d) (Video) 38. [Solution of integral equations using Hilbert transform-II](https://invisiblenetwork.ai/learn/nptel/111107103/45163951c73e) (Video) 39. [Calculus of variations: Introduction](https://invisiblenetwork.ai/learn/nptel/111107103/a4b49c5c4cbd) (Video) 40. [Calculus of variations: Basic concepts-I](https://invisiblenetwork.ai/learn/nptel/111107103/1bdaf91a4467) (Video) 41. [Calculus of variations: Basic concepts-II](https://invisiblenetwork.ai/learn/nptel/111107103/1599f121a190) (Video) 42. [Calculus of variations: Basic concepts and Euler equation](https://invisiblenetwork.ai/learn/nptel/111107103/d4451f5edd37) (Video) 43. [Euler equation: Some particular cases](https://invisiblenetwork.ai/learn/nptel/111107103/335a3d1c417f) (Video) 44. [Euler equation : A particular case and Geodesics](https://invisiblenetwork.ai/learn/nptel/111107103/9c1cc35e7769) (Video) 45. [Brachistochrone problem and Euler equation-I](https://invisiblenetwork.ai/learn/nptel/111107103/e766dc4f546a) (Video) 46. [Euler's equation-II](https://invisiblenetwork.ai/learn/nptel/111107103/f142c650cf78) (Video) 47. [Functions of several independent variables](https://invisiblenetwork.ai/learn/nptel/111107103/daf5185b71fe) (Video) 48. [Variational problems in parametric form](https://invisiblenetwork.ai/learn/nptel/111107103/df14ff5c88f9) (Video) 49. [Variational problems of general type](https://invisiblenetwork.ai/learn/nptel/111107103/009c0868518c) (Video) 50. [Variational derivative and invariance of Euler's equation](https://invisiblenetwork.ai/learn/nptel/111107103/ce77b1838bab) (Video) 51. [Invariance of Euler's equation and isoperimetric problem-I](https://invisiblenetwork.ai/learn/nptel/111107103/28f7a3412b7a) (Video) 52. [Isoperimetric problem-II](https://invisiblenetwork.ai/learn/nptel/111107103/96a3d33b0421) (Video) 53. [Variational problem involving a conditional extremum-I](https://invisiblenetwork.ai/learn/nptel/111107103/5a2c9e12f8bc) (Video) 54. [Variational problem involving a conditional extremum-II](https://invisiblenetwork.ai/learn/nptel/111107103/c1c9a5fe875b) (Video) 55. [Variational problems with moving boundaries-I](https://invisiblenetwork.ai/learn/nptel/111107103/92464ab3c376) (Video) 56. [Variational problems with moving boundaries-II](https://invisiblenetwork.ai/learn/nptel/111107103/a16a63478387) (Video) 57. [Variational problems with moving boundaries-III](https://invisiblenetwork.ai/learn/nptel/111107103/f9c779b6906d) (Video) 58. [Variational problems with moving boundaries; One sided variation](https://invisiblenetwork.ai/learn/nptel/111107103/1d172cb4f054) (Video) 59. [Variational problem with a movable boundary for a functional dependent on two functions](https://invisiblenetwork.ai/learn/nptel/111107103/0b8310d045b5) (Video) 60. [Hamilton's principle: Variational principle of least action](https://invisiblenetwork.ai/learn/nptel/111107103/dcbf6479613e) (Video)