Learn · Transform Calculus and its applications in Differential Equations

Lecture 14 of 68Week 3 :

Lecture 14: Evaluation of Integrals using Laplace Transform

Prof. Adrijit Goswami · IIT Kharagpur

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Transform Calculus and its applications in Differential Equations, IIT Kharagpur (at NPTEL)
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All the lectures

  1. Lecture 1 : Introduction to Integral Transform and Laplace Transform Video
  2. Lecture 2 : Existence of Laplace Transform Video
  3. Lecture 3 : Shifting Properties of Laplace Transform Video
  4. Lecture 4 : Laplace Transform of Derivatives and Integration of a Function - I Video
  5. Lecture 5 : Laplace Transform of Derivatives and Integration of a Function - II Video
  6. Lecture 06: Explanation of properties of Laplace Transform using Examples Video
  7. Lecture 07: Laplace Transform of Periodic Function Video
  8. Lecture 08: Laplace Transform of some special Functions Video
  9. Lecture 09: Error Function, Dirac Delta Function and their Laplace Transform Video
  10. Lecture 10: Bessel Function and its Laplace Transform Video
  11. Lecture 11: Introduction to Inverse Laplace Transform Video
  12. Lecture 12: Properties of Inverse Laplace Transform Video
  13. Lecture 13: Convolution and its Applications Video
  14. Lecture 14: Evaluation of Integrals using Laplace Transform Video
  15. Lecture 15: Solution of Ordinary Differential Equations with constant coefficients using Laplace Transform Video
  16. Lecture 16 : Solution of Ordinary Differential Equations with variable coefficients using Laplace Transform Video
  17. Lecture 17 : Solution of Simultaneous Ordinary Differential Equations using Laplace Transform Video
  18. Lecture 18 : Introduction to Integral Equation and its Solution Process Video
  19. Lecture 19 : Introduction to Fourier Series Video
  20. Lecture 20 : Fourier Series for Even and Odd Functions Video
  21. Lecture 21: Fourier Series of Functions having arbitrary period - I Video
  22. Lecture 22: Fourier Series of Functions having arbitrary period - II Video
  23. Lecture 23: Half Range Fourier Series Video
  24. Lecture 24: Parseval's Theorem and its Applications Video
  25. Lecture 25: Complex form of Fourier Series Video
  26. Lecture 26: Fourier Integral Representation Video
  27. Lecture 27: Introduction to Fourier Transform Video
  28. Lecture 28: Derivation of Fourier Cosine Transform and Fourier Sine Transform of Functions Video
  29. Lecture 29: Evaluation of Fourier Transform of various functions Video
  30. Lecture 30: Linearity Property and Shifting Properties of Fourier Transform Video
  31. Lecture 31: Change of Scale and Modulation Properties of Fourier Transform Video
  32. Lecture 32: Fourier Transform of Derivative and Integral of a Function Video
  33. Lecture 33: Applications of Properties of Fourier Transform - I Video
  34. Lecture 34: Applications of Properties of Fourier Transform - II Video
  35. Lecture 35: Fourier Transform of Convolution of two functions Video
  36. Lecture 36: Parseval's Identity and its Application Video
  37. Lecture 37: Evaluation of Definite Integrals using Properties of Fourier Transform Video
  38. Lecture 38: Fourier Transform of Dirac Delta Function Video
  39. Lecture 39: Representation of a function as Fourier Integral Video
  40. Lecture 40: Applications of Fourier Transform to Ordinary Differential Equations - I Video
  41. Lecture 41 : Applications of Fourier Transform to Ordinary Differential Equations - II Video
  42. Lecture 42 : Solution of Integral Equations using Fourier Transform Video
  43. Lecture 43 : Introduction to Partial Differential Equations Video
  44. Lecture 44 : Solution of Partial Differential Equations using Laplace Transform Video
  45. Lecture 45 : Solution of Heat Equation and Wave Equation using Laplace Transform Video
  46. Lecture 46 : Criteria for choosing Fourier Transform, Fourier Sine Transform, Fourier Cosine Transform in solving Partial Differential Equations Video
  47. Lecture 47 : Solution of Partial Differential Equations using Fourier Cosine Transform and Fourier Sine Transform Video
  48. Lecture 48 : Solution of Partial Differential Equations using Fourier Transform - I Video
  49. Lecture 49 : Solution of Partial Differential Equations using Fourier Transform - II Video
  50. Lecture 50 : Solving problems on Partial Differential Equations using Transform Techniques Video
  51. Lecture 51: Introduction to Finite Fourier Transform Video
  52. Lecture 52: Solution of Boundary Value Problems using Finite Fourier Transform - I Video
  53. Lecture 53: Solution of Boundary Value Problems using Finite Fourier Transform - II Video
  54. Lecture 54: Introduction to Mellin Transform Video
  55. Lecture 55: Properties of Mellin Transform Video
  56. Lecture 56: Examples of Mellin Transform - I Video
  57. Lecture 57: Examples of Mellin Transform - II Video
  58. Lecture 58: Introduction to Z-Transform Video
  59. Lecture 59: Properties of Z-Transform Video
  60. Lecture 60: Evaluation of Z-Transform of some functions Video
  61. Live Session 26-02-2021 Video
  62. Live Session 10-03-2021 Video
  63. Live Session 05-04-2021 Video
  64. Live Session 22-02-2020 Video
  65. Live Session 13-03-2020 Video
  66. Live Session 25-02-2022 Video
  67. Live Session 25-03-2022 Video
  68. Live Session 11-04-2022 Video