# Transform Calculus and its applications in Differential Equations

- Institution: IIT Kharagpur
- Department: Mathematics
- Teacher: Prof. Adrijit Goswami
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [NPTEL](https://nptel.ac.in/courses/111105123)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/111105123)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture 1 : Introduction to Integral Transform and Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/781715681130) (Video)
2. [Lecture 2 : Existence of Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/9f38b3de988f) (Video)
3. [Lecture 3 : Shifting Properties of Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/efec6a111e82) (Video)
4. [Lecture 4 : Laplace Transform of Derivatives and Integration of a Function - I](https://invisiblenetwork.ai/learn/nptel/111105123/41f70c68936e) (Video)
5. [Lecture 5 : Laplace Transform of Derivatives and Integration of a Function - II](https://invisiblenetwork.ai/learn/nptel/111105123/c82113b6edfc) (Video)
6. [Lecture 06: Explanation of properties of Laplace Transform using Examples](https://invisiblenetwork.ai/learn/nptel/111105123/69fde179a744) (Video)
7. [Lecture 07: Laplace Transform of Periodic Function](https://invisiblenetwork.ai/learn/nptel/111105123/5bae93886cdf) (Video)
8. [Lecture 08: Laplace Transform of some special Functions](https://invisiblenetwork.ai/learn/nptel/111105123/f2eac8b22742) (Video)
9. [Lecture 09: Error Function, Dirac Delta Function and their Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/c3723e9dca45) (Video)
10. [Lecture 10: Bessel Function and its Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/15c3e604fa59) (Video)
11. [Lecture 11: Introduction to Inverse Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/36519ef9d085) (Video)
12. [Lecture 12: Properties of Inverse Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/c268228ee522) (Video)
13. [Lecture 13: Convolution and its Applications](https://invisiblenetwork.ai/learn/nptel/111105123/eeb0ea6a7082) (Video)
14. [Lecture 14: Evaluation of Integrals using Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/a5c4dbcbacdb) (Video)
15. [Lecture 15: Solution of Ordinary Differential Equations with constant coefficients using Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/040f7d93b28c) (Video)
16. [Lecture 16 : Solution of Ordinary Differential Equations with variable coefficients using Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/98972da32d9f) (Video)
17. [Lecture 17 : Solution of Simultaneous Ordinary Differential Equations using Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/cf8d3c83dc2e) (Video)
18. [Lecture 18 : Introduction to Integral Equation and its Solution Process](https://invisiblenetwork.ai/learn/nptel/111105123/e28a1a12213f) (Video)
19. [Lecture 19 : Introduction to Fourier Series](https://invisiblenetwork.ai/learn/nptel/111105123/104d57ca567b) (Video)
20. [Lecture 20 : Fourier Series for Even and Odd Functions](https://invisiblenetwork.ai/learn/nptel/111105123/82d20aae78f2) (Video)
21. [Lecture 21: Fourier Series of Functions having arbitrary period - I](https://invisiblenetwork.ai/learn/nptel/111105123/74b3e6904acc) (Video)
22. [Lecture 22: Fourier Series of Functions having arbitrary period - II](https://invisiblenetwork.ai/learn/nptel/111105123/d71c9937c08b) (Video)
23. [Lecture 23: Half Range Fourier Series](https://invisiblenetwork.ai/learn/nptel/111105123/304e2d434c9d) (Video)
24. [Lecture 24: Parseval's Theorem and its Applications](https://invisiblenetwork.ai/learn/nptel/111105123/079efab1654e) (Video)
25. [Lecture 25: Complex form of Fourier Series](https://invisiblenetwork.ai/learn/nptel/111105123/2eea9a33f6eb) (Video)
26. [Lecture 26: Fourier Integral Representation](https://invisiblenetwork.ai/learn/nptel/111105123/45cd0c005b1d) (Video)
27. [Lecture 27: Introduction to Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105123/8d2dcc98e602) (Video)
28. [Lecture 28: Derivation of Fourier Cosine Transform and Fourier Sine Transform of Functions](https://invisiblenetwork.ai/learn/nptel/111105123/df803942e6c1) (Video)
29. [Lecture 29: Evaluation of Fourier Transform of various functions](https://invisiblenetwork.ai/learn/nptel/111105123/22b590e89fa6) (Video)
30. [Lecture 30: Linearity Property and Shifting Properties of Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105123/1b2907617fe5) (Video)
31. [Lecture 31: Change of Scale and Modulation Properties of Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105123/1814164bccad) (Video)
32. [Lecture 32: Fourier Transform of Derivative and Integral of a Function](https://invisiblenetwork.ai/learn/nptel/111105123/1ee7fbc7f4bd) (Video)
33. [Lecture 33: Applications of Properties of Fourier Transform - I](https://invisiblenetwork.ai/learn/nptel/111105123/9a4ae11fda7a) (Video)
34. [Lecture 34: Applications of Properties of Fourier Transform - II](https://invisiblenetwork.ai/learn/nptel/111105123/10949b32f417) (Video)
35. [Lecture 35: Fourier Transform of Convolution of two functions](https://invisiblenetwork.ai/learn/nptel/111105123/6d909fe86dfa) (Video)
36. [Lecture 36: Parseval's Identity and its Application](https://invisiblenetwork.ai/learn/nptel/111105123/f9de9c995d26) (Video)
37. [Lecture 37: Evaluation of Definite Integrals using Properties of Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105123/3b0695596d9d) (Video)
38. [Lecture 38: Fourier Transform of Dirac Delta Function](https://invisiblenetwork.ai/learn/nptel/111105123/e7cbcdbb10a2) (Video)
39. [Lecture 39: Representation of a function as Fourier Integral](https://invisiblenetwork.ai/learn/nptel/111105123/1d795225d722) (Video)
40. [Lecture 40: Applications of Fourier Transform to Ordinary Differential Equations - I](https://invisiblenetwork.ai/learn/nptel/111105123/ae6daa5154ca) (Video)
41. [Lecture 41 : Applications of Fourier Transform to Ordinary Differential Equations - II](https://invisiblenetwork.ai/learn/nptel/111105123/a5c292e076c4) (Video)
42. [Lecture 42 : Solution of Integral Equations using Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105123/eb8b3e553a79) (Video)
43. [Lecture 43 : Introduction to Partial Differential Equations](https://invisiblenetwork.ai/learn/nptel/111105123/3af1ec3189e8) (Video)
44. [Lecture 44 : Solution of Partial Differential Equations using Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/c04c0fcc17a5) (Video)
45. [Lecture 45 : Solution of Heat Equation and Wave Equation using Laplace Transform](https://invisiblenetwork.ai/learn/nptel/111105123/f4347484dbb1) (Video)
46. [Lecture 46 : Criteria for choosing Fourier Transform, Fourier Sine Transform, Fourier Cosine Transform in solving Partial Differential Equations](https://invisiblenetwork.ai/learn/nptel/111105123/0bc2e9660337) (Video)
47. [Lecture 47 : Solution of Partial Differential Equations using Fourier Cosine Transform and Fourier Sine Transform](https://invisiblenetwork.ai/learn/nptel/111105123/09091993a677) (Video)
48. [Lecture 48 : Solution of Partial Differential Equations using Fourier Transform - I](https://invisiblenetwork.ai/learn/nptel/111105123/d84c93437690) (Video)
49. [Lecture 49 : Solution of Partial Differential Equations using Fourier Transform - II](https://invisiblenetwork.ai/learn/nptel/111105123/204b1077caab) (Video)
50. [Lecture 50 : Solving problems on Partial Differential Equations using Transform Techniques](https://invisiblenetwork.ai/learn/nptel/111105123/2697d890fda8) (Video)
51. [Lecture 51: Introduction to Finite Fourier Transform](https://invisiblenetwork.ai/learn/nptel/111105123/797062a2dd86) (Video)
52. [Lecture 52: Solution of Boundary Value Problems using Finite Fourier Transform - I](https://invisiblenetwork.ai/learn/nptel/111105123/cbf9b3d8c33f) (Video)
53. [Lecture 53: Solution of Boundary Value Problems using Finite Fourier Transform - II](https://invisiblenetwork.ai/learn/nptel/111105123/1247c3e49bf2) (Video)
54. [Lecture 54: Introduction to Mellin Transform](https://invisiblenetwork.ai/learn/nptel/111105123/36b3fef8e4bc) (Video)
55. [Lecture 55: Properties of Mellin Transform](https://invisiblenetwork.ai/learn/nptel/111105123/6e500ae38e59) (Video)
56. [Lecture 56: Examples of Mellin Transform - I](https://invisiblenetwork.ai/learn/nptel/111105123/bf57c0a9fbb1) (Video)
57. [Lecture 57: Examples of Mellin Transform - II](https://invisiblenetwork.ai/learn/nptel/111105123/8656274a27f2) (Video)
58. [Lecture 58: Introduction to Z-Transform](https://invisiblenetwork.ai/learn/nptel/111105123/62bd7780fa52) (Video)
59. [Lecture 59: Properties of Z-Transform](https://invisiblenetwork.ai/learn/nptel/111105123/ebe7ad366d3a) (Video)
60. [Lecture 60: Evaluation of Z-Transform of some functions](https://invisiblenetwork.ai/learn/nptel/111105123/90fe38b6331a) (Video)
61. [Live Session 26-02-2021](https://invisiblenetwork.ai/learn/nptel/111105123/781715681130-2) (Video)
62. [Live Session 10-03-2021](https://invisiblenetwork.ai/learn/nptel/111105123/9f38b3de988f-2) (Video)
63. [Live Session 05-04-2021](https://invisiblenetwork.ai/learn/nptel/111105123/efec6a111e82-2) (Video)
64. [Live Session 22-02-2020](https://invisiblenetwork.ai/learn/nptel/111105123/41f70c68936e-2) (Video)
65. [Live Session 13-03-2020](https://invisiblenetwork.ai/learn/nptel/111105123/c82113b6edfc-2) (Video)
66. [Live Session 25-02-2022](https://invisiblenetwork.ai/learn/nptel/111105123/69fde179a744-2) (Video)
67. [Live Session 25-03-2022](https://invisiblenetwork.ai/learn/nptel/111105123/5bae93886cdf-2) (Video)
68. [Live Session 11-04-2022](https://invisiblenetwork.ai/learn/nptel/111105123/f2eac8b22742-2) (Video)