# Modeling Stochastic phenomena for Engineering applications: Part-1

- Institution: IIT Bombay
- Department: Chemical Engineering
- Teacher: Prof. Yelia Shankaranarayana Mayya
- Level: Undergraduate
- Language: English
- Subjects: Chemistry, Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/103101354)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/103101354)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Week1: Lecture1: Stirling’s Approximation](https://invisiblenetwork.ai/learn/nptel/103101354/f0fffd1ea10e) (Video)
2. [Week 1: Lecture 2: Fourier Transforms and characteristic function.](https://invisiblenetwork.ai/learn/nptel/103101354/236f0cf87f7c) (Video)
3. [Week 1: Lecture 3: Dirac Delta function](https://invisiblenetwork.ai/learn/nptel/103101354/265cdc9bd37e) (Video)
4. [Week 1: Lecture 4: Applications of delta function and Generating functions.](https://invisiblenetwork.ai/learn/nptel/103101354/1ac304e0df8e) (Video)
5. [Week 1: Lecture 5: Laplace Transforms & Convolution theorem](https://invisiblenetwork.ai/learn/nptel/103101354/ca7dcaf16e87) (Video)
6. [Week 2: Lecture 6: Generating function for discrete variables and Binomial distribution](https://invisiblenetwork.ai/learn/nptel/103101354/65765af89b69) (Video)
7. [Week 2: Lecture 7: Bernoulli and Poisson distributions](https://invisiblenetwork.ai/learn/nptel/103101354/fdd9980be66a) (Video)
8. [Week 2: Lecture 8: Waiting time distributions; Gaussian approximation to Poisson distribution](https://invisiblenetwork.ai/learn/nptel/103101354/d3fb8266f168) (Video)
9. [Week 2: Lecture 9: Introduction to Central Limit Theorem](https://invisiblenetwork.ai/learn/nptel/103101354/21486abb7b48) (Video)
10. [Week 2: Lecture 10: Proof of Central Limit Theorem (CLT)](https://invisiblenetwork.ai/learn/nptel/103101354/ae3006d04bd7) (Video)
11. [Week 3: Lecture 11: Universality of Normal distribution and Exceptions](https://invisiblenetwork.ai/learn/nptel/103101354/e160d738f10f) (Video)
12. [Week 3: Lecture 12: Introduction to Random Walk: Extension of Central Limit Theorem](https://invisiblenetwork.ai/learn/nptel/103101354/8ca503a42e8c) (Video)
13. [Week 3: Lecture 13: Random walk and Diffusion coefficient: Conditional and Transition](https://invisiblenetwork.ai/learn/nptel/103101354/48ba2efac726) (Video)
14. [Week 4: Lecture 14: Characteristics of Stochastic Phenomena: Markov Processes](https://invisiblenetwork.ai/learn/nptel/103101354/a774d5a3f7ae) (Video)
15. [Week 4: Lecture 15: Propagating Markov processes via Transition Probability Matrix with](https://invisiblenetwork.ai/learn/nptel/103101354/a36def209c6d) (Video)
16. [Week 4: Lecture 16: Chapman-Kolmogorov Equation for Multistep Transition probability and solution...](https://invisiblenetwork.ai/learn/nptel/103101354/5514608a3d03) (Video)
17. [Week 4: Lecture 17: Transient solutions and Continuous time Markov process](https://invisiblenetwork.ai/learn/nptel/103101354/a966cad56360) (Video)
18. [Week 5: Lecture 18: Exact solution to Symmetric (or unbiased) one-dimensional Random walk (1-D RW)..](https://invisiblenetwork.ai/learn/nptel/103101354/7efb2bbbc7e2) (Video)
19. [Week 5: Lecture 19: Properties of the solution for 1-D unbiased RW](https://invisiblenetwork.ai/learn/nptel/103101354/0a40a4db98dc) (Video)
20. [Week 5: Lecture 20: 1-D unbiased RW: Asymptotic form of occupancy probability and transition ...](https://invisiblenetwork.ai/learn/nptel/103101354/a12930236fc1) (Video)
21. [Week 6: Lecture 21: Solution to the problem of 1-D Random Walk with Bias](https://invisiblenetwork.ai/learn/nptel/103101354/e6a343cc497d) (Video)
22. [Week 6: Lecture 22: Generalized Random Walk with Bias and Pausing](https://invisiblenetwork.ai/learn/nptel/103101354/52694e3eae9c) (Video)
23. [Week 6: Lecture 23: Effect of Pausing on Mean and Variance of Random walk](https://invisiblenetwork.ai/learn/nptel/103101354/49ac88478422) (Video)
24. [Week 6: Lecture 24: Random-walk in the presence of reflecting barrier](https://invisiblenetwork.ai/learn/nptel/103101354/ef89a9972ce1) (Video)
25. [Week 6: Lecture 25: Boundary conditions for reflected Random-Walk and formulating absorbing ...](https://invisiblenetwork.ai/learn/nptel/103101354/287068acf326) (Video)
26. [Week 6: Lecture 26: The survival probability and first-passage time distribution for Random walker..](https://invisiblenetwork.ai/learn/nptel/103101354/63207530b189) (Video)
27. [Week 6: Lecture 27: Random Walk with Bias and Absorber](https://invisiblenetwork.ai/learn/nptel/103101354/c0dcd414a9ce) (Video)
28. [Week 6: Lecture 28: Drift and Survival probability for Random walk with bias and absorber](https://invisiblenetwork.ai/learn/nptel/103101354/2d52149d9e67) (Video)
29. [Week 7: Lecture 29: Introduction to gambler’s ruin problem](https://invisiblenetwork.ai/learn/nptel/103101354/672f7b800164) (Video)
30. [Week 7: Lecture 30: Solution for ultimate winning probability in Gambler’s ruin problem](https://invisiblenetwork.ai/learn/nptel/103101354/26bb4b54f30d) (Video)
31. [Week 7: Lecture 31: Solution to gambler’s ruin problem with site dependent jump probabilities](https://invisiblenetwork.ai/learn/nptel/103101354/0c72cf415526) (Video)
32. [Week 7: Lecture 32: Fourier transform method of solving lattice Random walks](https://invisiblenetwork.ai/learn/nptel/103101354/c1b797401eff) (Video)
33. [Week 7: Lecture 33: Two and higher dimensional Random walks](https://invisiblenetwork.ai/learn/nptel/103101354/4491c10de972) (Video)
34. [Week 7: Lecture 34: Formulating the problem of Probability of Return to the origin](https://invisiblenetwork.ai/learn/nptel/103101354/0a1c082547ea) (Video)
35. [Week 7: Lecture 35: Relationship between occupancy probability and first-time-return probability](https://invisiblenetwork.ai/learn/nptel/103101354/487fc7aa5715) (Video)
36. [Week 8: Lecture 36: Proof of Polya’s theorem on the probability of return](https://invisiblenetwork.ai/learn/nptel/103101354/cb9d0339460e) (Video)
37. [Week 8: Lecture 37: Return probability estimates in various dimensions and effect of bias in 1-D](https://invisiblenetwork.ai/learn/nptel/103101354/601ed47fc607) (Video)
38. [Week 8: Lecture 38: Dependence of first time return probability (Fk) on steps](https://invisiblenetwork.ai/learn/nptel/103101354/4573a50db3f7) (Video)
39. [Week 8: Lecture 39: Equilibrium solutions in lattice random walk models](https://invisiblenetwork.ai/learn/nptel/103101354/83f0d8ecd755) (Video)
40. [Week 8: Lecture 40: Equilibrium solution to Ehrenfest’s flea model](https://invisiblenetwork.ai/learn/nptel/103101354/ddd5dbb01832) (Video)
41. [Week 9: Lecture 41: Differential equation formulation of stochastic phenomena](https://invisiblenetwork.ai/learn/nptel/103101354/903b12bd6a59) (Video)
42. [Week 9: Lecture 42: Derivation of Fokker-Planck equation](https://invisiblenetwork.ai/learn/nptel/103101354/e297a378265b) (Video)
43. [Week 9: Lecture 43: Generalized transition probability functions for Fokker-Planck equation](https://invisiblenetwork.ai/learn/nptel/103101354/76a5c16ed458) (Video)
44. [Week 9: Lecture 44: Solution to 1-D Fokker-Planck equation for free particle: Method of Fourier...](https://invisiblenetwork.ai/learn/nptel/103101354/d243e58f0e93) (Video)
45. [Week 9: Lecture 45: General non-gaussian solution to translationally invariant Chapman-Kolmogorov...](https://invisiblenetwork.ai/learn/nptel/103101354/1d3de182748c) (Video)
46. [Week 10: Lecture 46: Cauchy distribution, power-law and other non-gaussian solutions](https://invisiblenetwork.ai/learn/nptel/103101354/547b0ce65f31) (Video)
47. [Week 10: Lecture 47: Wiener process and solution to absorbing barrier problems from Fokker-Planck...](https://invisiblenetwork.ai/learn/nptel/103101354/d10309167018) (Video)
48. [Week 10: Lecture 48: Application of Fourier Sine transform for single absorber problem](https://invisiblenetwork.ai/learn/nptel/103101354/5871920698f5) (Video)
49. [Week 10: Lecture 49: Setting up Langevin equation for velocity fluctuations of Brownian particles](https://invisiblenetwork.ai/learn/nptel/103101354/5871920698f5-2) (Video)
50. [Week 10: Lecture 48: Application of Fourier Sine transform for single absorber problem](https://invisiblenetwork.ai/learn/nptel/103101354/5871920698f5-3) (Video)
51. [Week 10: Lecture 49: Setting up Langevin equation for velocity fluctuations of Brownian particles](https://invisiblenetwork.ai/learn/nptel/103101354/5871920698f5-4) (Video)
52. [Week 10: Lecture 50: Understanding the origin of systematic and random parts of force from kinetic..](https://invisiblenetwork.ai/learn/nptel/103101354/27c809c99ad4) (Video)
53. [Week 11: Lecture 51: Kinetic derivation of a formula for delta-correlated random force](https://invisiblenetwork.ai/learn/nptel/103101354/d16f2a3e6e09) (Video)
54. [Week 11: Lecture 52: Mean square velocity, thermal equilibrium and relationship between relaxation..](https://invisiblenetwork.ai/learn/nptel/103101354/7f1df809e7fe) (Video)
55. [Week 11: Lecture 53: Velocity autocorrelation in Brownian motion](https://invisiblenetwork.ai/learn/nptel/103101354/d4019c010f62) (Video)
56. [Week 11: Lecture 54: Derivation of Stokes-Einstein relationship between diffusion coefficient and...](https://invisiblenetwork.ai/learn/nptel/103101354/049ce7b1b5b9) (Video)
57. [Week 11: Lecture 55: Alternative derivation of Stokes-Einstein relationship & Brownian motion with..](https://invisiblenetwork.ai/learn/nptel/103101354/67a1deb4d923) (Video)
58. [Week 12: Lecture 56: Numerical simulation of the Langevin equation](https://invisiblenetwork.ai/learn/nptel/103101354/1ee6a3dd1bd4) (Video)
59. [Week 12: Lecture 57: Derivation of Klein-Kramers equation from Langevin equation for joint...](https://invisiblenetwork.ai/learn/nptel/103101354/9c4d2a518ae3) (Video)
60. [Week 12: Lecture 58: Illustrative solutions to the Klein-Kramers equation](https://invisiblenetwork.ai/learn/nptel/103101354/3866a9cbd197) (Video)
61. [Week 12: Lecture 59: Numerical simulation: Sampling from general distributions and Central...](https://invisiblenetwork.ai/learn/nptel/103101354/370306ec53dc) (Video)
62. [Week 12: Lecture 60: Numerical simulation of Random walk trajectories and method of solving Fokker..](https://invisiblenetwork.ai/learn/nptel/103101354/6ac0fc789ae4) (Video)
63. [Live Session 05-03-2024](https://invisiblenetwork.ai/learn/nptel/103101354/f0fffd1ea10e-2) (Video)