Modules / Lectures

Module Name | Download |
---|---|

noc20_ma04_assigment_1 | noc20_ma04_assigment_1 |

noc20_ma04_assigment_10 | noc20_ma04_assigment_10 |

noc20_ma04_assigment_11 | noc20_ma04_assigment_11 |

noc20_ma04_assigment_12 | noc20_ma04_assigment_12 |

noc20_ma04_assigment_13 | noc20_ma04_assigment_13 |

noc20_ma04_assigment_2 | noc20_ma04_assigment_2 |

noc20_ma04_assigment_3 | noc20_ma04_assigment_3 |

noc20_ma04_assigment_4 | noc20_ma04_assigment_4 |

noc20_ma04_assigment_5 | noc20_ma04_assigment_5 |

noc20_ma04_assigment_6 | noc20_ma04_assigment_6 |

noc20_ma04_assigment_7 | noc20_ma04_assigment_7 |

noc20_ma04_assigment_8 | noc20_ma04_assigment_8 |

noc20_ma04_assigment_9 | noc20_ma04_assigment_9 |

Sl.No | Chapter Name | MP4 Download |
---|---|---|

1 | Prerequisite Measure Theory - Part 01 | Download |

2 | Prerequisite Measure Theory - Part 02 | Download |

3 | Prerequisite Measure Theory - Part 03 | Download |

4 | Random variable | Download |

5 | Stochastic Process | Download |

6 | Conditional Expectation | Download |

7 | Preliminary for Stochastic Integration - Part 01 | Download |

8 | Preliminary for Stochastic Integration - Part 02 | Download |

9 | Definition and properties of Stochastic Integration - Part 01 | Download |

10 | Definition and properties of Stochastic Integration - Part 02 | Download |

11 | Further properties of Stochastic Integration | Download |

12 | Extension of stochastic integral | Download |

13 | change of variable formula and proof - Part 1 | Download |

14 | change of variable formula and proof - Part 2 | Download |

15 | Brownian motion as the building block | Download |

16 | Brownian motion and its martingale property - Part 1 | Download |

17 | Brownian motion and its martingale property - Part 2 | Download |

18 | Application of Ito’s rule on Ito process | Download |

19 | Harmonic function and its properties | Download |

20 | Maximum principle of harmonic function | Download |

21 | Dirichlet Problem and bounded solution | Download |

22 | Example of a Dirichlet problem | Download |

23 | Regular points at the boundary | Download |

24 | Zarembas cone condition for regularity | Download |

25 | Summary of the Zaremba's cone condition | Download |

26 | Continuity of candidate solution at regular points - Part 1 | Download |

27 | Continuity of candidate solution at regular points - Part 2 | Download |

28 | Summary of bounded solution to the Dirichlet Problem | Download |

29 | Stochastic representation of bounded solution to a heat equation - Part 1 | Download |

30 | Stochastic representation of bounded solution to a heat equation - Part 2 | Download |

31 | Uniqueness of solution to the heat equation | Download |

32 | Remark on Tychonoff's Theorem | Download |

33 | Widder’s result and its extension on heat equation | Download |

34 | Solution to the mixed initial boundary value problem | Download |

35 | The Feynman-Kac formula | Download |

36 | Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 1 | Download |

37 | Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 2 | Download |

38 | Geometric Brownian motion | Download |

39 | A system of stochastic differential equations in application | Download |

40 | Brownian bridge | Download |

41 | Simulation of stochastic differential equations | Download |

42 | Stochastic differential equations: Uniqueness | Download |

43 | Stochastic differential equations: Existence part 1 | Download |

44 | Stochastic differential equations: Existence part 2 | Download |

45 | Stochastic differential equations: Existence part 3 | Download |

46 | Stochastic differential equations: Weak solution | Download |

47 | Functional Stochastic Differential Equations | Download |

48 | Statement of Dirichlet and Cauchy problems with variable coefficients elliptic operators | Download |

49 | Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 1 | Download |

50 | Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 2 | Download |

51 | Semigroup of bounded linear operators on Banach space - Part 1 | Download |

52 | Semigroup of bounded linear operators on Banach space part 2 | Download |

53 | Growth property of C0 semigroup | Download |

54 | Unique semigroup generated by a bounded linear operator | Download |

55 | Homogeneous initial value problem | Download |

56 | Mild solution to homogeneous initial value problem | Download |

57 | Mild solution to inhomogeneous initial value problem | Download |

58 | Sufficient condition for existence of classical solution of iIVP | Download |

59 | Tutorial on Resolvant operator | Download |

60 | Feynman-Kac formula and the formula of variations of constants | Download |

61 | Non-autonomous evolution problem and mild/generalized solution | Download |

62 | Sufficient condition for existence of an evolution system | Download |

63 | Y-valued solution | Download |

64 | " mild/generalized solution to Semi-linear Evolution Problem" | Download |

65 | Existence of classical solution part 1 | Download |

66 | Existence of classical solution part 2 | Download |

67 | Conclusion video | Download |

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

1 | Prerequisite Measure Theory - Part 01 | Download To be verified |

2 | Prerequisite Measure Theory - Part 02 | Download To be verified |

3 | Prerequisite Measure Theory - Part 03 | Download To be verified |

4 | Random variable | Download To be verified |

5 | Stochastic Process | Download To be verified |

6 | Conditional Expectation | Download To be verified |

7 | Preliminary for Stochastic Integration - Part 01 | Download To be verified |

8 | Preliminary for Stochastic Integration - Part 02 | Download To be verified |

9 | Definition and properties of Stochastic Integration - Part 01 | Download To be verified |

10 | Definition and properties of Stochastic Integration - Part 02 | Download To be verified |

11 | Further properties of Stochastic Integration | Download To be verified |

12 | Extension of stochastic integral | Download To be verified |

13 | change of variable formula and proof - Part 1 | Download To be verified |

14 | change of variable formula and proof - Part 2 | Download To be verified |

15 | Brownian motion as the building block | Download To be verified |

16 | Brownian motion and its martingale property - Part 1 | Download To be verified |

17 | Brownian motion and its martingale property - Part 2 | Download To be verified |

18 | Application of Ito’s rule on Ito process | Download To be verified |

19 | Harmonic function and its properties | Download To be verified |

20 | Maximum principle of harmonic function | Download To be verified |

21 | Dirichlet Problem and bounded solution | Download To be verified |

22 | Example of a Dirichlet problem | Download To be verified |

23 | Regular points at the boundary | Download To be verified |

24 | Zarembas cone condition for regularity | Download To be verified |

25 | Summary of the Zaremba's cone condition | Download To be verified |

26 | Continuity of candidate solution at regular points - Part 1 | Download To be verified |

27 | Continuity of candidate solution at regular points - Part 2 | Download To be verified |

28 | Summary of bounded solution to the Dirichlet Problem | Download To be verified |

29 | Stochastic representation of bounded solution to a heat equation - Part 1 | Download To be verified |

30 | Stochastic representation of bounded solution to a heat equation - Part 2 | Download To be verified |

31 | Uniqueness of solution to the heat equation | Download To be verified |

32 | Remark on Tychonoff's Theorem | Download To be verified |

33 | Widder’s result and its extension on heat equation | Download To be verified |

34 | Solution to the mixed initial boundary value problem | Download To be verified |

35 | The Feynman-Kac formula | Download To be verified |

36 | Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 1 | Download To be verified |

37 | Kac’s theorem on the stochastic representation of solution to a second-order linear ODE - Part 2 | Download To be verified |

38 | Geometric Brownian motion | Download To be verified |

39 | A system of stochastic differential equations in application | Download To be verified |

40 | Brownian bridge | Download To be verified |

41 | Simulation of stochastic differential equations | Download To be verified |

42 | Stochastic differential equations: Uniqueness | Download To be verified |

43 | Stochastic differential equations: Existence part 1 | Download To be verified |

44 | Stochastic differential equations: Existence part 2 | Download To be verified |

45 | Stochastic differential equations: Existence part 3 | Download To be verified |

46 | Stochastic differential equations: Weak solution | Download To be verified |

47 | Functional Stochastic Differential Equations | PDF unavailable |

48 | Statement of Dirichlet and Cauchy problems with variable coefficients elliptic operators | PDF unavailable |

49 | Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 1 | PDF unavailable |

50 | Cauchy Problem with variable coefficients: Feynman-Kac formula: Part 2 | PDF unavailable |

51 | Semigroup of bounded linear operators on Banach space - Part 1 | PDF unavailable |

52 | Semigroup of bounded linear operators on Banach space part 2 | PDF unavailable |

53 | Growth property of C0 semigroup | PDF unavailable |

54 | Unique semigroup generated by a bounded linear operator | PDF unavailable |

55 | Homogeneous initial value problem | PDF unavailable |

56 | Mild solution to homogeneous initial value problem | PDF unavailable |

57 | Mild solution to inhomogeneous initial value problem | PDF unavailable |

58 | Sufficient condition for existence of classical solution of iIVP | PDF unavailable |

59 | Tutorial on Resolvant operator | PDF unavailable |

60 | Feynman-Kac formula and the formula of variations of constants | PDF unavailable |

61 | Non-autonomous evolution problem and mild/generalized solution | PDF unavailable |

62 | Sufficient condition for existence of an evolution system | PDF unavailable |

63 | Y-valued solution | PDF unavailable |

64 | " mild/generalized solution to Semi-linear Evolution Problem" | PDF unavailable |

65 | Existence of classical solution part 1 | PDF unavailable |

66 | Existence of classical solution part 2 | PDF unavailable |

67 | Conclusion video | PDF unavailable |

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 |