Modules / Lectures

Module Name | Download |
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noc21_ma51_assignment_Week_0 | noc21_ma51_assignment_Week_0 |

noc21_ma51_assignment_Week_1 | noc21_ma51_assignment_Week_1 |

noc21_ma51_assignment_Week_10 | noc21_ma51_assignment_Week_10 |

noc21_ma51_assignment_Week_11 | noc21_ma51_assignment_Week_11 |

noc21_ma51_assignment_Week_2 | noc21_ma51_assignment_Week_2 |

noc21_ma51_assignment_Week_3 | noc21_ma51_assignment_Week_3 |

noc21_ma51_assignment_Week_4 | noc21_ma51_assignment_Week_4 |

noc21_ma51_assignment_Week_5 | noc21_ma51_assignment_Week_5 |

noc21_ma51_assignment_Week_6 | noc21_ma51_assignment_Week_6 |

noc21_ma51_assignment_Week_7 | noc21_ma51_assignment_Week_7 |

noc21_ma51_assignment_Week_8 | noc21_ma51_assignment_Week_8 |

noc21_ma51_assignment_Week_9 | noc21_ma51_assignment_Week_9 |

noc21_ma51assignment_Week12 | noc21_ma51assignment_Week12 |

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

1 | Lecture 1.1: Partial Differential Equations - Basic concepts and Nomenclature | Download |

2 | Lecture 2.1:First Order Partial Differential Equations- How they arise? Cauchy Problems, IVPs, IBVPs | Download |

3 | Lecture 2.2: First order Partial Differential Equations - Geometry of Quasilinear equations | Download |

4 | Lecture 2.3: FOPDE's - General Solutions to Linear and Semilinear equations | Download |

5 | Lecture 2.4: First order Partial Differential Equations- Lagrange's method for Quasilinear equations | Download |

6 | Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equations | Download |

7 | Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equations | Download |

8 | Lecture 2.6: FOPDE's - Method of characteristics for Quasilinear equations - 1 | Download |

9 | Lecture 2.8: First order Partial Differential Equations - Failure of transversality condition | Download |

10 | Lecture 2.9: First order Partial Differential Equations - Tutorial of Quasilinear equations | Download |

11 | Lecture 2.10: FOPDE's- General nonlinear equations 1 - Search for a characteristic direction | Download |

12 | Lecture 2.11:FOPDE's-General nonlinear equations 2-Characteristic direction and characteristic strip | Download |

13 | Lecture 2.12: FOPDE's - General nonlinear equations 3 - Finding an initial strip | Download |

14 | Lecture 2.13: FOPDE's - General nonlinear equations 4 - Local existence and uniqueness theorem | Download |

15 | Lecture 2.14: First order Partial Differential Equations - Tutorial on General nonlinear equations | Download |

16 | Lecture 2.15: First order Partial Differential Equations-Initial value problems for Burgers equation | Download |

17 | Lecture 2.16: FOPDE's - Conservation laws with a view towards global solutions to Burgers equation | Download |

18 | Lecture: 3.1: Second Order Partial Differential Equations - Special Curves associated to a PDE | Download |

19 | Lecture: 3.2: Second Order Partial Differential Equations - Curves of discontinuity | Download |

20 | Lecture 3.3: Second Order Partial Differential Equations - Classification | Download |

21 | Lecture 3.4: SOPDE's - Canonical form for an equation of Hyperbolic type | Download |

22 | Lecture 3.5: SOPDE's - Canonical form for an equation of Parabolic type | Download |

23 | Lecture 3.6: SOPDE's - Canonical form for an equation of Elliptic type | Download |

24 | Lecture 3.7: Second Order Partial Differential Equations - Characteristic Surfaces | Download |

25 | Lecture 3.8: SOPDE's - Canonical forms for constant coefficient PDEs | Download |

26 | Lecture 4.1: Wave Equation - A mathematical model for vibrating strings | Download |

27 | Lecture 4.2: Wave Equation in one space dimension - d'Alembert formula | Download |

28 | Lecture 4.3: Tutorial on One dimensional wave equation | Download |

29 | Lecture 4.4: Wave Equation in d space dimensions - Equivalent Cauchy problems via Spherical means | Download |

30 | Lecture 4.5: Cauchy problem for Wave Equation in 3 space dimensions - Poisson-Kirchhoff formulae | Download |

31 | Lecture 4.6: Cauchy problem for Wave Equation in 2 space dimensions - Hadamard's method of descent | Download |

32 | Lecture 4.7: Nonhomogeneous Wave Equation - Duhamel principle | Download |

33 | Lecture 4.8: Wellposedness of Cauchy problem for Wave Equation | Download |

34 | Lecture 4.9: Wave Equation on an interval in ? - Solution to an IBVP from first principles | Download |

35 | Lecture 4.10: Tutorial on IBVPs for wave equation | Download |

36 | Lecture 4.11: IBVP for Wave Equation - Separation of Variables Method | Download |

37 | Lecture 4.12: Tutorial on Separation of variables method for wave equation | Download |

38 | Lecture 5.1: Qualitative analysis of Wave equation - Parallelogram identity | Download |

39 | Lecture 5.2: Qualitative analysis of Wave equation - Domain of dependence, domain of influence | Download |

40 | Lecture 5.3: Qualitative analysis of Wave equation- Causality Principle, Finite speed of propagation | Download |

41 | Lecture 5.4: Qualitative analysis of Wave equation - Uniqueness by Energy method | Download |

42 | Lecture 5.5: Qualitative analysis of Wave equation - Huygens Principle | Download |

43 | Lecture 5.6: Qualitative analysis of Wave equation - Generalized solutions to Wave equation | Download |

44 | Lecture 5.7: Qualitative analysis of Wave equation - Propagation of waves | Download |

45 | Lecture 6.1: Laplace equation - Associated Boundary value problems | Download |

46 | Lecture 6.2: Laplace equation - Fundamental solution | Download |

47 | Lecture 6.3: Dirichlet BVP for Laplace equation - Green's function and Poisson's formula | Download |

48 | Lecture 6.4: Laplace equation - Weak maximum principle and its applications | Download |

49 | Lecture 6.5: Laplace equation - Dirichlet BVP on a disk in R2 for Laplace equations | Download |

50 | Lecture 6:6: Tutorial 1 on Laplace equation | Download |

51 | Lecture 6:7: Laplace equation- Mean value property | Download |

52 | Lecture 6:8: Laplace equation- More qualitative properties | Download |

53 | Lecture 6:9: Laplace equation- Strong Maximum Principle and Dirichlet Principle | Download |

54 | Lecture 6:10: Tutorial 2 on Laplace equation | Download |

55 | Lecture 7.1: Cauchy Problem for Heat Equation - 1 | Download |

56 | Lecture 7.2: Cauchy Problem for Heat Equation - 2 | Download |

57 | Lecture 7.3: IBVP for Heat equation Subtitle: Method of Separation of Variables | Download |

58 | Lecture 7.4: Maximum principle for heat equation | Download |

59 | Lecture 7.5: Tutorial on heat equation | Download |

60 | Lecture 7.6: Heat equation Subheading : Infinite speed of propagation, Energy, Backward Problem | Download |

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

1 | Lecture 1.1: Partial Differential Equations - Basic concepts and Nomenclature | Download Verified |

2 | Lecture 2.1:First Order Partial Differential Equations- How they arise? Cauchy Problems, IVPs, IBVPs | Download Verified |

3 | Lecture 2.2: First order Partial Differential Equations - Geometry of Quasilinear equations | Download Verified |

4 | Lecture 2.3: FOPDE's - General Solutions to Linear and Semilinear equations | Download Verified |

5 | Lecture 2.4: First order Partial Differential Equations- Lagrange's method for Quasilinear equations | Download Verified |

6 | Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equations | PDF unavailable |

7 | Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equations | PDF unavailable |

8 | Lecture 2.6: FOPDE's - Method of characteristics for Quasilinear equations - 1 | PDF unavailable |

9 | Lecture 2.8: First order Partial Differential Equations - Failure of transversality condition | PDF unavailable |

10 | Lecture 2.9: First order Partial Differential Equations - Tutorial of Quasilinear equations | PDF unavailable |

11 | Lecture 2.10: FOPDE's- General nonlinear equations 1 - Search for a characteristic direction | PDF unavailable |

12 | Lecture 2.11:FOPDE's-General nonlinear equations 2-Characteristic direction and characteristic strip | PDF unavailable |

13 | Lecture 2.12: FOPDE's - General nonlinear equations 3 - Finding an initial strip | PDF unavailable |

14 | Lecture 2.13: FOPDE's - General nonlinear equations 4 - Local existence and uniqueness theorem | PDF unavailable |

15 | Lecture 2.14: First order Partial Differential Equations - Tutorial on General nonlinear equations | PDF unavailable |

16 | Lecture 2.15: First order Partial Differential Equations-Initial value problems for Burgers equation | PDF unavailable |

17 | Lecture 2.16: FOPDE's - Conservation laws with a view towards global solutions to Burgers equation | PDF unavailable |

18 | Lecture: 3.1: Second Order Partial Differential Equations - Special Curves associated to a PDE | PDF unavailable |

19 | Lecture: 3.2: Second Order Partial Differential Equations - Curves of discontinuity | PDF unavailable |

20 | Lecture 3.3: Second Order Partial Differential Equations - Classification | PDF unavailable |

21 | Lecture 3.4: SOPDE's - Canonical form for an equation of Hyperbolic type | PDF unavailable |

22 | Lecture 3.5: SOPDE's - Canonical form for an equation of Parabolic type | PDF unavailable |

23 | Lecture 3.6: SOPDE's - Canonical form for an equation of Elliptic type | PDF unavailable |

24 | Lecture 3.7: Second Order Partial Differential Equations - Characteristic Surfaces | PDF unavailable |

25 | Lecture 3.8: SOPDE's - Canonical forms for constant coefficient PDEs | PDF unavailable |

26 | Lecture 4.1: Wave Equation - A mathematical model for vibrating strings | PDF unavailable |

27 | Lecture 4.2: Wave Equation in one space dimension - d'Alembert formula | PDF unavailable |

28 | Lecture 4.3: Tutorial on One dimensional wave equation | PDF unavailable |

29 | Lecture 4.4: Wave Equation in d space dimensions - Equivalent Cauchy problems via Spherical means | PDF unavailable |

30 | Lecture 4.5: Cauchy problem for Wave Equation in 3 space dimensions - Poisson-Kirchhoff formulae | PDF unavailable |

31 | Lecture 4.6: Cauchy problem for Wave Equation in 2 space dimensions - Hadamard's method of descent | PDF unavailable |

32 | Lecture 4.7: Nonhomogeneous Wave Equation - Duhamel principle | PDF unavailable |

33 | Lecture 4.8: Wellposedness of Cauchy problem for Wave Equation | PDF unavailable |

34 | Lecture 4.9: Wave Equation on an interval in ? - Solution to an IBVP from first principles | PDF unavailable |

35 | Lecture 4.10: Tutorial on IBVPs for wave equation | PDF unavailable |

36 | Lecture 4.11: IBVP for Wave Equation - Separation of Variables Method | PDF unavailable |

37 | Lecture 4.12: Tutorial on Separation of variables method for wave equation | PDF unavailable |

38 | Lecture 5.1: Qualitative analysis of Wave equation - Parallelogram identity | PDF unavailable |

39 | Lecture 5.2: Qualitative analysis of Wave equation - Domain of dependence, domain of influence | PDF unavailable |

40 | Lecture 5.3: Qualitative analysis of Wave equation- Causality Principle, Finite speed of propagation | PDF unavailable |

41 | Lecture 5.4: Qualitative analysis of Wave equation - Uniqueness by Energy method | PDF unavailable |

42 | Lecture 5.5: Qualitative analysis of Wave equation - Huygens Principle | PDF unavailable |

43 | Lecture 5.6: Qualitative analysis of Wave equation - Generalized solutions to Wave equation | PDF unavailable |

44 | Lecture 5.7: Qualitative analysis of Wave equation - Propagation of waves | PDF unavailable |

45 | Lecture 6.1: Laplace equation - Associated Boundary value problems | PDF unavailable |

46 | Lecture 6.2: Laplace equation - Fundamental solution | PDF unavailable |

47 | Lecture 6.3: Dirichlet BVP for Laplace equation - Green's function and Poisson's formula | PDF unavailable |

48 | Lecture 6.4: Laplace equation - Weak maximum principle and its applications | PDF unavailable |

49 | Lecture 6.5: Laplace equation - Dirichlet BVP on a disk in R2 for Laplace equations | PDF unavailable |

50 | Lecture 6:6: Tutorial 1 on Laplace equation | PDF unavailable |

51 | Lecture 6:7: Laplace equation- Mean value property | PDF unavailable |

52 | Lecture 6:8: Laplace equation- More qualitative properties | PDF unavailable |

53 | Lecture 6:9: Laplace equation- Strong Maximum Principle and Dirichlet Principle | PDF unavailable |

54 | Lecture 6:10: Tutorial 2 on Laplace equation | PDF unavailable |

55 | Lecture 7.1: Cauchy Problem for Heat Equation - 1 | PDF unavailable |

56 | Lecture 7.2: Cauchy Problem for Heat Equation - 2 | PDF unavailable |

57 | Lecture 7.3: IBVP for Heat equation Subtitle: Method of Separation of Variables | PDF unavailable |

58 | Lecture 7.4: Maximum principle for heat equation | PDF unavailable |

59 | Lecture 7.5: Tutorial on heat equation | PDF unavailable |

60 | Lecture 7.6: Heat equation Subheading : Infinite speed of propagation, Energy, Backward Problem | 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 |