Modules / Lectures

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Assignment-10-Solution | Assignment-10-Solution |

Assignment-11-Solution | Assignment-11-Solution |

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Assignment-12-Solution | Assignment-12-Solution |

Assignment-2 | Assignment-2 |

Assignment-2-Solution | Assignment-2-Solution |

Assignment-3 | Assignment-3 |

Assignment-3-Solution | Assignment-3-Solution |

Assignment-4 | Assignment-4 |

Assignment-4-Solution | Assignment-4-Solution |

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Assignment-7-Solution | Assignment-7-Solution |

Assignment-8 | Assignment-8 |

Assignment-8-Solution | Assignment-8-Solution |

Assignment-9-Solution | Assignment-9-Solution |

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

1 | Lecture 01 - Introduction to Ordinary Differential Equations (ODE) | Download Verified |

2 | Lecture 02 - Methods for First Order ODE's - Homogeneous Equations | Download Verified |

3 | Lecture 03 - Methods for First order ODE's - Exact Equations | Download Verified |

4 | Lecture 04 - Methods for First Order ODE's - Exact Equations ( Continued ) | Download Verified |

5 | Lecture 05 - Methods for First order ODE's - Reducible to Exact Equations | Download Verified |

6 | Lecture 06 - Methods for First order ODE's - Reducible to Exact Equations ( Continued ) | Download Verified |

7 | Lecture 07 - Non-Exact Equations - Finding Integrating Factors | Download Verified |

8 | Lecture 08 - Linear First Order ODE and Bernoulli's Equation | Download Verified |

9 | Lecture 09 - Introduction to Second order ODE's | Download Verified |

10 | Lecture 10 - Properties of solutions of second order homogeneous ODE's | Download Verified |

11 | Lecture 11 - Abel's formula to find the other solution | Download Verified |

12 | Lecture 12 - Abel's formula - Demonstrstion | Download Verified |

13 | Lecture 13 - Second Order ODE's with constant coefficients | Download Verified |

14 | Lecture 14 - Euler - Cauchy equation | Download Verified |

15 | Lecture 15 - Non homogeneous ODEs Variation of Parameters | Download Verified |

16 | Lecture 16 - Method of undetermined coefficients | Download Verified |

17 | Lecture 17 - Demonstration of Method of undetermined coefficients | Download Verified |

18 | Lecture 18 - Power Series and its properties | Download Verified |

19 | Lecture 19 - Power Series Solutions to Second Order ODE's | Download Verified |

20 | Lecture 20 - Power Series Solutions ( Continued ) | Download Verified |

21 | Lecture 21 - Legendre Differential Equation | Download Verified |

22 | Legendre Polynomials | Download Verified |

23 | Properties of Legendre Polynomials | Download Verified |

24 | Power series solutions around a regular singular point | Download Verified |

25 | Frobenius method of solutions | Download Verified |

26 | Frobenius method of solutions (continued) | Download Verified |

27 | Examples on Frobenius method | Download Verified |

28 | Bessel differential equation | Download Verified |

29 | Frobenius solutions for Bessel Equation | Download Verified |

30 | Properties of Bessel functions | Download Verified |

31 | Properties of Bessel functions (continued) | Download Verified |

32 | Introduction to Sturm-Liouville theory | Download Verified |

33 | Sturm-Liouville Problems | Download Verified |

34 | Regular Sturm-Liouville problem | Download Verified |

35 | Periodic and singular Sturm-Liouville Problems | Download Verified |

36 | Generalized Fourier series | Download Verified |

37 | Examples of Sturm-Liouville systems | Download Verified |

38 | Examples of Sturm-Liouville systems (continued) | Download Verified |

39 | Examples of regular Sturm-Liouville systems | Download Verified |

40 | Second order linear PDEs | Download Verified |

41 | Classification of second order linear PDEs | Download Verified |

42 | Reduction to canonical form for equations with constant coefficients | Download Verified |

43 | Reduction to canonical form for equations with variable coefficients | Download Verified |

44 | Reduction to Normal form-More examples | Download Verified |

45 | D'Alembert solution for wave equation | Download Verified |

46 | Uniqueness of solutions for wave equation | Download Verified |

47 | Vibration of a semi-infinite string | Download Verified |

48 | Vibration of a finite string | Download Verified |

49 | Finite length string vibrations | Download Verified |

50 | Finite length string vibrations (continued) | Download Verified |

51 | Non-homogeneous wave equation | Download Verified |

52 | Vibration of a circular drum | Download Verified |

53 | Solutions of heat equation-Properties | Download Verified |

54 | Temperature in an infinite rod | Download Verified |

55 | Temperature in a semi-infinite rod | Download Verified |

56 | Non-homogeneous heat equation | Download Verified |

57 | Temperature in a finite rod | Download Verified |

58 | Temperature in a finite rod with insulated ends | Download Verified |

59 | Laplace equation over a rectangle | Download Verified |

60 | Laplace equation over a rectangle with flux boundary conditions | Download Verified |

61 | Laplace equation over circular domains | Download Verified |

62 | Laplace equation over circular Sectors | Download Verified |

63 | Uniqueness of the boundary value problems for Laplace equation | Download Verified |

64 | Conclusions | Download Verified |

Sl.No | Chapter Name | Hindi |
---|---|---|

1 | Lecture 01 - Introduction to Ordinary Differential Equations (ODE) | Download |

2 | Lecture 02 - Methods for First Order ODE's - Homogeneous Equations | Download |

3 | Lecture 03 - Methods for First order ODE's - Exact Equations | Download |

4 | Lecture 04 - Methods for First Order ODE's - Exact Equations ( Continued ) | Download |

5 | Lecture 05 - Methods for First order ODE's - Reducible to Exact Equations | Download |

6 | Lecture 06 - Methods for First order ODE's - Reducible to Exact Equations ( Continued ) | Download |

7 | Lecture 07 - Non-Exact Equations - Finding Integrating Factors | Download |

8 | Lecture 08 - Linear First Order ODE and Bernoulli's Equation | Download |

9 | Lecture 09 - Introduction to Second order ODE's | Download |

10 | Lecture 10 - Properties of solutions of second order homogeneous ODE's | Download |

11 | Lecture 11 - Abel's formula to find the other solution | Download |

12 | Lecture 12 - Abel's formula - Demonstrstion | Download |

13 | Lecture 13 - Second Order ODE's with constant coefficients | Download |

14 | Lecture 14 - Euler - Cauchy equation | Download |

15 | Lecture 15 - Non homogeneous ODEs Variation of Parameters | Download |

16 | Lecture 16 - Method of undetermined coefficients | Download |

17 | Lecture 17 - Demonstration of Method of undetermined coefficients | Download |

18 | Lecture 18 - Power Series and its properties | Download |

19 | Lecture 19 - Power Series Solutions to Second Order ODE's | Download |

20 | Lecture 20 - Power Series Solutions ( Continued ) | Download |

21 | Lecture 21 - Legendre Differential Equation | Download |

22 | Legendre Polynomials | Download |

23 | Properties of Legendre Polynomials | Download |

24 | Power series solutions around a regular singular point | Download |

25 | Frobenius method of solutions | Download |

26 | Frobenius method of solutions (continued) | Download |

27 | Examples on Frobenius method | Download |

28 | Bessel differential equation | Download |

29 | Frobenius solutions for Bessel Equation | Download |

30 | Properties of Bessel functions | Download |

31 | Properties of Bessel functions (continued) | Download |

32 | Introduction to Sturm-Liouville theory | Download |

33 | Sturm-Liouville Problems | Download |

34 | Regular Sturm-Liouville problem | Download |

35 | Periodic and singular Sturm-Liouville Problems | Download |

36 | Generalized Fourier series | Download |

37 | Examples of Sturm-Liouville systems | Download |

38 | Examples of Sturm-Liouville systems (continued) | Download |

39 | Examples of regular Sturm-Liouville systems | Download |

40 | Second order linear PDEs | Download |

41 | Classification of second order linear PDEs | Download |

42 | Reduction to canonical form for equations with constant coefficients | Download |

43 | Reduction to canonical form for equations with variable coefficients | Download |

44 | Reduction to Normal form-More examples | Download |

45 | D'Alembert solution for wave equation | Download |

46 | Uniqueness of solutions for wave equation | Download |

47 | Vibration of a semi-infinite string | Download |

48 | Vibration of a finite string | Download |

49 | Finite length string vibrations | Download |

50 | Finite length string vibrations (continued) | Download |

51 | Non-homogeneous wave equation | Download |

52 | Vibration of a circular drum | Download |

53 | Solutions of heat equation-Properties | Download |

54 | Temperature in an infinite rod | Download |

55 | Temperature in a semi-infinite rod | Download |

56 | Non-homogeneous heat equation | Download |

57 | Temperature in a finite rod | Download |

58 | Temperature in a finite rod with insulated ends | Download |

59 | Laplace equation over a rectangle | Download |

60 | Laplace equation over a rectangle with flux boundary conditions | Download |

61 | Laplace equation over circular domains | Download |

62 | Laplace equation over circular Sectors | Download |

63 | Uniqueness of the boundary value problems for Laplace equation | Download |

64 | Conclusions | Download |

Sl.No | Chapter Name | Tamil |
---|---|---|

1 | Lecture 01 - Introduction to Ordinary Differential Equations (ODE) | Download |

2 | Lecture 02 - Methods for First Order ODE's - Homogeneous Equations | Download |

3 | Lecture 03 - Methods for First order ODE's - Exact Equations | Download |

4 | Lecture 04 - Methods for First Order ODE's - Exact Equations ( Continued ) | Download |

5 | Lecture 05 - Methods for First order ODE's - Reducible to Exact Equations | Download |

6 | Lecture 06 - Methods for First order ODE's - Reducible to Exact Equations ( Continued ) | Download |

7 | Lecture 07 - Non-Exact Equations - Finding Integrating Factors | Download |

8 | Lecture 08 - Linear First Order ODE and Bernoulli's Equation | Download |

9 | Lecture 09 - Introduction to Second order ODE's | Download |

10 | Lecture 10 - Properties of solutions of second order homogeneous ODE's | Download |

11 | Lecture 11 - Abel's formula to find the other solution | Download |

12 | Lecture 12 - Abel's formula - Demonstrstion | Download |

13 | Lecture 13 - Second Order ODE's with constant coefficients | Download |

14 | Lecture 14 - Euler - Cauchy equation | Download |

15 | Lecture 15 - Non homogeneous ODEs Variation of Parameters | Download |

16 | Lecture 16 - Method of undetermined coefficients | Download |

17 | Lecture 17 - Demonstration of Method of undetermined coefficients | Download |

18 | Lecture 18 - Power Series and its properties | Download |

19 | Lecture 19 - Power Series Solutions to Second Order ODE's | Download |

20 | Lecture 20 - Power Series Solutions ( Continued ) | Download |

21 | Lecture 21 - Legendre Differential Equation | Download |

22 | Legendre Polynomials | Download |

23 | Properties of Legendre Polynomials | Download |

24 | Power series solutions around a regular singular point | Download |

25 | Frobenius method of solutions | Download |

26 | Frobenius method of solutions (continued) | Download |

27 | Examples on Frobenius method | Download |

28 | Bessel differential equation | Download |

29 | Frobenius solutions for Bessel Equation | Download |

30 | Properties of Bessel functions | Download |

31 | Properties of Bessel functions (continued) | Download |

32 | Introduction to Sturm-Liouville theory | Download |

33 | Sturm-Liouville Problems | Download |

34 | Regular Sturm-Liouville problem | Download |

35 | Periodic and singular Sturm-Liouville Problems | Download |

36 | Generalized Fourier series | Download |

37 | Examples of Sturm-Liouville systems | Download |

38 | Examples of Sturm-Liouville systems (continued) | Download |

39 | Examples of regular Sturm-Liouville systems | Download |

40 | Second order linear PDEs | Download |

41 | Classification of second order linear PDEs | Download |

42 | Reduction to canonical form for equations with constant coefficients | Download |

43 | Reduction to canonical form for equations with variable coefficients | Download |

44 | Reduction to Normal form-More examples | Download |

45 | D'Alembert solution for wave equation | Download |

46 | Uniqueness of solutions for wave equation | Download |

47 | Vibration of a semi-infinite string | Download |

48 | Vibration of a finite string | Download |

49 | Finite length string vibrations | Download |

50 | Finite length string vibrations (continued) | Download |

51 | Non-homogeneous wave equation | Download |

52 | Vibration of a circular drum | Download |

53 | Solutions of heat equation-Properties | Download |

54 | Temperature in an infinite rod | Download |

55 | Temperature in a semi-infinite rod | Download |

56 | Non-homogeneous heat equation | Download |

57 | Temperature in a finite rod | Download |

58 | Temperature in a finite rod with insulated ends | Download |

59 | Laplace equation over a rectangle | Download |

60 | Laplace equation over a rectangle with flux boundary conditions | Download |

61 | Laplace equation over circular domains | Download |

62 | Laplace equation over circular Sectors | Download |

63 | Uniqueness of the boundary value problems for Laplace equation | Download |

64 | Conclusions | Download |