| Module Name | Download |
|---|---|
| Assignment-1 | Assignment-1 |
| Assignment-1-Solution | Assignment-1-Solution |
| Assignment-10-Solution | Assignment-10-Solution |
| Assignment-11-Solution | Assignment-11-Solution |
| Assignment-12 | Assignment-12 |
| 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 |
| Assignment-5 | Assignment-5 |
| Assignment-5-Solution | Assignment-5-Solution |
| Assignment-6 | Assignment-6 |
| Assignment-6-Solution | Assignment-6-Solution |
| 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 | MP4 Download |
|---|---|---|
| 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 | 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 | Bengali |
|---|---|---|
| 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 | Gujarati |
|---|---|---|
| 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 | 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 | Kannada |
|---|---|---|
| 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 |
| Sl.No | Chapter Name | Telugu |
|---|---|---|
| 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 | Not Available |
| 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 |