Learn · Differential Equations for Engineers
Lecture 21 of 64Week 4
Lesson 21 - Legendre Differential Equation
Prof. Srinivasa Rao Manam · IIT Madras
Credits and licence
- From
- Differential Equations for Engineers, IIT Madras (at NPTEL)
- Licence
- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
- Attribution
- NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
- Who can watch
- Tweens profiles and older. How courses are placed
All the lectures
- Lesson 01 - Introduction to Ordinary Differential Equations (ODE)
- Lesson 02 - Methods for First Order ODE's - Homogeneous Equations
- Lesson 03 - Methods for First order ODE's - Exact Equations
- Lesson 04 - Methods for First Order ODE's - Exact Equations ( Continued )
- Lesson 05 - Methods for First order ODE's - Reducible to Exact Equations
- Lesson 06 - Methods for First order ODE's - Reducible to Exact Equations ( Continued )
- Lesson 07 - Non-Exact Equations - Finding Integrating Factors
- Lesson 08 - Linear First Order ODE and Bernoulli's Equation
- Lesson 09 - Introduction to Second order ODE's
- Lesson 10 - Properties of solutions of second order homogeneous ODE's
- Lesson 11 - Abel's formula to find the other solution
- Lesson 12 - Abel's formula - Demonstrstion
- Lesson 13 - Second Order ODE's with constant coefficients
- Lesson 14 - Euler - Cauchy equation
- Lesson 15 - Non homogeneous ODEs Variation of Parameters
- Lesson 16 - Method of undetermined coefficients
- Lesson 17 - Demonstration of Method of undetermined coefficients
- Lesson 18 - Power Series and its properties
- Lesson 19 - Power Series Solutions to Second Order ODE's
- Lesson 20 - Power Series Solutions ( Continued )
- Lesson 21 - Legendre Differential Equation
- Lesson 22 - Legendre Polynomials
- Lesson 23 - Properties of Legendre Polynomials
- Lesson 24 - Power series solutions around a regular singular point
- Lesson 25 - Frobenius method of solutions'
- Lesson 26 - Frobenius method of solutions (continued)
- Lesson 27 - Examples on Frobenius method
- Lesson 28 - Bessel differential equation
- Lesson 29 - Frobenius solutions for Bessel Equation
- Lesson 30 - Properties of Bessel functions
- Lesson 31 - Properties of Bessel functions (continued)
- Lesson 32 - Introduction to Sturm-Liouville theory
- Lesson 33 - Sturm-Liouville Problems
- Lesson 34 - Regular Sturm-Liouville problem
- Lesson 35 - Periodic and singular Sturm-Liouville Problems
- Lesson 36 - Generalized Fourier series
- Lesson 37 - Examples of Sturm-Liouville systems
- Lesson 38 - Examples of Sturm-Liouville systems (continued)
- Lesson 39 - Examples of regular Sturm-Liouville systems
- Lesson 40 - Second order linear PDEs
- Lesson 41 - Classification of second order linear PDEs
- Lesson 42 - Reduction to canonical form for equations with constant coefficients
- Lesson 43 - Reduction to canonical form for equations with variable coefficients
- Lesson 44 - Reduction to Normal form-More examples
- Lesson 45 - D'Alembert solution for wave equation
- Lesson 46 - Uniqueness of solutions for wave equation
- Lesson 47 - Vibration of a semi-infinite string
- Lesson 48 - Vibration of a finite string
- Lesson 49 - Finite length string vibrations
- Lesson 50 - Finite length string vibrations (continued)
- Lesson 51 - Non-homogeneous wave equation
- Lesson 52 - Vibration of a circular drum
- Lesson 53 - Solutions of heat equation-Properties
- Lesson 54 - Temperature in an infinite rod
- Lesson 55 - Temperature in a semi-infinite rod
- Lesson 56 - Non-homogeneous heat equation
- Lesson 57 - Temperature in a finite rod
- Lesson 58 - Temperature in a finite rod with insulated ends
- Lesson 59 - Laplace equation over a rectangle
- Lesson 60 - Laplace equation over a rectangle with flux boundary conditions
- Lesson 61 - Laplace equation over circular domains
- Lesson 62 - Laplace equation over circular Sectors
- Lesson 63 - Uniqueness of solutions-Laplace equation
- Lesson 64 - Conclusions