Learn · Ordinary Differential Equations : Power series, eigenvalues and Green functions
Lecture 17 of 20Week 4
Lecture 17: Orthogonality of Eigenfunctions
Prof. Somnath Bhattacharyya · IIT Kharagpur
Credits and licence
- From
- Ordinary Differential Equations : Power series, eigenvalues and Green functions, IIT Kharagpur (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
- Lecture 01: Introduction to ODE, IVP, BVP and conversion of IVP to first order ODE
- Lecture 02: Existance and uniqueness of solution, Lipschitz Function
- Lecture 03: Picard Method of Successive Approximations
- Lecture 04: Systems of first-order ODEs, Eigenvalues and eigenvectors
- Lecture 05: Introduction to Linear Stability Analysis
- Lecture 06: Series solution of ODE, ordinary point
- Lecture 07: Legendre Polynomial
- Lecture 08: Recursion relation of Legendre polynomials
- Lecture 09: Rodrigues Formula and Orthogonality of Legendre Polynomial
- Lecture 10: Properties of Legendre Polynomial
- Lecture 11: Generating Function
- Lecture 12: Singular Point and Frobenius Series
- Lecture 13: Bessel function and Recurrence Relation
- Lecture 14: Properties of Bessel Functions and Reduciable to Bessel Equation
- Lecture 15: Boundary Value Problems, Self-adjoint Differential Operator
- Lecture 16: Eigenfunction and eigenvalues of self adjoint operator
- Lecture 17: Orthogonality of Eigenfunctions
- Lecture 18: Sturm-Liouville Problem and Eigenfunction Expansion Technique
- Lecture 19: Derac Delta Function and Green's Function
- Lecture 20: Green's Function for ODE