Ordinary Differential Equations : Power series, eigenvalues and Green functions 31G4GQ8M2M

URI	`m2://res/31G4GQ8M2M`
Kind	course
Creators	Somnath Bhattacharyya (instructor)
Date	2026-07-06
MSC	34-XX
Scope	in
Ids	course 03w5sq511:111105003

Expressions

Language	en
Date	2026-07-06

Contents

part 1: Week 1
session 1: Lecture 01: Introduction to ODE, IVP, BVP and conversion of IVP to first order ODE
session 2: Lecture 02: Existance and uniqueness of solution, Lipschitz Function
session 3: Lecture 03: Picard Method of Successive Approximations
session 4: Lecture 04: Systems of first-order ODEs, Eigenvalues and eigenvectors
session 5: Lecture 05: Introduction to Linear Stability Analysis
part 2: Week 2
session 6: Lecture 06: Series solution of ODE, ordinary point
session 7: Lecture 07: Legendre Polynomial
session 8: Lecture 08: Recursion relation of Legendre polynomials
session 9: Lecture 09: Rodrigues Formula and Orthogonality of Legendre Polynomial
session 10: Lecture 10: Properties of Legendre Polynomial
part 3: Week 3
session 11: Lecture 11: Generating Function
session 12: Lecture 12: Singular Point and Frobenius Series
session 13: Lecture 13: Bessel function and Recurrence Relation
session 14: Lecture 14: Properties of Bessel Functions and Reduciable to Bessel Equation
session 15: Lecture 15: Boundary Value Problems, Self-adjoint Differential Operator
part 4: Week 4
session 16: Lecture 16: Eigenfunction and eigenvalues of self adjoint operator
session 17: Lecture 17: Orthogonality of Eigenfunctions
session 18: Lecture 18: Sturm-Liouville Problem and Eigenfunction Expansion Technique
session 19: Lecture 19: Derac Delta Function and Green's Function
session 20: Lecture 20: Green's Function for ODE