Module 1

Total Lectures

51

Examples of Sturm-Liouville systems

Lectures

Examples of Sturm-Liouville systems
Bessel differential equation
Classification of second order linear PDEs
Introduction to Sturm-Liouville theory
Regular Sturm-Liouville problem
Examples of regular Sturm-Liouville systems
Non-homogeneous wave equation
Legendre Polynomials
Properties of Legendre Polynomials
Power series solutions around a regular singular point
Periodic and singular Sturm-Liouville Problems
Frobenius solutions for Bessel Equation
Generalized Fourier series
Second order linear PDEs
Reduction to Normal form-More examples
Frobenius method of solutions
Temperature in a finite rod
Frobenius method of solutions (continued)
Reduction to canonical form for equations with variable coefficients
Vibration of a finite string
Laplace equation over a rectangle with flux boundary conditions
Laplace equation over circular Sectors
Laplace equation over circular domains
Laplace equation over a rectangle
Properties of Bessel functions
Examples on Frobenius method
Vibration of a semi-infinite string
Properties of Bessel functions (continued)
Sturm-Liouville Problems
Uniqueness of the boundary value problems for Laplace equation
Finite length string vibrations
Solutions of heat equation-Properties
Examples of Sturm-Liouville systems (continued)
Temperature in a semi-infinite rod
Reduction to canonical form for equations with constant coefficients
Uniqueness of solutions for wave equation
Finite length string vibrations (continued)
Vibration of a circular drum
Temperature in an infinite rod
Non-homogeneous heat equation
Temperature in a finite rod with insulated ends
Conclusions
Lecture 01 - Introduction to Ordinary Differential Equations (ODE)
Lecture 07 - Non-Exact Equations - Finding Integrating Factors
Lecture 14 - Euler - Cauchy equation
Lecture 15 - Non homogeneous ODEs Variation of Parameters
Lecture 16 - Method of undetermined coefficients
Lecture 17 - Demonstration of Method of undetermined coefficients
Lecture 18 - Power Series and its properties
Lecture 20 - Power Series Solutions ( Continued )
Lecture 21 - Legendre Differential Equatio
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