Lecture 1 - Introduction to Ordinary Differential Equations (ODE)

Lecture 2 - Methods for First Order ODE's - Homogeneous Equations

Lecture 3 - Methods for First order ODE's - Exact Equations

Lecture 4 - Methods for First Order ODE's - Exact Equations (Continued...)

Lecture 5 - Methods for First order ODE's - Reducible to Exact Equations

Lecture 6 - Methods for First order ODE's - Reducible to Exact Equations (Continued...)

Lecture 7 - Non-Exact Equations - Finding Integrating Factors

Lecture 8 - Linear First Order ODE and Bernoulli's Equation

Lecture 9 - Introduction to Second order ODE's

Lecture 10 - Properties of solutions of second order homogeneous ODE's

Lecture 11 - Abel's formula to find the other solution

Lecture 12 - Abel's formula - Demonstration

Lecture 13 - Second Order ODE's with constant coefficients

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 19 - Power Series Solutions to Second Order ODE's

Lecture 20 - Power Series Solutions (Continued...)

Lecture 21 - Legendre Differential Equation

Lecture 22 - Legendre Polynomials

Lecture 23 - Properties of Legendre Polynomials

Lecture 24 - Power series solutions around a regular singular point

Lecture 25 - Frobenius method of solutions

Lecture 26 - Frobenius method of solutions (Continued...)

Lecture 27 - Examples on Frobenius method

Lecture 28 - Bessel differential equation

Lecture 29 - Frobenius solutions for Bessel Equation

Lecture 30 - Properties of Bessel functions

Lecture 31 - Properties of Bessel functions (Continued...)

Lecture 32 - Introduction to Sturm-Liouville theory

Lecture 33 - Sturm-Liouville Problems

Lecture 34 - Regular Sturm-Liouville problem

Lecture 35 - Periodic and singular Sturm-Liouville Problems

Lecture 36 - Generalized Fourier series

Lecture 37 - Examples of Sturm-Liouville systems

Lecture 38 - Examples of Sturm-Liouville systems (Continued...)

Lecture 39 - Examples of regular Sturm-Liouville systems

Lecture 40 - Second order linear PDEs

Lecture 41 - Classification of second order linear PDEs

Lecture 42 - Reduction to canonical form for equations with constant coefficients

Lecture 43 - Reduction to canonical form for equations with variable coefficients

Lecture 44 - Reduction to Normal form-More examples

Lecture 45 - D'Alembert solution for wave equation

Lecture 46 - Uniqueness of solutions for wave equation

Lecture 47 - Vibration of a semi-infinite string

Lecture 48 - Vibration of a finite string

Lecture 49 - Finite length string vibrations

Lecture 50 - Finite length string vibrations (Continued...)

Lecture 51 - Non-homogeneous wave equation

Lecture 52 - Vibration of a circular drum

Lecture 53 - Solutions of heat equation-Properties

Lecture 54 - Temperature in an infinite rod

Lecture 55 - Temperature in a semi-infinite rod

Lecture 56 - Non-homogeneous heat equation

Lecture 57 - Temperature in a finite rod

Lecture 58 - Temperature in a finite rod with insulated ends

Lecture 59 - Laplace equation over a rectangle

Lecture 60 - Laplace equation over a rectangle with flux boundary conditions

Lecture 61 - Laplace equation over circular domains

Lecture 62 - Laplace equation over circular Sectors

Lecture 63 - Uniqueness of the boundary value problems for Laplace equation

Lecture 64 - Conclusions