NOC:Differential Equations


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