Lecture 1 - Introduction to differential equations - I

Lecture 2 - Introduction to differential equations - II

Lecture 3 - Existence and uniqueness of solutions of differential equations - I

Lecture 4 - Existence and uniqueness of solutions of differential equations - II

Lecture 5 - Existence and uniqueness of solutions of differential equations - III

Lecture 6 - Existence and uniqueness of solutions of a system of differential equations

Lecture 7 - Linear System

Lecture 8 - Properties of Homogeneous Systems

Lecture 9 - Solution of Homogeneous Linear System with Constant Coefficients - I

Lecture 10 - Solution of Homogeneous Linear System with Constant Coefficients - II

Lecture 11 - Solution of Homogeneous Linear System with Constant Coefficients - III

Lecture 12 - Solution of Non-Homogeneous Linear System with Constant Coefficients

Lecture 13 - Power Series

Lecture 14 - Uniform Convergence of Power Series

Lecture 15 - Power Series Solution of Second Order Homogeneous Equations

Lecture 16 - Regular singular points - I

Lecture 17 - Regular singular points - II

Lecture 18 - Regular singular points - III

Lecture 19 - Regular singular points - IV

Lecture 20 - Regular singular points - V

Lecture 21 - Critical points

Lecture 22 - Stability of Linear Systems - I

Lecture 23 - Stability of Linear Systems - II

Lecture 24 - Stability of Linear Systems - III

Lecture 25 - Critical Points and Paths of Non-linear Systems

Lecture 26 - Boundary value problems for second order differential equations

Lecture 27 - Self - adjoint Forms

Lecture 28 - Sturm - Liouville problem and its properties

Lecture 29 - Sturm - Liouville problem and its applications

Lecture 30 - Green’s function and its applications - I

Lecture 31 - Green’s function and its applications - II

Lecture 32 - Origins and Classification of First Order PDE

Lecture 33 - Initial Value Problem for Quasi-linear First Order Equations

Lecture 34 - Existence and Uniqueness of Solutions

Lecture 35 - Surfaces orthogonal to a given system of surfaces

Lecture 36 - Nonlinear PDE of first order

Lecture 37 - Cauchy method of characteristics - I

Lecture 38 - Cauchy method of characteristics - II

Lecture 39 - Compatible systems of first order equations

Lecture 40 - Charpit’s method - I

Lecture 41 - Charpit’s method - II

Lecture 42 - Second Order PDE with Variable Coefficients

Lecture 43 - Classification and Canonical Form of Second Order PDE - I

Lecture 44 - Classification and Canonical Form of Second Order PDE - II

Lecture 45 - Classification and Characteristic Curves of Second Order PDEs

Lecture 46 - Review of Integral Transforms - I

Lecture 47 - Review of Integral Transforms - II

Lecture 48 - Review of Integral Transforms - III

Lecture 49 - Laplace Equation - I

Lecture 50 - Laplace Equation - II

Lecture 51 - Laplace Equation - III

Lecture 52 - Laplace and Poisson Equations

Lecture 53 - One dimensional wave equation and its solution - I

Lecture 54 - One dimensional wave equation and its solution - II

Lecture 55 - One dimensional wave equation and its solution - III

Lecture 56 - Two dimensional wave equation and its solution - I

Lecture 57 - Solution of non-homogeneous wave equation

Lecture 58 - Solution of homogeneous diffusion equation - I

Lecture 59 - Solution of homogeneous diffusion equation - II

Lecture 60 - Duhamel’s principle