NOC:Ordinary and Partial Differential Equations and Applications


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