NOC:Ordinary and Partial Differential Equations and Applications (USB)

Media Storage Type : 32 GB USB Stick

NPTEL Subject Matter Expert : Prof.D. N Pandey, Prof. P.N. Agrawal

NPTEL Co-ordinating Institute : IIT Roorkee

NPTEL Lecture Count : 60

NPTEL Course Size : 11 GB

NPTEL PDF Text Transcription : Available and Included

NPTEL Subtitle Transcription : Available and Included (SRT)

Lecture Titles:

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