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Course11110711160 lectures

Ordinary and Partial Differential Equations and Applications

Prof. P.N. Agrawal Prof. D. N Pandey · IIT Roorkee

Start with lecture 1 At NPTEL

Lectures

Unit-1

  1. Introduction to differential equations-I Video
  2. Introduction to differential equations-II Video
  3. Existence and uniqueness of solutions of differential equations-I Video
  4. Existence and uniqueness of solutions of differential equations-II Video
  5. Existence and uniqueness of solutions of differential equations-III Video

Unit-2

  1. Existence and uniqueness of solutions of a system of differential equations Video
  2. Linear System Video
  3. Properties of Homogeneous Systems Video
  4. Solution of Homogeneous Linear System with Constant Coefficients-I Video
  5. Solution of Homogeneous Linear System with Constant Coefficients-II Video

Unit-3

  1. Solution of Homogeneous Linear System with Constant Coefficients-III Video
  2. Solution of Non-Homogeneous Linear System with Constant Coefficients Video
  3. Power Series Video
  4. Uniform Convergence of Power Series Video
  5. Power Series Solution of Second Order Homogeneous Equations Video

Unit-4

  1. Regular singular points-I Video
  2. Regular singular points-II Video
  3. Regular singular points-III Video
  4. Regular singular points-IV Video
  5. Regular singular points-V Video

Unit-5

  1. Critical points Video
  2. Stability of Linear Systems-I Video
  3. Stability of Linear Systems-II Video
  4. Stability of Linear Systems-III Video
  5. Critical Points and Paths of Non-linear Systems Video

Unit-6

  1. Boundary value problems for second order differential equations Video
  2. Self - adjoint Forms Video
  3. Sturm -Liouville problem and its properties Video
  4. Sturm -Liouville problem and its applications Video
  5. Green's function and its applications-I Video

Unit-7

  1. Green's function and its applications-II Video
  2. Origins and Classification of First Order PDE Video
  3. Initial Value Problem for Quasi-linear First Order Equations Video
  4. Existence and Uniqueness of Solutions Video
  5. Surfaces orthogonal to a given system of surfaces Video

Unit-8

  1. Nonlinear PDE of first order Video
  2. Cauchy method of characteristics-I Video
  3. Cauchy method of characteristics-II Video
  4. Compatible systems of first order equations Video
  5. Charpit's method-I Video

Unit-9

  1. Charpit's method-II Video
  2. Second Order PDE with Variable Coefficients Video
  3. Classification and Canonical Form of Second Order PDE-I Video
  4. Classification and Canonical Form of Second Order PDE-II Video
  5. Classification and Characteristic Curves of Second Order PDEs Video

Unit-10

  1. Review of Integral Transforms-I Video
  2. Review of Integral Transforms-II Video
  3. Review of Integral Transforms-III Video
  4. Laplace Equation-I Video
  5. Laplace Equation-II Video

Unit-11

  1. Laplace Equation-III Video
  2. Laplace and Poisson Equations Video
  3. One dimensional wave equation and its solution-I Video
  4. One dimensional wave equation and its solution-II Video
  5. One dimensional wave equation and its solution-III Video

Unit-12

  1. Two dimensional wave equation and its solution-I Video
  2. Solution of non-homogeneous wave equation Video
  3. Solution of homogeneous diffusion equation-I Video
  4. Solution of homogeneous diffusion equation-II Video
  5. Duhamel's principle Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Roorkee
Department
Mathematics
Teacher
Prof. P.N. Agrawal Prof. D. N Pandey
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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