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Lecture 13 of 32Week-03: Ordinary Differential Equations: ODE, Homogeneous and Non-homogeneous ODEs, Second Order Linear ODE, Higher…

Lecture-13: ODE: Solution of Exact ODEs, First Order Linear Systems

Prof. Ashoke De · IIT Kanpur

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Computational Science in Engineering, IIT Kanpur (at NPTEL)
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CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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All the lectures

  1. Lecture-01: Linear Algebra: Introduction Video
  2. Lecture-02: Linear Algebra: Introduction (contd.) Video
  3. Lecture-03: Linear Algebra: Permutation Matrix, Existence of Solution Video
  4. Lecture-04: Linear Algebra: Permutation Matrix, Existence of Solution (contd.) Video
  5. Lecture-05: Linear Algebra: Linear Independence, Basis Vector and Dimensions Video
  6. Lecture-06: Linear Algebra: Null Space, Column Space, Row Space, Introduction to Orthogonal System Video
  7. Lecture-07: Linear Algebra: Orthogonal System, Projection, Determinant Video
  8. Lecture-08: Linear Algebra: Orthogonal System, Projection, Determinant (contd.) Video
  9. Lecture-09: Linear Algebra: Properties of Determinant, Cramer's Rule, Introduction to Eigen Values Video
  10. Lecture-10: Linear Algebra: Eigen Values, Eigen Vectors, SVD Video
  11. Lecture-11: Linear Algebra: Eigen Values, Eigen Vectors, SVD (contd.) Video
  12. Lecture-12: ODE: Introduction to ODEs, Initial Value Problem, Separation of Variables Video
  13. Lecture-13: ODE: Solution of Exact ODEs, First Order Linear Systems Video
  14. Lecture-14: ODE: Solution of Second Order Linear ODEs Video
  15. Lecture-15: ODE: Existence and Uniqueness of Solution, Non-Homogeneous System Video
  16. Lecture-21: PDE: First Order PDEs, Dilation Invariant Solution of Differential Equations Video
  17. Lecture-22: PDE: Solution of Linear PDEs Video
  18. Lecture-23: PDE: Separation of Variables, Eigenvalue Problem, Poisson Integral Representation Video
  19. Lecture-24: PDE: Boundary Conditions, Solution of 2D systems Video
  20. Lecture-25: Introduction to Numerical Methods, Mathematical Models, Errors Video
  21. Lecture-26: Errors, Numerical Differentiation, Stability Video
  22. Lecture-27: Roots of Equations: Graphical Method, Bi-Section Mehtod, False-Position Method Video
  23. Lecture-28: Secant Method, Brent's Method, Multipoint Iteration Method, Derative Free Method Video
  24. Lecture-29: Complex Roots, Birge-Vieta Method, Bairstow's method Video
  25. Lecture-30: Solution of Linear Algebric Equations, Gauss Elimination Method Video
  26. Lecture-31: Direct Methods: Gauss Elimination, Gauss-Jordan, Crout's Method, Cholesky Method, Iterative Methods: Jacobi Iteration Method, Gauss-Seidel Video
  27. Lecture-32: Extrapolation Method, Eigenvalue Problem, Jacobi Method, Householder's Method for Symmetric Matrices, Power Method, Inverse Power Method Video
  28. Lecture-33: Interpolation: Taylor's Series, Lagrange and Newton Interpolation, Iterated Interpolation, Hermite Interpolation, Finite Difference Operations Video
  29. Lecture-34: Piecewise and Spline Interpolation, Bivariate Interpolation, Least Square Approximation, Uniform Polynomial Approximation Video
  30. Lecture-35: Numerical Differentiation and Intergration, Methods Based on Finite Differences, Methods based on Undetermined Coefficients, Extrapolation Methods, Partial Differentiation Video
  31. Live Session 24-03-2021 Video
  32. Live Session 15-03-2022 Video