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Course10110408632 lectures

Computational Science in Engineering

Prof. Ashoke De · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Week-01: Linear Algebra: Introduction to Vectors, Vector spaces and subspaces, Solving Linear systems

  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

Week-02: Linear Algebra: Orthogonality, Determinants, Eigenvalues & Eigen vectors, SVD

  1. Lecture-06: Linear Algebra: Null Space, Column Space, Row Space, Introduction to Orthogonal System Video
  2. Lecture-07: Linear Algebra: Orthogonal System, Projection, Determinant Video
  3. Lecture-08: Linear Algebra: Orthogonal System, Projection, Determinant (contd.) Video
  4. Lecture-09: Linear Algebra: Properties of Determinant, Cramer's Rule, Introduction to Eigen Values Video
  5. Lecture-10: Linear Algebra: Eigen Values, Eigen Vectors, SVD Video

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

  1. Lecture-11: Linear Algebra: Eigen Values, Eigen Vectors, SVD (contd.) Video
  2. Lecture-12: ODE: Introduction to ODEs, Initial Value Problem, Separation of Variables Video
  3. Lecture-13: ODE: Solution of Exact ODEs, First Order Linear Systems Video
  4. Lecture-14: ODE: Solution of Second Order Linear ODEs Video
  5. Lecture-15: ODE: Existence and Uniqueness of Solution, Non-Homogeneous System Video

Week-04: Solution of Higher Order ODEs, Fourier Analysis, Fourier Integrals, Laplace Transforms

  1. Lecture-21: PDE: First Order PDEs, Dilation Invariant Solution of Differential Equations Video
  2. Lecture-22: PDE: Solution of Linear PDEs Video
  3. Lecture-23: PDE: Separation of Variables, Eigenvalue Problem, Poisson Integral Representation Video
  4. Lecture-24: PDE: Boundary Conditions, Solution of 2D systems Video
  5. Lecture-25: Introduction to Numerical Methods, Mathematical Models, Errors Video

Week-05: Partial Differential Equations: Classification, 1D & 2D Equations, BC, 2nd Order PDEs

  1. Lecture-26: Errors, Numerical Differentiation, Stability Video
  2. Lecture-27: Roots of Equations: Graphical Method, Bi-Section Mehtod, False-Position Method Video
  3. Lecture-28: Secant Method, Brent's Method, Multipoint Iteration Method, Derative Free Method Video
  4. Lecture-29: Complex Roots, Birge-Vieta Method, Bairstow's method Video
  5. Lecture-30: Solution of Linear Algebric Equations, Gauss Elimination Method Video

Week-06: Basis of Numerical Analysis, Errors, Stability, Interpolation and Extrapolation

  1. Lecture-31: Direct Methods: Gauss Elimination, Gauss-Jordan, Crout's Method, Cholesky Method, Iterative Methods: Jacobi Iteration Method, Gauss-Seidel Video
  2. Lecture-32: Extrapolation Method, Eigenvalue Problem, Jacobi Method, Householder's Method for Symmetric Matrices, Power Method, Inverse Power Method Video
  3. Lecture-33: Interpolation: Taylor's Series, Lagrange and Newton Interpolation, Iterated Interpolation, Hermite Interpolation, Finite Difference Operations Video
  4. Lecture-34: Piecewise and Spline Interpolation, Bivariate Interpolation, Least Square Approximation, Uniform Polynomial Approximation Video
  5. Lecture-35: Numerical Differentiation and Intergration, Methods Based on Finite Differences, Methods based on Undetermined Coefficients, Extrapolation Methods, Partial Differentiation Video

Live Session

  1. Live Session 24-03-2021 Video
  2. Live Session 15-03-2022 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Aerospace Engineering
Teacher
Prof. Ashoke De
Level
Undergraduate
Language
English
Subjects
Engineering
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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