# Computational Science in Engineering

- Institution: IIT Kanpur
- Department: Aerospace Engineering
- Teacher: Prof. Ashoke De
- Level: Undergraduate
- Language: English
- Subjects: Engineering
- Source: [NPTEL](https://nptel.ac.in/courses/101104086)
- Licence: [CC BY-NC-SA](https://nptel.ac.in/faq) (Non-commercial use only.)
- Syllabus: [at the source](https://nptel.ac.in/courses/101104086)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

## Lectures

1. [Lecture-01: Linear Algebra: Introduction](https://invisiblenetwork.ai/learn/nptel/101104086/ec399fbc6f5f) (Video)
2. [Lecture-02: Linear Algebra: Introduction (contd.)](https://invisiblenetwork.ai/learn/nptel/101104086/089bbb5c52ef) (Video)
3. [Lecture-03: Linear Algebra: Permutation Matrix, Existence of Solution](https://invisiblenetwork.ai/learn/nptel/101104086/1db7c2bbed77) (Video)
4. [Lecture-04: Linear Algebra: Permutation Matrix, Existence of Solution (contd.)](https://invisiblenetwork.ai/learn/nptel/101104086/953f4e976df0) (Video)
5. [Lecture-05: Linear Algebra: Linear Independence, Basis Vector and Dimensions](https://invisiblenetwork.ai/learn/nptel/101104086/ceba4fd9ce11) (Video)
6. [Lecture-06: Linear Algebra: Null Space, Column Space, Row Space, Introduction to Orthogonal System](https://invisiblenetwork.ai/learn/nptel/101104086/7e53e7d9c923) (Video)
7. [Lecture-07: Linear Algebra: Orthogonal System, Projection, Determinant](https://invisiblenetwork.ai/learn/nptel/101104086/07a179579bd3) (Video)
8. [Lecture-08: Linear Algebra: Orthogonal System, Projection, Determinant (contd.)](https://invisiblenetwork.ai/learn/nptel/101104086/1e2aa2200a76) (Video)
9. [Lecture-09: Linear Algebra: Properties of Determinant, Cramer's Rule, Introduction to Eigen Values](https://invisiblenetwork.ai/learn/nptel/101104086/2de5e1aa9579) (Video)
10. [Lecture-10: Linear Algebra: Eigen Values, Eigen Vectors, SVD](https://invisiblenetwork.ai/learn/nptel/101104086/18d97a8fbbbd) (Video)
11. [Lecture-11: Linear Algebra: Eigen Values, Eigen Vectors, SVD (contd.)](https://invisiblenetwork.ai/learn/nptel/101104086/b7e386137027) (Video)
12. [Lecture-12: ODE: Introduction to ODEs, Initial Value Problem, Separation of Variables](https://invisiblenetwork.ai/learn/nptel/101104086/9c3003cdf593) (Video)
13. [Lecture-13: ODE: Solution of Exact ODEs, First Order Linear Systems](https://invisiblenetwork.ai/learn/nptel/101104086/ee8462f8a863) (Video)
14. [Lecture-14: ODE: Solution of Second Order Linear ODEs](https://invisiblenetwork.ai/learn/nptel/101104086/75d45afb643a) (Video)
15. [Lecture-15: ODE: Existence and Uniqueness of Solution, Non-Homogeneous System](https://invisiblenetwork.ai/learn/nptel/101104086/53c19a08bf82) (Video)
16. [Lecture-21: PDE: First Order PDEs, Dilation Invariant Solution of Differential Equations](https://invisiblenetwork.ai/learn/nptel/101104086/d5dd65a23ceb) (Video)
17. [Lecture-22: PDE: Solution of Linear PDEs](https://invisiblenetwork.ai/learn/nptel/101104086/88f3e8421430) (Video)
18. [Lecture-23: PDE: Separation of Variables, Eigenvalue Problem, Poisson Integral Representation](https://invisiblenetwork.ai/learn/nptel/101104086/7651cca13ddd) (Video)
19. [Lecture-24: PDE: Boundary Conditions, Solution of 2D systems](https://invisiblenetwork.ai/learn/nptel/101104086/42737468a77d) (Video)
20. [Lecture-25: Introduction to Numerical Methods, Mathematical Models, Errors](https://invisiblenetwork.ai/learn/nptel/101104086/0209f98807c2) (Video)
21. [Lecture-26: Errors, Numerical Differentiation, Stability](https://invisiblenetwork.ai/learn/nptel/101104086/5e4b89387001) (Video)
22. [Lecture-27: Roots of Equations: Graphical Method, Bi-Section Mehtod, False-Position Method](https://invisiblenetwork.ai/learn/nptel/101104086/a15ebd1680c5) (Video)
23. [Lecture-28: Secant Method, Brent's Method, Multipoint Iteration Method, Derative Free Method](https://invisiblenetwork.ai/learn/nptel/101104086/f40f2d1ec5a2) (Video)
24. [Lecture-29: Complex Roots, Birge-Vieta Method, Bairstow's method](https://invisiblenetwork.ai/learn/nptel/101104086/52eb4068d9e7) (Video)
25. [Lecture-30: Solution of Linear Algebric Equations, Gauss Elimination Method](https://invisiblenetwork.ai/learn/nptel/101104086/f11c8fadcaeb) (Video)
26. [Lecture-31: Direct Methods: Gauss Elimination, Gauss-Jordan, Crout's Method, Cholesky Method, Iterative Methods: Jacobi Iteration Method, Gauss-Seidel](https://invisiblenetwork.ai/learn/nptel/101104086/e2f28679e586) (Video)
27. [Lecture-32: Extrapolation Method, Eigenvalue Problem, Jacobi Method, Householder's Method for Symmetric Matrices, Power Method, Inverse Power Method](https://invisiblenetwork.ai/learn/nptel/101104086/e47f40ac4f4c) (Video)
28. [Lecture-33: Interpolation: Taylor's Series, Lagrange and Newton Interpolation, Iterated Interpolation, Hermite Interpolation, Finite Difference Operations](https://invisiblenetwork.ai/learn/nptel/101104086/edf8d04eaa16) (Video)
29. [Lecture-34: Piecewise and Spline Interpolation, Bivariate Interpolation, Least Square Approximation, Uniform Polynomial Approximation](https://invisiblenetwork.ai/learn/nptel/101104086/50dc4eed8019) (Video)
30. [Lecture-35: Numerical Differentiation and Intergration, Methods Based on Finite Differences, Methods based on Undetermined Coefficients, Extrapolation Methods, Partial Differentiation](https://invisiblenetwork.ai/learn/nptel/101104086/2408c1f28156) (Video)
31. [Live Session 24-03-2021](https://invisiblenetwork.ai/learn/nptel/101104086/ec399fbc6f5f-2) (Video)
32. [Live Session 15-03-2022](https://invisiblenetwork.ai/learn/nptel/101104086/089bbb5c52ef-2) (Video)