By Prof. Madhumangal Pal |
Vidyasagar University

Learners enrolled: 2017

Week 1: **Errors in Numerical
Computations**1. Ch 1 Mod 1: Error in Numerical Computations.

2. Ch 1 Mod 2: Propagation of Errors and Computer Arithmetic.

Week 2: Interpolation - I

3. Ch 1 Mod 3: Operators in Numerical Analysis.

4. Ch 2 Mod 1: Lagrange’s. Interpolation.

5. Ch 2 Mod 2: Newton’s Interpolation Methods.

6. Ch 2 Mod 3: Central Deference Interpolation
Formulae.

Week 3: Interpolation - II

7. Ch 2 Mod 4: Aitken’s and Hermite’s Interpolation
Methods.

8. Ch 2 Mod 5: Spline Interpolation.

9. Ch 2 Mod 6: Inverse Interpolation.

10. Ch 2 Mod 7: Bivariate Interpolation.

Week 4: Approximation of
Functions

11. Ch 3 Mod 1: Least Squares Method.

12. Ch 3 Mod 2: Approximation of Function by Least
Squares Method.

13. Ch 3 Mod 3: Approximation of Function by Chebyshev
Polynomials.

Week 5: Solution of Algebraic and Transcendental Equation

14. Ch 4 Mod 1: Newton’s Method to Solve Transcendental
Equation.

15. Ch 4 Mod 2: Roots of a Polynomial Equation.

16. Ch 4 Mod 3: Solution of System of Non-linear
Equations.

Week 6: Solution of System of Linear
Equations-I

17. Ch 5 Mod 1: Matrix Inverse Method.

18. Ch 5 Mod 2: Iteration Methods to Solve System of
Linear Equations.

19. Ch 5 Mod 3: Methods of Matrix Factorization.

Week 7: Solution of System of Linear
Equations-II

20. Ch 5 Mod 4: Gauss Elimination Method and Tri-diagonal
Equations.

21. Ch 5 Mod 5: Generalized Inverse of Matrix.

22. Ch 5 Mod 6: Solution of Inconsistent and Ill
Conditioned Systems.

Week 8: Assessment

Week 9: Eigenvalues and Eigenvectors of Matrices

23. Ch 6 Mod 1: Construction of Characteristic Equation
of a Matrix.

24. Ch 6 Mod 2: Eigenvalue and Eigenvector of Arbitrary
Matrices.

25. Ch 6 Mod 3: Eigenvalues and Eigenvectors of Symmetric
Matrices.

Week 10: Differentiation and
Integration-I

26. Ch 7 Mod 1: Numerical Differentiation.

27. Ch 7 Mod 2: Newton-Cotes Quadrature.

Week 11: Differentiation and
Integration-II

28. Ch 7 Mod 3: Gaussian Quadrature.

29. Ch 7 Mod 4: Monte-Carlo Method and Double
Integration.

Week 12: Ordinary Differential
Equations-I

30. Ch 8 Mod 1: Runge-Kutta Methods.

31. Ch 8 Mod 2: Predictor-Corrector Methods.

Week 13: Ordinary Differential
Equations-II

32. Ch 8 Mod 3: Finite Difference Method and its
Stability.

33. Ch 8 Mod 4: Shooting Method and Stability Analysis.

Week 14: Partial Differential Equations

34. Ch 9 Mod 1: Partial Differential Equation: Parabolic.

35. Ch 9 Mod 2: Partial Differential Equations:
Hyperbolic.

36. Ch 9 Mod 3: Partial Differential Equations: Elliptic

Week 15: Final examination

Jain,
M.K., Iyengar, S.R.K., and Jain, R.K. Numerical Methods for Scientific and Engineering
Computation. New Delhi: New Age International (P) Limited,
1984.**Pal, M.** Numerical Analysis for Scientists and Engineers:
Theory and C Programs. New Delhi: Narosa, Oxford: Alpha Sciences, 2007.

Krishnamurthy, E.V., and Sen, S.K.

Mathews, J.H.

Danilina, N.I., Dubrovskaya, S.N., and Kvasha, O.P., and Smirnov, G.L. Computational Mathematics. Moscow: Mir Publishers, 1998.

Hildebrand, F.B. Introduction of Numerical Analysis. New York: London: McGraw-Hill, 1956.

**Prof. Madhumangal Pal is currently a Professor of Applied Mathematics, Vidyasagar University. He has received Gold and Silver medals from Vidyasagar University for rank first and second in M.Sc. and B.Sc. examinations respectively. Also, he received “Computer Division Medal” from Institute of Engineers (India) in 1996 for best research work. Prof. Pal has successfully guided 35 research scholars for Ph.D. degrees and has published more than 360 articles in international and national journals. His specializations include Algorithmic and Fuzzy Graph Theory, Fuzzy Matrices, Genetic and Parallel Algorithms. He has evaluated more than 91 Ph.D. theses from Indian and Abroad. Prof. Pal is the author of nine text books including Numerical Analysis and two edited books published from India, United Kingdom and USA. He has published 23 chapters in several edited books. Prof. Pal completed three research project funded by UGC and DST and is ongoing. Prof. Pal is the Editor-in-Chief of two journals and area editor of SCIE Indexed journal, and member of the editorial Boards of several journals. Also, he has visited China, Greece, London, Taiwan, Malaysia, Thailand, Hong Kong, Dubai and Bangladesh for academic purpose. He is also a member of the American Mathematical Society, USA, Calcutta Mathematical Society, Advanced Discrete Mathematics and Application, Neutrosophic Science International Association, USA, Ramanujam Mathematical Society, India, etc. As per Google Scholar, the citation of Prof. Pal is 7913, h-index is 47 and i10-index is 207, as on 28.05.2021. He was a member of the several selection committees and several administrative and academic bodies in Vidyasagar University and other institutes. He is recently included in the list of top 2% scientists among all disciplines prepared by Stanford University.**

**Certificate policy **The course is
free for all to enroll. But, for getting a certificate, learner have to
register and deposit the registration fee (amount is to be declared latter).

The final examination will be held in first week of May 2021.

Registration url: Announcements will be made when the registration form is open for registrations.

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Criteria to get a certificate

Assignment score
= 30% among best 8 assignments out of the total 13 assignments given in the
course.

Exam score = 70%
of the proctored certification exam score out of 100.

Final score =
Assignment score + Exam score.

Assignment score
and final score must be at least 40% separately.

Final score must
be at least 40% to get a certificate.

How to get
certificate

Certificate
contains learner name, photograph and the score in the final exam with the
breakup.

Only the
e-certificate will be made available.

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