By Prof. Madhumangal Pal |
Vidyasagar University

Learners enrolled: 1433

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: Eigen Values and Eigen
Function 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**

**1. Danilina, N.I., Dubrovskaya, S.N., and Kvasha,
O.P., and Smirnov, G.L.** Computational Mathematics. Moscow: Mir Publishers, 1998.**2. Pal, M.** Numerical Analysis for Scientists and Engineers: Theory and C Programs. New Delhi: Narosa, Oxford: Alpha Sciences, 2007. **3. Hildebrand, F.B.** Introduction of Numerical Analysis. New York:
London: McGraw-Hill, 1956.**4. 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. **5. Krishnamurthy, E.V., and Sen, S.K.** Numerical Algorithms. New Delhi: Affiliated East-West Press Pvt.
Ltd., 1986. **6. Mathews, J.H.** Numerical Methods for Mathematics, Science, and Engineering, 2nd ed.,
NJ: Prentice-Hall, Inc., 1992.

**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 34 research
scholars for Ph.D. degrees and has published more than 330 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 eight text books including **Numerical Analysis** and two edited books published from India, United Kingdom
and USA. He has published 21 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 6128, h-index is 40 and i10-index is 182, as on 20.05.2020. He was a
member of the several selection committees and several administrative and
academic bodies in Vidyasagar University and other institutes.

**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 on 26 March 2021 during 9 am to 12 noon.

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

The online registration form for examination has to be filled and the certification examination fee has to be paid. More details will be made available when the examination registration form is published. Any changes will be informed accordingly.

Please check the form for more details on the exam cities and other information.

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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