By Prof. Madhumangal Pal |
Vidyasagar University

Learners enrolled: 2298

**numerical analysis/ method** is a very important and common topic for
computational mathematics and hence studied by students from many disciplines
like mathematics, computer science, physics, statistics and other subjects of
physical sciences and engineering. The numerical analysis/method is an
interdisciplinary course used by students/ teachers/ researchers from several
branches of science and technology, particularly **mathematics, statistics, computer science, physics, chemistry,
electronics****,** etc.
This subject is also known as computational mathematics. To design several
functions of a computer and to solve a problem by computer numerical method is
essential. It is not possible to solve any large-scale problem without the help
of numerical methods. Numerical methods also simplify the conventional methods
to solve problems, like definite integration, solution of equations, solution
of differential equations, interpolation from the known to the unknown, etc. To
explore complex systems, mathematicians, engineers, and physicists require
computational methods since mathematical models are only rarely solvable
algebraically. The numerical methods based on computational mathematics are the
basic algorithms underpinning computer predictions in modern systems science.
After completing the course, the students can design algorithms and program
codes to solve real-life problems. In each module, an exercise is provided to
test the students’ performance. Also, some more references are added in the
learn more section to investigate the subject more thoroughly and to learn more
topics of numerical analysis. The entire course is divided into nine chapters
and thirty-six modules. It is a **15 weeks** one-semester course including assignments, discussions and evaluation.
Almost all Indian universities offer this course as a **core course**.

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 Difference 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, at Vidyasagar University. He has
received Gold and Silver medals from Vidyasagar University for ranking first
and second in M.Sc. and B.Sc. examinations, respectively. Also, he received the
“Computer Division Medal” from the Institute of Engineers (India) in 1996 for
best research work. Prof. Pal has successfully guided 39 research scholars for
Ph.D. degrees and has published more than 390 articles in international and
national journals. His specializations include Algorithmic and Fuzzy Graph
Theory, Fuzzy Matrices, and Genetic and Parallel Algorithms. He has evaluated
more than 160 Ph.D. theses from Indian and Abroad. Prof. Pal is the author of
nine textbooks, including ****Numerical Analysis**** and
two edited books published in India, the United Kingdom and the USA. He has
published 23 chapters in several edited books. Prof. Pal completed three
research projects 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 a 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 purposes. 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 10303, the h-index is 53 and the i10-index is 252, as of
02.12.2022. He was a member of several selection committees and several
administrative and academic bodies at Vidyasagar University and other
institutes. He is recently included in the list of the top 2% of 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.

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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