Numerical Analysis

By Prof. Madhumangal Pal | Vidyasagar University

Learners enrolled: 1635

The numerical analysis/ method is a very important and common topic for computational mathematics and hence studied by the students from many disciplines like mathematics, computer science, physics, statistics and other subject of physical sciences and engineering. The numerical analysis / method is an interdisciplinary course used by the students/ teachers/ researchers from several branches of science and technology, particularly from mathematics, computer science, physics, chemistry, electronics, etc. This subject is also known as computational mathematics. To design several functions of computer and to solve a problem by computer numerical method is essential. It is not possible to solve any large scale problem without help of numerical methods. Numerical methods are 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, physicists require computational methods since mathematical models are only rarely solvable algebraically. The numerical methods based on the computational mathematics are the basic algorithms underpinning computer predictions in modern systems science. After completion of the course, the students can design algorithms and program codes to solve the real life problems. In each module, an exercise is provided to test the performance of the students. 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 assignment, discussion and evaluation. This course is offered by almost all Indian universities as a core course.

Summary

Course Status :	Completed
Course Type :	Core
Duration :	15 weeks
Category :	Mathematics
Credit Points :	4
Level :	Postgraduate
Start Date :	13 Jan 2020
End Date :	30 Apr 2020
Enrollment Ends :	08 Mar 2020
Exam Date :	10 May 2020 IST

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Week 1: Errors in Numerical Computations

1. Error in Numerical Computations.

2. Propagation of Errors and Computer Arithmetic.

Week 2: Interpolation - I

3. Operators in Numerical Analysis.

4. Lagrange’s. Interpolation.

5. Newton’s Interpolation Methods.

6. Central Deference Interpolation Formulae.

Week 3: Interpolation - II

7. Aitken’s and Hermite’s Interpolation Methods.

8. Spline Interpolation.

9. Inverse Interpolation.

10. Bivariate Interpolation.

Week 4: Approximation of Functions

11. Least Squares Method.

12. Approximation of Function by Least Squares Method.

13. Approximation of Function by Chebyshev Polynomials.

Week 5: Solution of Algebraic and Transcendental Equation

14. Newton’s Method to Solve Transcendental Equation.

15. Roots of a Polynomial Equation.

16. Solution of System of Non-linear Equations.

Week 6: Solution of System of Linear Equations-I

17. Matrix Inverse Method.

18. Iteration Methods to Solve System of Linear Equations.

19. Methods of Matrix Factorization.

Week 7: Solution of System of Linear Equations-II

20. Gauss Elimination Method and Tri-diagonal Equations.

21. Generalized Inverse of Matrix.

22. Solution of Inconsistent and Ill Conditioned Systems.

Week 8:

Assessment

Week 9: Eigen Values and Eigen Function of Matrices

23. Construction of Characteristic Equation of a Matrix.

24. Eigenvalue and Eigenvector of Arbitrary Matrices.

25. Eigenvalues and Eigenvectors of Symmetric Matrices.

Week 10: Differentiation and Integration-I

26. Numerical Differentiation.

27. Newton-Cotes Quadrature.

Week 11: Differentiation and Integration-II

28. Gaussian Quadrature.

29. Monte-Carlo Method and Double Integration.

Week 12: Ordinary Differential Equations-I

30. Runge-Kutta Methods.

31. Predictor-Corrector Methods.

Week 13: Ordinary Differential Equations-II

32. Finite Difference Method and its Stability.

33. Shooting Method and Stability Analysis.

Week 14: Partial Differential Equations

34. Partial Differential Equation: Parabolic.

35. Partial Differential Equations: Hyperbolic.

36. Partial Differential Equations: Elliptic

Week 15

Final examination

Books and references

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

2. M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods for Scientific and Engineering Computation, New Age International (P) Limited, New Delhi, 1984.

3. E.V. Krishnamurthy and S.K. Sen, Numerical Algorithms, Affiliated East-West Press Pvt. Ltd., New Delhi, 1986.

4. J.H. Mathews, Numeical Methods for Mathematics, Science, and Engineering, 2nd ed., Prentice-Hall, Inc., N.J., U.S.A., 1992.

5. M.Pal, Numerical Analysis for Scientists and Engineers: Theory and C Programs, Narosa, New Delhi and Alpha Sciences, Oxford, UK,

2007.

Instructor bio

Prof. Madhumangal Pal

Vidyasagar University

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 31 research scholars for Ph.D. degrees and has published more than 310 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 84 Ph.D. theses from Indian and Abroad. Prof. Pal is the author of eight text books published from India and United Kingdom. One of them is Numerical Analysis for Scientists and Engineers: Theory and C Program, published by Narosa, New Delhi. He has published 15 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 “Journal of Physical Sciences”, “Annals of Pure and Applied Mathematics”, section editor of “International Journal of Computational Intelligence Systems (SCIE Index Journal)” and member of the editorial Boards of many journals. Also, he has visited China, Greece, London, Taiwan, Malaysia, Thailand, Hong Kong, Dubai and Bangladesh to participated, delivered invited talk and to chair conference, seminar, etc. 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 5711, h-index is 38 and i10-index is 173, as on 07.12.2019. He was a member of the several selection committees and several administrative and academic bodies in Vidyasagar University and other institutes.

Course certificate

• 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 2020.

• 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 = 20% among best 8 assignments out of the total 12 assignments given in the course.

• Exam score = 80% 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.