The 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.
| Course Status : | Completed |
| Course Type : | Core |
| Language for course content : | English |
| Duration : | 15 weeks |
| Category : |
|
| Credit Points : | 4 |
| Level : | Postgraduate |
| Start Date : | 15 Jan 2024 |
| End Date : | 28 Apr 2024 |
| Enrollment Ends : | 29 Feb 2024 |
| Exam Date : | 26 May 2024 IST |
| Shift - II : | 3PM - 6PM |
Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.
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
Pal, M. Numerical Analysis for Scientists and Engineers: Theory and C Programs. New Delhi: Narosa, Oxford: Alpha Sciences, 2007.
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.
Krishnamurthy, E.V., and Sen, S.K. Numerical Algorithms. New Delhi: Affiliated East-West Press Pvt. Ltd., 1986.
Mathews, J.H. Numerical Methods for Mathematics, Science, and
Engineering, 2nd ed., NJ: Prentice-Hall, Inc., 1992.
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.
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 2024 (tentative date).
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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