MATH-605                 Numerical Analysis-I

This course is designed to teach the students about numerical methods and their theoretical bases. The course aims at inculcating in the students the skill to apply various techniques in numerical analysis, understand and do calculations about errors that can occur in numerical methods and understand and be able to use the basics of matrix analysis. It is optimal to verifying numerical methods by using computer programming (MatLab, Maple, C++, etc)

Contents

1. Error analysis: Floating point arithmetic
2. Approximations and errors
3. Methods for the solution of nonlinear equations
4. Bisection method, regula-falsi method
5. Fixed point iteration method,
6. Newton-Raphson method, secant method, error analysis for iterative methods
7. Interpolation and polynomial approximation
8. Forward, backward and centered difference formulae,
9. Lagrange interpolation, Newton’s divided difference formula
10. Interpolation with a cubic spline, Hermite interpolation, least squares approximation.
11. Numerical differentiation and Integration: Forward, backward and central difference formulae
12.  Richardson’s extrapolation, Newton-Cotes formulae, Numerical integration
13. Rectangular rule, trapezoidal rule, Simpson’s 1/3 and 3/8 rules
14. Boole’s and Weddle’s rules,  Gaussian quadrature
15. Numerical solution of a system of linear equations
16. Direct methods: Gaussian elimination method
17. Gauss-Jordan method; matrix inversion; LU-factorization
18. Doolittle’s, Crout’s and Cholesky’s methods
19. Iterative methods: Jacobi, Gauss-Seidel and SOR
20. Eigen values problems
21. Introduction, Power Method, Jaccobi's Method.
22. The use of software packages/ programming languages for above mentioned topics is recommended.

Recommended Books

1. C.F. Gerald and P.O. Wheatley, Applied Numerical Analysis, (Pearson Education, Singapore, 2005)
2. R. L. Burden and J. D. Faires: Numerical Analysis, (Latest edition, PWS Pub. Co)
3. J.H. Mathews, Numerical Methods for Mathematics, (Latest Edition, Prentice Hall International)

Suggested Books

1. S. C. Chapra and R. P. Canale: Numerical Methods for Engineers, (6th edition, McGraw Hill. Sankara K. 2005)

Numerical Methods for Scientists and Engineers.(2nd ed. New  Delhi: Prentice Hall)

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50

KEY DATES AND TIME OF CLASS MEETING

Wednesday                                                                            11:00 am-12:30 pm (Regular)

Friday                                                                                    09:30 am-11:00 pm (Regular)

Tuesday                                                                                11:00 am-12:30 pm (Self-Support)

Wednesday                                                                            02:00 pm-03:30 pm (Self-Support)

Commencement of Classes                                                   October 12, 2020

Mid Term Examination                                                            December 14-18, 2020

Final Term Examination                                                          February 08-12, 2020

Declaration of Result                                                               February 19, 2020