This course is designed to teach the students about numerical methods and their theoretical bases for solving mathematical problems. It deals with the theory and application of numerical approximation techniques. Knowledge of calculus and linear algebra would help in learning these methods.

Pre-Requisites:

Calculus-I & Linear Algebra

Intended Learning Outcomes

Upon successful completion of this course, students should be able to

1. Develop an understanding of the core ideas and concepts of Numerical Methods.
2.   Be able to recognize the power of abstraction and generalization, and to carry out investigative mathematical work with independent judgment.
3. Be able to apply rigorous, analytic, highly numerate approach to analyze and solve problems using Numerical Methods.
4. Be able to communicate problem solutions using correct mathematical terminology and good English.

Contents

1. Computer Arithmatic; approximations and errors
2. Methods for the solutions of non-linear equations and their convergence
3. Bisection method
4. Regular Falsi method
5. Fixed point iteration method
6. Newton-Rephson method
7. Secant method; error analysis for iterative method
8. Interpolation and polynomial approximation
9. Lagrange interpolation
10. Newton's divided difference, forward difference and backward difference formulae
11. Hermite interpolation
12. Numerical integration and error estimates
13. Rectangular rule, Trapezoidal rule, Simpson's rules
14. Numerical solution of systems of algebraic linear equations
15. Gauss-elimination method
16. Matrix inversion
17. LU-factorization
18. Doolittle's Crount's, Cholesk's methods
19. Gauss-Seidal and Jacobi methods
20. Matrix norms
21. Method of least square
22. Eigenvalues and eigenvectors
23. Inclusion methods
24. Power method

Recommended Books:

1. Gerald C.F. and Wheatley P.O. Applied Numerical Analysis, Pearson Education, Singapore, 2005.

2. Burden R. L. and Faires J. D. Numerical Analysis, latest edition, PWS Pub. Co.

Suggusted Books:

1. Mathews J.H. Numerical Methods for Mathematics, latest Edition, Prentice Hall International.

2. Chapra S. C. and Canale R. P. Numerical Methods for Engineers, 6th edition, McGraw Hill.

3. Sankara K. Numerical Methods for Scientists and Engineers. 2nded. New  Delhi: Prentice Hall, 2005.

Description of system of evaluation (homework, midterms, final,  assignments etc.): 

1. Homework, Exercises, Attendance, Assignments: 20%
2. Midterm: 30%, Final Term: 50 %

Key Dates and Time of Class Meeting

Tuesday & Friday:  9:30am-11:00am 

Commencement of Classes                                                   January 13, 2020

Mid Term Examination                                                            March 09-13, 2020

Final Term Examination                                                          May 04-08, 2020

Declaration of Result                                                              May 19, 2020