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

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

**Contents**

- Computer Arithmatic; approximations and errors
- Methods for the solutions of non-linear equations and their convergence
- Bisection method
- Regular Falsi method
- Fixed point iteration method
- Newton-Rephson method
- Secant method; error analysis for iterative method
- Interpolation and polynomial approximation
- Lagrange interpolation
- Newton's divided difference, forward difference and backward difference formulae
- Hermite interpolation
- Numerical integration and error estimates
- Rectangular rule, Trapezoidal rule, Simpson's rules
- Numerical solution of systems of algebraic linear equations
- Gauss-elimination method
- Matrix inversion
- LU-factorization
- Doolittle's Crount's, Cholesk's methods
- Gauss-Seidal and Jacobi methods
- Matrix norms
- Method of least square
- Eigenvalues and eigenvectors
- Inclusion methods
- 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.): **

- Homework, Exercises, Attendance, Assignments: 20%
- Midterm: 30%, Final Term: 50 %

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