Numerical Analysis

Syllabus:
- Solutions of equations in one variable: Bisection algorithm. Method of false position. Fixed point iteration, Newton-Raphson method, Error Analysis iteration for iterative method, Accelerating limit of convergence.
- Interpolation and polynomial approximation: Taylor polynomial, interpolation and Lagrange polynomial. Iterated Interpolation. Extrapolation.
- Differentiation and Integration: Numerical differentiation. Richardson’s extrapolation. Elements of Numerical integration. Adaptive quadrature method, Romberg’s integration, Gaussian quadrature. Solutions of linear system, pivoting strategies, L U decomposition method.


Course Objective: This course is designed to achieve the following objectives -
- The objectives of studying this module are to make the students familiarise with the ways of solving complicated mathematical problems numerically.
- To help you become familiar with MATLAB and other convenient numerical software such as Microsoft Excel and with simple programming.
- Obtaining numerical solutions to problems of mathematics.
- Describing and understanding of the several errors and approximations in numerical methods.
- The understanding of several available Solutions of Equations in One Variable.
- The explanation and understanding of the several available methods to Solve the simultaneous equations.
- The study of Curve Fitting and Interpolation.


Learning Outcomes: By the end of this course the students must learn the following -
- Analyse a problem and identify the computing requirements appropriate for its solution.
- The students should be familiarized with the ways of solving complicated mathematical problems numerically.
- The students can use MATLAB and other convenient numerical software such as Microsoft Excel to solve and analyse different mathematical problems.
- The students will be able to analyse and solve several errors and approximations in numerical methods.
- The students will be able to apply several methods to solve the Equations in One Variable.
- The students will be able to apply several methods to solve the simultaneous equations.
- The students will be able to apply several methods to solve Curve Fitting and Interpolation questions and its related techniques.