#### Objective

#### Content

This course provides a fundamental introduction to numerical analysis suitable for undergraduate students in Physics / Electronics, and engineering. It is assumed that the reader is familiar with calculus and has taken a structured programming course. MatLab programs are the vehicle for presenting the underlying numerical algorithms.
COURSE DESCRIPTION
Ch. 1 : Number representation (4H)
Binary system
Octal system
Converting between systems
Applications
Ch. 2: Solutions of Equations in one variable f(x) =0 (8H)
Bracketing Methods for locating a Root
Initial Approximation and Convergence Criteria
The Bisection Algorithm
Fixed-Point iteration
Newton-Raphson Method
Lagrange Method
Method of False Position (or Regular Falsi)
Ch 3: Interpolation and polynomial Approximation (6 H)
Introduction to interpolation
Lagrange Approximation
Newton Polynomials
Aitken algorithm
La formule Barycentrique
Error Analysis
Ch 4: Numerical Integration (6 H)
Introduction to Quadrature
The Rectangle Rule
TheTrapezoidal Rule
Gauss-Legendre integration
The Simpson’s Rule
Errors of Integration
Applications
Ch 5: Approximation Theory (6 H)
Introduction
Discrete Least-Squares Approximation
Orthogonal Polynomials and Least-Squares Approximation
Rational function and Approximation
Trigonometric Polynomial Approximation
Spline interpolation
Curve Fitting
Applications
Ch 6: Solution of Differential Equations (6 H)
Introduction to Differential Equations
Elementary Theory of Initial-value problem
Euler’s Method
Higher-order Taylor Methods
Runge-Kutta method
Applications
Ch 7: Solution of Linear Systems A.X = B (8 H)
Introduction to vector and Matrix
Upper (Lower) triangular Systems
Gaussian Elimination and Pivoting
Triangular Factorization (L.U, L.LT)
Gauss-Jordan Method
Gauss-Siedel (iterative Method)
Ch. 8 : Lab Work: Matlab (4 H)
Introduction to MatLab
Solutions of Equations in one variable f(x) =0
Numerical Integration
Solution of Differential Equations
Approximations and errors