Course Serial:

BS300

Title:

Numerical Analysis

Credits Hrs:

3 (2+ 1)

Pre-requisite:

Nil

Text Books:

1.     “Numerical methods for Engineers”, by Steven. C. Chapra/Raymond P. Canale.

2.      “Numerical Analysis”, by Dr. S.A Bhatti.

3.      “Applied Numerical Analysis”, by Gerald/Wheatley.

Reference Books:

1. “Numerical Mathematics”, by Jerome C.R Li.

2. “Computer Applications of Numerical Methods”, by Kuo.

Goals/Objectives:

The main aim of this course is to provide students with the adequate understanding of numerical methods that must be useful in solving various practical engineering related problems.    

Topics of the Course:

Basic Introductory Concepts: Mathematical Modelling, Approximation and errors, Error Definitions (Round-off error, Truncation Error, Error Propagation, Total Numerical Error). Taylor Series.

 

Roots (Zeros) of Equation:

Bracketing Methods: Graphical Methods, Bisection method, False Position Method, Quasi Linearization,

Open Methods: Simple One-point Iteration technique, The Newton-Raphson Method, The Secant Method, Systems of Nonlinear equations.

 

Systems of Linear Algebraic Equations: Guass Elimination technique (Linear Equations, Non-linear Equations, Complex Systems), Error Analysis and System Condition, iterative Techniques (Guass Siedel Technique, Jacobi method, System Over Relaxation (SOR)), Inversion of Matrix using Guass Elimination/Guass-Siedel Techniques. Matrix factorization (LU-decomposition, Crout Decomposition), Banded System.

 

Curve Fitting: Least Squares Regression: Linear regression, Polynomial regression, Multiple linear regression, Nonlinear regression,

Interpolation Methods: Newton’s Divided Difference interpolating polynomials, Lagrange Interpolation and Spline Interpolation.

 

Numerical Differentiation and Integration:

Numerical methods for Integrations: Trapezoidal Rule, Simpson’s Rule, and Integration with unequal segments.

Differentiation Numerical Methods: Richardson’s Extrapolation.

 

Ordinary Differential Equations: Numerical Solution of 1st and 2nd order ODE, Euler’s method, Runge-Kutta Method (Simple and Adaptive step size control).