Numerical Methods

Abstract

<p><b>First Learning Activity: Types and Causes of Errors</b></p> <p>The first learning activity aims at making the learner appreciate the need for numerical methods. It is also felt that this is the right moment to define the concept of a mathematical error, point out the sources and types of errors and mention some practical ways of reducing their cumulative effect on the numerical solution.</p>

<p><b>Second Learning Activity: Interpolation</b></p> <p>The second learning activity deals with the concept of interpolation. Both linear and higher order polynomial interpolation methods, based on Lagrange, Newton’s divided differences and finite difference interpolation techniques are presented.</p>

<p><b>Third Learning Activity: Numerical Integration</b></p> <p>The third learning activity looks at the problem of numerical integration. The discussion is limited to Newton-Cotes formulae. Specific attention is given to the Trapezoidal and Simpson’s rules and the application of Richardson’s extrapolation technique on both the Trapezoidal and Simpson’s rules in deriving Romberg integration schemes. </p> <p><b>Fourth Learning Activity: Roots of functions</b></p> <p>The fourth and final learning activity presents the root finding problem associated with solving the nonlinear equation and solving the coupled system of two nonlinear equations. </p> <p> <b>In addition to downloading the files below, you can also view them directly:</b> </p> <ul> <li><a href="http://www.scribd.com/doc/44852485/Numerical-Methods" target="_blank" >The full module (Scribd)</a></li> <li><a href="http://www.youtube.com/watch?v=RARHCsQLbmg" target="_blank" >Intro to module (YouTube)</a></li> <li><a href="http://www.youtube.com/watch?v=hvCAYryFxoI" target="_blank" >Overview of module (YouTube)</a></li> </ul>