Modelling with mathematica.

Abstract

In this thesis a number of mathematical models are investigated with the aid of the modelling package Mathematica. Some of the models are of a mechanical nature and some of the models are laboratories that have been constructed for the purpose of assisting researchers in a particular field. In the early sections of the thesis mechanical models are investigated. After the equations of motion for the model have been presented, Mathematica is employed to generate solutions which are then used to drive animations of the model. The frames of the animations are graphical snapshots of the model in motion. Mathematica proves to be an ideal tool for this type of modelling since it combines algebraic, numeric and graphics capabilities on one platform. In the later sections of this thesis, Mathematica laboratories are created for investigating models in two different fields. The first laboratory is a collection of routines for performing Phase-Plane analysis of planar autonomous systems of ordinary differential equations. A model of a mathematical concept called a bifurcation is investigated and an animation of this mathematical event is produced. The second laboratory is intended to help researchers in the tomography field. A standard filtered back-projection algorithm for reconstructing images from their projections is implemented. In the final section of the thesis an indication of how the tomography laboratory could be used is presented. Wavelet theory is used to construct a new filter that could be used in filtered back-projection tomography.