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. / Thesis (Ph.D.)-University of Natal, Durban, 1994.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/5052 |
| Date | January 1994 |
| Creators | Murrell, Hugh. |
| Contributors | Sartori-Angus, Alan G. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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