Mathebula, Agreement2018-01-042018-01-042017Mathebula, Agreement (2017) Symmetry analysis and invariant properties of some partial differential equations, University of the Witwatersrand, Johannesburg, <http://hdl.handle.net/10539/23609>http://hdl.handle.net/10539/23609A dissertation submitted to the Faculty of Science, University of the Witwatersrand, in requirement for the degree Master of Science, January 2017.This dissertation contains evolutionary partial differential equations (PDEs). The PDEs are used to investigate ecological phenomena. The main goal is to determine Lie point symmetries, perform Lie reduction, obtain analytical solutions and visualize the solutions in 3D plots using the help of Mathematica. Drift diffusion, biased diffusion and the Kierstead, Slobodkin and Skellam (KiSS) models arising in population ecology are discussed. The importance of these PDEs in ecology is to analyse the movements of organisms and their long-term existence especially in heterogeneous environments.Online resource (47 leaves)enDifferential equations, PartialThesis