Browsing by Author "Jugoo, Vikash Ramanand."

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Computer analysis of equations using Mathematica.
(2001) Jugoo, Vikash Ramanand.; Govinder, Keshlan Sathasiva.; Maharaj, Sunil Dutt.
In this thesis we analyse particular differential equations that arise in physical situations. This is achieved with the aid of the computer software package called Mathematica. We first describe the basic features of Mathematica highlighting its capabilities in performing calculations in mathematics. Then we consider a first order Newtonian equation representing the trajectory of a particle around a spherical object. Mathematica is used to solve the Newtonian equation both analytically and numerically. Graphical plots of the trajectories of the planetary bodies Mercury, Earth and Jupiter are presented. We attempt a similar analysis for the corresponding relativistic equation governing the orbits of gravitational objects. Only numerical results are possible in this case. We also perform a perturbative analysis of the relativistic equation and determine the amount of perihelion shift. The second equation considered is the Emden-Fowler equation of order two which arises in many physical problems, including certain inhomogeneous cosmological applications. The analytical features of this equation are investigated using Mathematica and the Lie analysis of differential equations. Different cases of the related autonomous form of the Emden-Fowler equation are investigated and graphically represented. Thereafter, we generate a number of profiles of the energy density and the pressure for a particular solution which demonstrates that a numerical approach for studying inhomogeneity, in cosmological models in general relativity, is feasible.
Exploring higher education engagement in computer programming within a blended learning environment : an action research approach
(2014) Jugoo, Vikash Ramanand.; Mudaly, Vimolan.
Many novice programmers in higher education find computer programming particularly difficult due to its problem solving nature. High dropout rates have been observed both internationally and locally, but in South Africa, the circumstances of students coming from disadvantaged schools where they struggle in subjects like Mathematics and Science, especially compounds their challenges in computer programming when they enrol at a tertiary institute. In this study, I explore the engagement of computer programming at a higher education institution using an innovative approach of incorporating tools in the form of online learning and support structures to supplement the existing face-to-face and practical lessons thereby creating a blended learning environment (BLE). This study, which is a qualitative one, used an interpretivist paradigm to explore the engagement of sixty, first year students in an introductory computer-programming course at a selected university in South Africa, using an action research approach within the context of a BLE. Action research refers to an evaluation of one’s own practice with a view to improving one’s effectiveness, in this case, analysing my own efficacy as a teacher, and the learning that occurred by my students (McNiff, 2013; Whitehead, 1989). This study used two lenses: The first lens was my own as a lecturer/researcher who developed a variety of support structures in the form of notes, videos, animations, and blogging, to support student engagement in computer programming, and the second lens was the students’ engagement with these tools. The study explored this dual engagement and asked two critical questions: 1) How does engagement of computer programming take place within a BL context using an action research approach, and, 2) Why does engagement of computer programming take place within a BL context using an action research approach, in the way it does? A dual form of engagement occurred creating a dynamic BLE. In the study, students were exposed to one theory classroom lesson, and three practical lessons. As the lecturer, I received feedback from the students which informed my attempts to improve the environment. Observations, a personal diary, electronic questionnaires, and focus group meetings were used to gather feedback on how students engaged in the BLE. The action research methodology was based on planning, acting, observing and reflecting. The analysis of the reflections was used in the re-planning phase of the next cycle and a total of three cycles were used. Although there were three main action research cycles, each tool was transformed resulting in smaller cycles emanating within the main action research cycle. Activity Theory was used as a theoretical framework to describe and analyse the actions and engagement that transpired within the BLE. The results from this study highlight positive student engagement in learning through the use of examples and visual tools although the use of language was found to be a barrier under certain circumstance. Support and planning were also identified as important factors for both student and lecture engagement. Other aspects concerning feedback and reflection were established as important during the dual engagement employed resulting in the creation of a dynamic action research model of engagement.