A FINITE DIFFERENCES SOLUTION TO THE VIBRATING MEMBRANE PROBLEM

Abstract A realistic approach to the solution of mechanical systems containing multiple parameters must take into account the fact that dependent variables depend not only on, but on more space variables. The modelling of such problems leads to partial differential equations (P.D.Es), rather than Ordinary Differential Equations (O.D.Es). Here, the wave equation, a P.D E that governs the vibrating membrane problem is considered. A finite difference method (F.D.M) is provided as an alternative to the analytic methods. F.D.Ms  basically involve three steps; dividing the solution into grids of nodes, approximating the given differential equation by finite difference equivalences that relate the solutions to grid points and solving the difference equations subject to the prescribed boundary and/or initial conditions. It is shown here that the error in the result is relatively negligible, and the conclusion made that the method developed can further be used to solve certain non-linear P.D.Es. Key words; Wave Equation, Vibrating membrane, Fouling, Analytic solution, Numerical solution, Local truncation Error, Stabilit

Factors Inhibiting Acquisition of Mathematical Knowledge in Kenyan Institutions of Higher Learning

Kenya is a developing country which has done fairly well in terms of development. However it has developed a strategy called vision 2030 which will see it get more developed. Before this is achieved a lot has to be done in training the personnel in all areas. One important area that requires a lot of attention is level of mathematical knowledge in Kenya. Mathematics is fundamental to change in all aspects of development. In our paper we identify some factors which inhibit performance in mathematics at the Kenyan institutions of higher learning especially at the universities. Key words: Mathematical Knowledge, Kenyan institutions of higher learning