A Software Tool for Analytical Solutions of Laplace's Equation

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A software tool which presents analytical solutions of Laplace's equation offers several advantages over numerical techniques. Students in many areas of engineering and physics will benefit from the opportunity to study parametric dependence of the solutions. Aspects of potential theory that are difficult for numerical techniques, such as highly curved surfaces and derivative variables, are simple for analytical methods, so both analysis and design of new structures and devices will become more accurate. The principal obstacles to the use of analytical solutions have been the difficulty of matching the shape to a solution, and the need to perform a large number of tedious symbolic calculations using algebra and calculus. These difficulties are overcome in the proposed work by implementing an interface which guides the user through a sequence of graphical menus leading to the desired solution in a variety of formats, including, graphs, computer subprograms, and word processing elements. Phase I of the project is devoted to working out the techniques which will enable the solutions of Laplace's equation to be generated using a computer based symbolic mathematics package (Mathematica), and to testing a minimal version of the program for the suitability of the interface for Junior level engineering students.