Browsing by Author "Brew, Lewis"

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    Applications of integral equations to boundary value problems and their applicability to local musical instruments.
    (2009-08-19) Brew, Lewis
    This thesis is designed to provide the application of integral equations to boundary value problems and their application to local musical instruments. In this work we demonstrated the methods of converting boundary and initial value problems of ordinary differential equations into Fredholm integral equations and Voltera integral equations respectively. The stringed instruments provided the solutions in the form of integral representations of the product of two functions whilst the membranes solutions manifested as the integral representations of the product of the three functions. Although the solutions of the boundary and initial values may be readily obtained, the thesis only dealt with the representation of the solutions in integral form. The solutions of the integral representations is the solution of the boundary and initial value problems of the wave equation that provided practical insight into Bessel functions and their impact on the local drums.