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ABSTRACT
Mathematics is frequently discussded in the cartesian coordinate system, but this has its downfalls. In most cases, it does not represents its curved shape of the physical world. Guass saw the need for several coordinate system that would allow one to explore the properties of the curved surfaces. It's only then that the curvilinear coordinate system was born. With Riemann's insight, it grew to represent infinite space, and curvilinear coordinates were utilized in physical applications. Orthogonal curvilinear coordinates, in particular, were used in serving selected partial differential equations, including the Laplace and Helmholtz. The focus of the study was restricted to the derivation and application of orthogonal three-dimensional coordinates system.
