Several Ways of Calculating the Gradient, Curl and Divergence under Orthogonal Curvilinear Coordinate Systems

Abstract

Calculating gradient, curl and divergence is very important in physics, especially in electrodynam ics and fluid mechanics. To calculate the gradient, curl and divergence under orthogonal curvilin ear coordinate systems, one must consider the Lame coefficients. Also, in many textbooks the calculation of gradient, curl and divergence under orthogonal coordinate systems are not well discussed. In this thesis the concepts such as manifold, tensors, differential forms and Lame coefficients are defined and three different ways-differential form method, covariant derivative method, and Hodge star operator method-of calculating gradient, curl and divergence are discussed. The gra dient, curl and divergence under three different orthogonal curvilinear coordinate systems are obtained.