Author Description

Most of the physics text and university physics and engineering courses require the use of the del, Gradient of a scalar field, Laplacian, Divergence of a vector and Curl of a vector formulas. This book was prepared with the intention to guide students who find themselves interested in deriving the frequently used del, Gradient of a scalar field, Laplacian, Divergence of a vector and Curl of a vector using traditional approaches and tensor notations. These equations are usually just listed out by the instructors or authors in most physics texts without any mathematical discussion of their origin. From the experience of teaching undergraduates Physics courses, such as special theory of relativity, general theory of relativity and classical electrodynamics, it is the author's wish that this short manuscript could plug the gap and answer the questions of how do these del, Gradient, Divergence, Laplacian, and Curl equations in various three-dimension curvilinear coordinates system come about. In summary, students will gain confident and mathematical skills set to work on other new materials without the trials and errors approaches. The book is intended to help self-starters to pick up and learn the crucial mathematical skill using only papers and pencil method. If time is "of the essence" for any physics students to learn fundamental tensor in the undergraduate level as well as a fresher course for graduate students, they are advised to jump straight pass the Lorentz transformation in the beginning of the text. The text begins with the discussion to introduce the basic theory of tensor, its notation, and tensor shorthand. Traditional derivation method of all the del equations are presented first as a comparison to the tensor derivation with Kronecker delta function, Levi-Civita symbols, Christoffel symbols approaches that come after it. Simple orthogonal Cartesian coordinate del, Gradient, Divergence, Laplacian, and Curl equations are derived