Vector Algebra and Analysis in Curvilinear Coordinates

Abstract

In this chapter we derive and compile some fundamental relations concerning the 3-D vector algebra and calculus in curvilinear coordinates. More detailed treatments (containing additional material which is less important for our needs) can be found in standard works on vectors and tensors such as Borisenko and Tarapov (1968), Wrede (1963), and Spiegel (1959). Classic textbooks on mathematical physics such as Morse and Feshbach (1953), Margenau and Murphy (1976), Mathews and Walker (1970) and Butkov (1968), contain some instructive chapters on the subject matter. Also worth mentioning are the treatments in well-known physics and engineering books such as Symon (1971, Mechanics), Stratton (1941, Electromagnetic Theory), Milne-Thomson (1968, Hydrodynamics) and Bird, Stewart and Lightfoot (1960, Transport Phenomena).