Appendixes

Abstract

Definitions and formulae used at various points in the text to manipulate vectors are listed below. Additional useful formulae, including geometrical and physical interpretations complementary to those provided in this text, can be found in standard texts on vector analysis and in mathematical handbooks. The Standard Mathematical Tables published by CRC Press (Boca Raton, Florida) is a particularly handy resource, and most college-level calculus texts cover introductory vector analysis as part of the material intended for a third-semester course. Appendix A in Bird, Stewart, and Lightfoot (1960) is a very good summary of vector and tensor notation presented in the context of fluid mechanics. Section 17.1.1 begins with several basic definitions of vector quantities that generally apply to any orthogonal coordinate system. The notation for unit vectors in Cartesian coordinates, i, j, and k, are used in this section, but it is understood that this notation may be directly replaced with symbols for unit vectors associated with other orthogonal coordinates. Section 17.1.2 then covers differential operations for Cartesian coordinates. Although the notation used for these differential operations in Cartesian coordinates is the same as that for other coordinate systems, the actual operations connoted by the notation are different, and must be defined separately (Appendix 17.2). Let S and T denote scalar functions, and let U, V, and W denote vectors. If U = 〈U1, U2, U3〉, then . . . U = U1i + U2j + U3k . . . . . . (17.1) . . .