Basics of Experience

Abstract

In this more technical chapter, the notions of space, time, and experimental evidence are introduced as the foundation on which (theoretical) physics rests. Vector and tensor algebra and analysis are discussed, including the theorems of Gauss, Stokes, and Green, and also the Christoffel symbols. Use is made of general, Cartesian, spherical, and cylindrical coordinates, but also rectilinear oblique covariant and contravariant coordinates and Euler angles. We discuss the kind of coordinate transformation properties used in differential equations in many more advanced theories. The chapter ends with error analysis, the normal (Gauss) distribution, averages, standard deviations, and error propagation.

List of Symbols

We stick closely to the recommendations of the International Union of Pure and Applied Physics (IUPAP) and the Deutsches Institut für Normung (DIN). These are listed in Symbole, Einheiten und Nomenklatur in der Physik (Physik-Verlag, Weinheim 1980) and are marked here with an asterisk. However, one and the same symbol may represent different quantities in different branches of physics. Therefore, we have to divide the list of symbols into different parts (Table 1.4).

Table 1.4 Standard notation and symbols