Mathematical Appendix

TL;DR: The book assumes familiarity with basic linear algebra and introduces notation and techniques for vectors and functions. It defines vector components, zero vector, and spatial vectors.

Abstract: The book assumes a familiarity with basic methods of linear algebra, differential equations, and probability theory, as covered in standard texts. This chapter describes the notation we use and briefly sketches highlights of various techniques. The references provide further information. An operation O on a quantity z is called linear if, applied to any two instances z 1 and z 2 , O(z 1 + z 2) = O(z 1) + O(z 2). In this section, we consider linear operator linear operations on vectors and functions. We define a vector v as an ar-vector v ray of N numbers which are called its components. These are sometimes listed in a single N-row column v = When necessary, we write component a of v as [v] a =v a. We use 0 0 0 to denote zero vector 0 0 0 the vector with all its components equal to zero. Spatial vectors, which are related to displacements in space, are a special case, and we donate them by v with components v x and v y in two-dimensional space or v x , v y , and spatial vector v v z in three-dimensional space.