TABLE OF CONTENTS A number of mathematical operations and functions, as well as their associated properties, are applied repeatedly throughout this review. For this reason, these operations are collected in this chapter and are briefly outlined for the convenience and ease of reference later. This chapter is not intended to serve as a treatise for defining these mathematical operations and functions. For a more thorough treatment of these topics, the references identified with each operation, function or property should be consulted.
A number of symbols and functions frequently encountered in coastal and ocean engineering are summarized below.
It is often necessary to estimate the relative magnitude of terms. For example, approximating a function f(x) by an asymptotic series and then estimating the error associated with truncating the expansion at the nth term in the series. The residual of the nth term in an asymptotic series for a function f(x) as the independent variable x ? c is usually given in terms of the Landau symbols O( ?) and o( ?) that are commonly referred to as Big O and small o, respectively.
Order Big O( ?) If an asymptotic series for the function f(x) is approximated by
and if there exists a positive-definite number 0< A<+ ?, say, that is...
