ABSTRACT
All readers should at least skim through the chapter to become familiar with the notation that the people use. The notation is standard, for the most part. Readers who are familiar with the topics in the chapter can move on quickly to later chapters, perhaps never needing to refer back. There are several equivalent ways to define closed sets and compact sets in Euclidean spaces. The authors use standard matrix notation and assume the reader is familiar with the elements of matrix algebra, determinants, and linear algebra as they commonly occur in a first course in differential equations or earlier. Linear dependence and linear independence can be thought of informally as distinguishing when a set of vectors contains redundant information from when it does not. Linear integral operators which transform input functions into output functions by integration are continuous analogues of matrix operators.
