ABSTRACT
In Chapter 2 we considered differential equations with only time or a time-like (initial value) independent variable. Thus we considered ODEs. In analyzing many physical systems, however, we must consider how the state variables or dependent variable(s) vary with both time and one or more spatial variables. Thus, we have at least two dependent variables to consider which naturally leads to PDEs. In this chapter, we consider PDEs in which time (or the initial value variable) appears only in first-order derivatives. To illustrate how such PDEs occur in applications, we consider a series of examples, starting with a one dimensional heat transfer system.
