ABSTRACT
This chapter considers a variety of models, concepts, and techniques that give the reader some of the basic tools needed in solving and analyzing first-order differential equations (ODE). It introduces slope fields. Slope fields provided a qualitative view of solutions of first-order differential equations. Slope fields provide information about rates of change since they are derived from information given by the derivative. Interpreting the derivative as the slope of the line tangent to the graph of the function is useful in gaining information about the solution to the differential equation. From this information, it is possible to sketch qualitatively the solution curves to the equations from any real initial condition. The chapter illustrates the commands to both solve an ODE and to plot an ODE using Maple. Euler’s method takes a step along the tangent line to predict a new point.
