In this chapter, we introduce these three points of view by considering differential equations of the form dy/dx=g(x). We start with a brief introduction, definitions, and examples, which make use of prior knowledge of antiderivatives. Then we spend the next two sections illustrating graphical techniques, including slope fields and isoclines. These techniques often let us discover many properties of the solution of a specific differential equation by simply analyzing the differential equation from a graphical point of view. We end this chapter with a discussion of Taylor series, which are especially useful when solutions are given by integrals that do not have simple antiderivatives.

The purpose of this chapter is to illustrate graphical, numerical, and analytical approaches in the familiar setting of antiderivatives. We want to make sure you have a firm foundation in these approaches so you can quickly grasp the new ideas in subsequent chapters.