ABSTRACT
The singular concept which characterizes calculus and simultaneously sets it apart from arithmetic, algebra, geometry, and trigonometry is the notion of a limit. Calculus, as presently taught, begins with differential calculus, continues with the consideration of integral calculus, and then analyzes the relationship between the two. Historically, however, integral calculus was developed much earlier than differential calculus. Until approximately the middle of the seventeenth century, integral and differential calculus appeared to be two distinct branches of mathematics. Until the beginning of the nineteenth century, the central theme of differential equations was to find the general solution of a specified equation or class of equations. There are two fundamental subdivisions in the study of differential equations: quantitative theory and qualitative theory. Early in the development of the subject of differential equations, it was thought that elementary functions were sufficient for representing the solutions of differential equations.
