ABSTRACT
This chapter introduces the qualitative theory of ordinary differential equations when properties of solutions can be determined without actually solving equations explicitly or implicitly. It considers an electric circuit consisting of a capacitor, a resistor, and an inductor, in series. Nonlinear differential equations and systems of simultaneous nonlinear differential equations have been encountered in many applications. It is often difficult to solve a given nonlinear differential equation or system of equations. This is not simply because ingenuity fails, but because the repertory of standard functions in terms of which solutions may be expressed is too limited to accommodate the variety of solutions to differential equations encountered in practice. Even if a solution can be found, its expression is often too complicated to display clearly the principal features of the solution. The points where the nullclines cross are precisely the critical points.
