First Order Ordinary
Differential Equations
Numerical Methods
Differential equations do not always have solutions which you can obtained using analytical methods. In fact, the majority of real world problems you will encountered, are next to impossible to solve this way. This does not, however, stop you the scientist or mathemathician from attacking these problems.
In this section, some elementary methods of approximation are introduced which you can use to study ODE's. All of these methods are based on the simple fact that a differential equation gives you direct information about the slope of the solution at any given point in the Cartesian plane.
Numerical methods, until recently, have been used primarily as an aid in helping students understand the concepts behind the subject of differential equations. That is until the advent of the computer. Because of the power and wide spread availability of computers, numerical solutions to differential equations have taken on a much larger importance.
The purpose of this section is not to provide you with a complete discussion of these methods, for there are whole books on the subject that can do that for you. The section introduces the subject and its link to what you have studied thus far and, hopefully, provides motivation for further study.
