ABSTRACT
Ordinary differential equations, or ODEs, which are equations that consist of functions of a single independent variable and their derivatives, arise in many diverse engineering problems. Several physical laws, such as those concerned with the transport of mass, momentum, and energy, are expressed in terms of differential equations. In many cases, only one independent variable, such as time or distance, exists in the problem, because of the nature of the problem or because of simpli˜cations and approximations made with respect to the other variables. Also, in a few circumstances, the functional dependence on two or more independent variables can be expressed, by suitable transformations, in terms of a single variable. Therefore, many problems of engineering interest are described by ODEs. These equations arise, for instance, in heat and mass transfer, dynamics of particles, vibrations of systems, electrical circuitry, and chemical kinetics. Although analytical methods may be employed for the solution of some ODEs, numerical techniques are generally needed for most of the equations that arise in engineering applications.
