Applications to linear differential equations

Abstract

Differential equations have played an important part in the development of mathematics since the time of Newton. They have also been central to many applications of mathematics to the physical sciences and technology. Often the equations relevant to practical applications are so difficult to solve explicitly that they can only be handled with approximation techniques on large computer systems. In this chapter we will be concerned with a simple form of differential equation, and systems thereof, namely, linear differential equations with constant coefficients. These systems have a great deal in common with systems of linear equations, and we are in a position to apply the hard-won knowledge about Jordan canonical forms to solve such systems. We begin with a short excursion into the subject of differential equations.