7: Systems of Equations
Systems of coupled linear differential equations can result, for example, from linear stability analyses of nonlinear equations, and from normal mode analyses of coupled oscillators. We will first consider the simplest case of a system of two coupled homogeneous linear first-order equations with constant coefficients. These two first-order equations are in fact equivalent to a single second-order equation, and the methods of Chapter 4 could be used for solution. Nevertheless, viewing the problem as a system of first-order equations introduces the important concept of the phase space, and can easily be generalized to higher-order linear systems. We will then discuss the physical problem of two coupled oscillators.