chapter  2
24 Pages

Linear Equations

ByR. Grimshaw

Although this text is largely concerned with nonlinear equations, we shall find it necessary to have at our disposal some key results for linear equations, and these form the subject matter of this chapter. The first-order system (2.2) is said to be a linear system whenever f(x,t) is a linear function of x. Thus the general form for a first-order linear system is () x ′ = A ( t ) x + g ( t ) ,