Advanced Engineering Mathematics, 7th Edition

10.1 Theory of Linear Systems

INTRODUCTION

Recall that in Section 3.12 we illustrated how to solve systems of n linear differential equations in n unknowns of the form

(1)

where the P_ij were polynomials of various degrees in the differential operator D. In this chapter we confine our study to systems of first-order DEs that are special cases of systems that have the normal form

(2)

A system such as (2) of n first-order equations is called a first-order system.

Linear Systems

When each of the functions g₁, g₂, … , g_n in (2) is linear in the ...