To illustrate the complexity of the case when the origin is

To illustrate the complexity of the case when the origin is not the only critical point of a linear system, consider the system

Solution

You will not finda “suggested syl-labus” in this preface; we will not pretend to be so wise as to tell other teachers what toteach. We feel that there is plenty of material here to pick from and to form a course toyour liking. The textbook strikes a reasonable balance between the analytical, qualita-tive, and quantitative approaches to the study of differential equations. As far as our “underlying philosophy” it is this: An undergraduate textbook should be written withthe student’s understanding kept firmlyin mind, which means to me that the materialshould be presented in a straightforward, readable, and helpful manner, while keepingthe level of theory consistent with the notion of a “first course.For those who are familiar with the previous editions, we would like to mentiona few of the improvements made in this edition.•Eight new projects appear at the beginning of the book. Each project includesa related problem set, and a correlation of the project material with a chapter in the text.•Many exercise sets have been updated by the addition of new problems to better test and challenge the students. In like manner, some exercise sets have been improved by sending some problems into retirement.•Additional examples and figures have been added to many sections•Several instructors took the time to e-mail us expressing their concernsabout our approach to linear first-orderdifferential equations. In response,Section2.3, Linear Equations, has been rewritten with the intent to simplifythe discussion.•This edition contains a new section on Green’s functions in Chapter 4 for thosewho have extra time in their course to consider this elegant application of variation of parameters in the solution of initial-value and boundary-value prob-lems. Section 4.8 is optional and its content does not impact any other section.•Section 5.1 now includes a discussion on how to use both trigonometricformsin describing simple harmonic motion.•At the request of users of the previous editions, a new section on the reviewof power series has been added to Chapter 6. Moreover, much of this chapter has been rewritten to improve clarity. In particular, the discussion of themodifiedBessel functions and the spherical Bessel functions in Section 6.4has been greatly expanded.