Appendix A

This appendix anticipates the discussion of the Extended Linearity Principle in Section 4.1. If time permits, we recommend covering this material right after Section 1.8. If this appendix is used as a replacement for Section 1.8, make sure that the students are familiar with the terminology introduced on page 113.

Comments on selected exercises

Exercises 1-8 provide routine practice of the method.

Exercises 11-16 illustrate how do deal with forcing functions that are sums of the elementary examples.

Exercises 17-20 are qualitative in nature. In fact, they are a little tricky. If you assign them, you may want to hint to your students that they should visualize the slope fields.

Many instructors like to discuss power series in this course. We talk about linearization in Section 5.1, but we do not include the typical power series techniques that occupy a significant portion of the traditional course. The last three exercises in this appendix hint at the basic idea of power series solutions, and they give the students a little practice with the technique.

Appendix B

This appendix is not intended to teach students about the arithmetic of complex numbers, but it does summarize the basic properties that we use, especially in Chapters 3 and 4. There is a power series derivation of Euler's formula and a brief mention of the polar representation of a complex number. Both of these ideas play important roles in Sections 3.4, 4.2, 4.3, and 4.4.