In our book, there is a number of chapters we are not covering.
Let me just inform you where this material fits in our curriculum.

Chapter 5 isn't too different from what we *are* covering, but is rather
an enhancement thereof. Exception: 5.4 and 5.7

Chapter 6 is an enhancement of Chapter 4 (higher order), and the way
I have been teaching Ch. 4 you won't be missing too much of Ch. 6 anyways,
except that it employs some more sophisticated language. 

Ch 8 and Ch 9 and Ch 5.4 make up most of what we are teaching in our 
second ODE course (M431), even though that course may use a different 
book. Understanding Ch.9 requires Linear Algebra in the style of our M251. 

Ch.10 constitutes a part of what you can learn in our M435 (PDEs);
not sure how much of that course, but I'd say 30% is a good guess. 
If you want more math details on the brief remarks I made, concerning
the writing of any given periodic function as an infinite sum of trigs,
then 10.3 and 10.4 are for you.