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º»¹®³»¿ë CHAPTER 3 Higher Order Linear ODEs
This chapter is new. Its material is a rearranged and somewhat extended version of material
previously contained in some of the sections of Chap 2. The rearrangement is such that
the presentation parallels that in Chap. 2 for second-order ODEs, to facilitate comparisons.
Root Finding
For higher order ODEs you may need Newton¡¯s method or some other method from
Sec. 19.2 (which is independent of other sections in numerics) in work on a calculator
or with your CAS (which may give you a root-finding method directly).
Linear Algebra
The typical student may have taken an elementary linear algebra course simultaneously
with a course on calculus and will know much more than is needed in Chaps. 2 and 3.
Thus Chaps. 7 and 8 need not be taken before Chap. 3.
In particular, although the Wronskian becomes useful in Chap. 3 (whereas for n  2
one hardly needs it), a very modest knowledge of determinants will suffice. (For n  2
and 3, determinants are treated in a reference section, Sec. 7.6.)
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