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kreyszig °ø¾÷¼öÇÐ 9ÆÇ ¿¬½À¹®Á¦Ç®ÀÌ(4Àå.¦¼ö)

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º»¹®³»¿ë CHAPTER 4 Systems of ODEs. Phase Plane.
Qualitative Methods
Major Changes
This chapter was completely rewritten in the previous edition, on the basis of suggestions
by instructors who have taught from it and my own recent experience. The main reason
for rewriting was the increasing emphasis on linear algebra in our standard curricula, so
that we can expect that students taking material from Chap. 4 have at least some working
knowledge of 2  2 matrices.
Accordingly, Chap. 4 makes modest use of 2 2 matrices. nn matrices are mentioned
only in passing and are immediately followed by illustrative examples of systems of two
ODEs in two unknown functions, involving 2  2 matrices only. Section 4.2 and the
beginning of Sec. 4.3 are intended to give the student the impression that for first-order
systems, one can develop a theory that is conceptually and structurally similar to that in
Chap. 2 for a single ODE. Hence if the instructor feels that the class may be disturbed by
n  n matrices, omission of the latter and explanation of the material in terms of two
ODEs in two unknown functions will entail no disadvantage and will leave no gaps of
understanding or skill.
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