Key Changes from the Preliminary Edition
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We streamlined examples and exposition, making the book easier to
teach and learn from. The development of standard techniques has been condensed
while comparisons between nonlinear and linear equations, autonomous and
nonautonomous have been expanded. We put additional emphasis on the interplay
between first order systems and second order equations and treated
spring-mass systems, pendulums, and electric circuits in a parallel fashion.
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We added new material on nonlinearity, chaos, and qualitative reasoning and
included many more interesting and realistic examples and exercises.
More emphasis was placed on having students understand the reason for each
step in the development as well as their importance and usefulness. Some of
this occurs under the new heading "Where We Are Going—And Why" at the
start of each chapter, where we explain why the subject of the chapter is
important.
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We added pedagogical devices to promote clarity, understanding, ease of use
and importance of ideas. For example, we:
- included more mathematical models where obtaining an explicit
solution is not possible (or, if it is possible, gives a solution
which is impossible to graph directly) yet the solution behavior is
easy to determine by graphical techniques.
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moved many tables and figures into the margin to make the book much
more readable.
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rearranged exercises so similar ones are together.
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put "key words'' in the margin to help students keep the strategies
in mind and added "subheadings'' for the same reason.
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included the answers to most odd-numbered problems.
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