Key Changes from the Preliminary Edition

  • 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.
  • 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.
  • 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.
    • moved many tables and figures into the margin to make the book much more readable.
    • rearranged exercises so similar ones are together.
    • put "key words'' in the margin to help students keep the strategies in mind and added "subheadings'' for the same reason.
    • included the answers to most odd-numbered problems.

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