The authors show how differential equations model physical phenomena and how the study of this topic has meaningful scientific and real-world value. They examine themes such as error analysis and predictability many times throughout the text. It is organized by important phenomena instead of techniques. Rote solution methods are de-emphasized, and the study of nonlinearity is introduced and compared with linear systems. Original multi-stepped problems may be used as traditional homework exercises, group projects, or lab worksheets. Work with technology is included but the text is not keyed to any specific program or tool.

Fundamental Ideas, Exponential Growth, Fundamental Theory, Linearity, Oscillatory Motion, The Geometry of Systems of Differential Equations, The Analysis of Linear Systems, Nonlinear Differential Equations, Numerical Methods, The Laplace Transform

For all readers interested in introductory differential equations.