This textbook develops a coherent view of differential equations by
progressing through a series of typical examples in science and
engineering that arise as mathematical models. All steps of the
modeling process are covered: formulation of a mathematical model;
the development and use of mathematical concepts that lead to
constructive solutions; validation of the solutions; and
consideration of the consequences. The volume engages students in
thinking mathematically, while emphasizing the power and relevance
of mathematics in science and engineering. There are just a few
guidelines that bring coherence to the construction of solutions as
the book progresses through ordinary to partial differential
equations using examples from mixing, electric circuits, chemical
reactions and transport processes, among others. The development of
differential equations as mathematical models and the construction
of their solution is placed center stage in this volume.
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