This textbook develops a coherent view of differential equations by progressingthrough a series of typical examples in science and engineering that arise asmathematical models. All steps of the modeling process are covered: formulationof a mathematical model; the development and use of mathematical concepts that lead to construct 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 solutions are places center stage in this volume