Abstract
This chapter reviews some mathematical techniques such as dimensional homogeneity, abstraction and scaling, conservation and balance principles, and consequences of linearity. Modeling is a cognitive activity of thinking about and making models to describe how devices or objects of interest behave. There are many ways in which devices and behaviors can be described. Words, drawings or sketches, physical models, computer programs, or mathematical formulas can be used for this purpose. In other words, modeling activity can be done in several languages, often simultaneously. A mathematical model is a representation in mathematical terms of the behavior of real devices and objects. In the practices of science and of engineering design, models are often applied to predict what will happen in a future situation. In engineering design, however, the predictions are used in ways that have far different consequences than simply anticipating the outcome of an experiment. Various tools for modeling, such as dimensional analysis, abstraction and scaling, balance laws, and linearity are outlined in the chapter.
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