WhatIsMathematical Modeling? - Simon Fraser University

1 What Is MathematicalModeling?We begin this book with a dictionary definition of the wordmodel:model(n): a miniature representation of something; a pattern of some-thing to be made; an example for imitation or emulation; a description oranalogy used to help visualize something ( , an atom) that cannot be dir-ectly observed; a system of postulates, data and inferences presented as amathematical description of an entity or state of affairsThis definition suggests thatmodelingis an activity, acognitive activityinwhich we think about and make models to describe how devices or objectsof interest are many ways in which devices and behaviors can be can use words, drawings or sketches, physical models, computer pro-grams, or mathematical formulas. In other words, the modeling activitycan be done in several languages, often simultaneously. Since we are par-ticularly interested in using the language of mathematics to make models,34 Chapter 1 What Is Mathematical Modeling?

In that discussion we will also review the important distinction between physical dimensions that relate a (derived) quantity to fundamental physi-cal quantities and units that are numerical expressions of a quantity’s dimensions expressed in terms of a given physical standard. 1.3.2 AbstractionandScaling

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