1.3 Differential Equations as Mathematical Models


In this section we introduce the notion of a mathematical model. Roughly speaking, a mathematical model is a mathematical description of something. This description could be as simple as a function. For example, Leonardo da Vinci (1452–1519) was able to deduce the speed v of a falling body by examining a sequence. Leonardo allowed water drops to fall, at equally spaced intervals of time, between two boards covered with blotting paper. When a spring mechanism was disengaged, the boards were clapped together. See FIGURE 1.3.1. By carefully examining the sequence of water blots, Leonardo discovered that the distances between consecutive drops increased in “a continuous arithmetic ...

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