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By Walter J. Meyer
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Extra info for Concepts of Mathematical Modeling
Figure 4 Example 5 Figure 5 shows a schematic diagram of the human eye, which is meant to illustrate how the eye muscles move the eyeball around in its socket. Two of the muscles are shown as shaded areas. Within these shaded areas are springs and dashpots (shock absorbers). Naturally the eye muscles don’t really have springs or shock absorbers inside them. These mechanisms are used to represent, or to model, the muscle. Presumably the authors did this because the average person is familiar with springs and shock absorbers and how they work, and this familiarity will help people understand how the eye muscles work.
By covering sections out of order, an instructor can easily replace my organization of the material with a more mathematical organization. For example, a substantial part of a course could be devoted to applications of difference and differential equations by starting with the long Section 2 in Chapter 5 and adding to it Sections 3 and 4 of Chapter 1 and Section 5 of Chapter 3. Likewise, a course segment on probabilistic models could use the long Section 3 of Chapter 5, together with Section 6 of Chapter 1, Section 2 of Chapter 2, and Section 1 of Chapter 5.
In other words, its acceleration is a constant value of 32 feet/ second. This is true no matter what the weight of the object is. The italicized phrases are escape clauses, and we shall soon see their significance. We can express Galileo’s assumption with any one of the following equivalent equations: (1) (2) (3) where v(0) denotes the initial velocity. Example 1 A golf ball is at rest at t = 0 and dropped to the earth at that instant. 5 seconds to reach the earth. How fast is it going when it lands?