A Concrete Approach to Mathematical Modelling by Mike Mesterton-Gibbons

By Mike Mesterton-Gibbons

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O) ~ £. 0 R = (o k a ~ *o). 62). 10, and we leave that to you. You should check that, as t oo i n your solution, th e product concentration £ tends t o m i n ( a , b ); whereas th e reactant concentrations tend to 0 and m a x ( a , b )-min(a , b ). I n other words, the less abundant of the tw o reactants i s completely converted int o a constituent of the product. 10, notice how many phenomena are described by a single differentia l equation. S. 62). That diverse phenomena may have a c o m m on mathematical structur e is a re› currin g theme of applied mathematics, and furthe r examples wil l appear throughout the text.

4. Notice that they are correct t o at least one significant figure unti l 1950. I n fact, the percentage error , that is, i. 5% throughout thi s entir e period, except for the year 1860, when the error i s a littl e over 5%. 4). 60) by about 20%. 60), which we derived empirically , could also have been conceptually derived by th e followin g simple argument. Assume that there i s a maximum population K, th e capacity, that the land can sustain. When th e population is x, th e unused fractio n of the capacity is 1 - xlK.

0 Fig. 28). There are 36, not 37, data points because the uppermost point represents both 1901 and 1902. 29) might even be a better description of overall economic growt h than th e diagram itself, because even the briefest of glances at Fig. , 1917); and such abnormalities may be associated wit h the outlyin g points. 29) as a model of economic growth in Massachusetts. A possible criticis m of thi s proposal immediately springs t o mind. Sup› pose we accept that there is some lin e that captures the essential features of the distributio n of point s in Fig.

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