A Concrete Approach to Mathematical Modelling - download pdf or read online

By Mike Mesterton-Gibbons

ISBN-10: 0470171073

ISBN-13: 9780470171073

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Science it’ s generally a bad idea t o rely exclusively upon one’s intuition . Therefore, in Chapter 4, we wil l test thi s model mor e objectively. 13 Traffi c Dynamic s Suppose that there are Ν vehicles i n a lane of traffic . We wil l label t h em N, wit h j = 1 corresponding t o th e leading vehicle. Let us j = 1, assume that their masses and lengths are equal. Thi s might be at least approximately tru e on a bridg e or i n a tunnel fro m which truck s have been barred . Let th e fron t bumper of th e j t h vehicle have displacement Zj(t) at tim e t, measured fro m th e beginning of th e road.

Dynamical System» 0 1 2 3 4 5 Fig. 6 A mischievous polluter deceives the environmental police. Whenever integer values of t are the only relevant ones, it is customary to write x(t) as x,. 45) is K n+l = e-«vx « = 0,1,2,. 46). 46) is dubbed a recurrence relation. 46). 46), because it says just as much with far less risk that it might actually be wrong. 46) suffices as a model. 10) is false! What can we do about mis? Notice from Fig. 6 that the short-term dynamics appears cyclic. 46). We might regard the short-term model as imbedded in the long-term one.

The more adult s there are, the more larvae that are eaten. Th e simplest assumption incorporatin g thi s observation is that the larval population decays at a rat e proportiona l t o the adult population which , in the short term, is fixed. Thu s 1 dy = (1-50) where β is a constant. 47), g{y) = -0x„y, where x„ is constant i n the embedded model. 50) fro m t t o t gives the number of (hundreds of million s of) larvae that survive t o matur e int o young salmon: a b yih) = y[t ) e x p ( - / ? x ( / - Q) = ax„ e x p ( - / ?

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A Concrete Approach to Mathematical Modelling (Wiley-Interscience Paperback Series) by Mike Mesterton-Gibbons

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