Biomathematics: An Introduction by David Machin (auth.)

By David Machin (auth.)

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Hence (3/4) 1 / 2 tan 11/6 = sin = 3112 ;2. 17 arise in biology often as solutions to differential equations. Maynard-Smith (1968) discusses many biological systems that can be expressed as differential equations and goes on to describe their solution. 37 Mean of (no. 7 Mean number of normal births in each hour, fitted with a sine curve We shall discuss some differential equations in chapters 4 and 5. 17 has been used empirically to describe observed data. Some data collected by P. D. 7, which is taken from Bliss (1970, page 244).

Let xA and xB denote the respective mean weights and nA, nB the corresponding number of mice. Show that x, the overall mean of the mice, is given by Evaluate x for these data. 2 Graphs of Some Important Functions In this chapter we investigate in greater detail some of the functions introduced in chapter 1. We also discuss the parabola, hyperbola and circle and describe some of their properties, together with those of the trigonometric functions sine, cosine and tangent. The radian, an alternative to the degree as a measure of angle, is also introduced.

8 Evaluate e 1/2 approximately by use of the first five terms of the infinite series for ex. 718282 ... •. 17 we would have been closer to this value. 5 PROBLEMS FOR SOLUTION 1. Write out in full the terms of the following series: 3 (a) r La ~. where a is a constant; r. 4 ( -y) s r=O L S S:• (b) s=l where S is a constant; (c) evaluate (a) and (b) with a = 3, x y ,;, 1/2. 1 and S -384, 2. Write out the terms of the series n S n = L qr r=O and subtract from the series you obtain the series qSn. Hence show that n+l 1 - q 1 - q 52 We call this latter expression the sum of the series.

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