2: Functions as Descriptions of Biological Patterns.

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Where are we going?

Relations between quantities are so central to science and mathematics that the concept has been carefully defined and is named function. You will see how tables of data, graphs, and equations are unified into a single concept, function. This chapter will present examples of some unusual relations between quantities that suggest the usefulness of the general concept, and it will introduce three definitions of function with increasing levels of precision.

Electrocardiograms are examples of relations between voltage and time that are functions. Equations to describe the relation are difficult to find, and once found, are not informative. It is better to think of each trace as simply a function.

$electrocardiogram.JPG$

Many biological relations may be described by equations — linear, quadratic, hyperbolic, exponential, and logarithmic. These together with the trigonometric equations cover most of the commonly encountered equations. Scientific calculators readily compute these values that in the past were laboriously computed by hand and recorded in lengthy tables. There are some relations between measured quantities that are not so easily described by equations, and in this chapter we see how we can extend the use of equations to describe relations to a general concept referred to as a function. Formal definitions of function and ways of combining functions are presented.