Mathematical Modelling Skills pp 102-120 | Cite as

# Modelling with Differential Equations

## Abstract

In most of the examples of Chapter 8 we were given or assumed that our variable was modelled by a particular function of time, *y* = *f*(*t*), and then we found the rate of change, *y′* = *f′*(*t*). Very often our modelling **assumptions** are expressed in terms of **rates of change.** For example, we may assume that the rate of change, *y*′, is related to the value of *y* itself at any time *t*. The rate of change of the size of a population, for example, clearly depends on the existing size of the population. This gives us the problem of working back from *y′* to find *y*. (Note that in all the examples in this chapter we use ′ to stand for d/d*t*.)

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