This document describes some Maple commands that will be useful to you in working with the project. However, it doesn't tell you exactly how to use the commands described here for your project work - that is up to you.

The Maple commands described here can be used to more easily define
functions for the drug concentration. The main difficulty is that the
concentration is defined by different formulas in different time
intervals. However, it turns out that by using the Maple `sum` and
`floor` commands, the desired function can be defined rather
simply.

In the project, a new dose of the drug is given every **L** hours. In
between doses, the concentration decays exponentially from its value
just after the dose is given to that just before the next dose is
given. That is, between doses the concentration behaves like

where **td** is the time at which the most recent dose was given, and
**C** is the concentration just after the most recent dose was given.
The problem is that both **C** and **td** depend on how many doses have
been given. One of the questions in the project asks you to derive a
formula for **C**, so you are on your own there. This document is
intended to help you understand how to calculate **td** and introduce
you to some Maple commands that will help you define the function
in a simple manner.

Given a value of **t**, the time the last dose was given can be
calculated if we know the number of doses that have been given and the
time **L** between doses. For example, if only one dose has been given,
then the time of the most recent dose must be **td = 0**. If two doses
have been given, then the time of the most recent dose is **td = L**. In
general, you should be able to convince yourself that if **N** doses
have been given, then the time of the most recent dose is .
Given a value of **t**, the number of doses, **N** given up to that time can be
calculated easily by dividing **t** by **L**, the time between doses,
taking the integer part of the result, and then adding 1 (for the
initial dose). For example, suppose that doses were being given every
**4** hours. After **21** hours, the number of doses given can be
calculated to be **6** by taking the integer part of (
**=5**) and adding **1**. However, since what we really need to calculate **td** is
**N-1** we can just divide **t** by **L** and take the integer
part of the result. The next section contains further mathematical
background and examples of Maple commands that will be useful to you.

Fri Feb 9 15:13:22 EST 1996