Mathematical Tools

by Poul Einer Hansen

The purpose of the following pages is to offer a little help to those readers— biologists and others—who do not make frequent use of mathematics above the elementary level, and who find themselves unable to appreciate the extensive use of mathematics in the present volume, there is no shortcut to getting familiar with mathematics, and it should be stressed that reading the appendix will certainly not provide you with a full understanding of the methods and results involved, nor will it enable you to use them independently. However, it may give you some idea of what goes on and perhaps inspire a few to seek more thorough information elsewhere; there are numerous suitable textbooks in the field.

To start mathematically from scratch is not possible (and besides, if you were there you would hardly be reading this book in the first place). So let us assume that the reader is, or was once, familiar with subjects such as: arithmetics, elementary algebra, trigonometry, exponentials and logarithms, combinatorials, analytic geometry and some vector algebra in two and (less deeply) three dimensions, and introductory differential and integral calculus.

The two most important subjects to be dealt with in the appendix are matrices and differential equations; the question of numerical methods will also be touched upon. To get to the second floor of a house you have to pass through the first, meaning that we will have to treat some topics that are not directly relevant for the rest of the book, but are necessary to understand other topics that are.

A few exercises are interspersed in the text. It is strongly recommended that you try to solve these exercises along with reading. If you are stuck, ask a colleague or a friend for help. But remember: only just enough to get you going again!

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