Preface

Preface Preface

Introduction.

This is an interactive online version of the Basic Maths for Natural Sciences textbook. As such, at the end of most section it contains interactive exercises (Checkpoints) that students can use to practice and verify their understanding. Most questions are randomized, meaning that by clicking the Show new example question button, students can get a new random variant of the question to practice with.

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The technology for these questions is called STACK. These got beyond multiple choice questions and allow you to enter mathematical expressions. The next paragraphs explain how this is done.

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Typing answers in interactive questions.

This book contains interactive STACK questions. When you enter your answers in response to a question, you will have to adhere to certain syntax. In the following, we show the most common examples.

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In STACK you often need to enter an answer which is an algebraic expression. You should type in your answers using the same syntax as that used in the symbolic mathematics package Maxima.

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The syntax is broadly similar to the syntax used for mathematical formulae in graphical calculators, general programming languages such as Maple, Java, C and Basic and in spreadsheet programs, so you will find it useful to master it.

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Checkpoint 0.0.1.

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Basic operations.

Use a star for multiplication. For example, \(3x\) should be entered as 3*x.

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Use a caret (^) for raising something to a power: for example, \(x^2\) should be entered as x^2

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\(x^{-2}\) should be entered as x^(-2)

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\(\displaystyle x^{\frac{1}{3}}\) should be entered as x^(1/3)

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Brackets are important to group terms in an expression.

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Functions and Greek letters.

Functions always have their arguments in brackets. For example:

\(\cos x\) or \(\ln x\) have to be typed as cos(x) or ln(x).

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\(e^x\) can be typed as e^x or exp(x).

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Square roots \(\sqrt{x}\) are typed as sqrt(x), though you can also use x^(1/2).

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Greek letters have to be typed using their English names, e.g. \(\alpha\) is typed as alpha.

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Below is the full list of Greek letters.

\(\alpha\)	`alpha`
\(\beta\)	`beta`
\(\gamma\)	`gamma`
\(\delta\)	`delta`
\(\epsilon\)	`epsilon`
\(\zeta\)	`zeta`
\(\eta\)	`eta`
\(\theta\)	`theta`
\(\iota\)	`iota`
\(\kappa\)	`kappa`
\(\lambda\)	`lambda`
\(\mu\)	`mu`
\(\nu\)	`nu`
\(\xi\)	`xi`
\(\omicron\)	`omicron`
\(\pi\)	`pi`
\(\rho\)	`rho`
\(\sigma\)	`sigma`
\(\tau\)	`tau`
\(\upsilon\)	`upsilon`
\(\phi\)	`phi`
\(\chi\)	`chi`
\(\psi\)	`psi`
\(\omega\)	`omega`