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5.1 Writing formulas in TeX

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Theory

Exercises

Contents:

LaTeX maths

Learning outcomes:

After this section you will have learned how to:

Write simple maths formulas in LaTeX.
Avoid common mistakes when coding maths in LaTeX.

To write mathematics efficiently on a computer in your individual assignment and the group task you will need write the maths in a coded form called LaTeX syntax. In this section you will learn the fundamentals of constructing LaTeX code that yields simple maths formulas.

How to write basic expressions

To indicate the start of math formatting, use the tag <math>. To end math formatting, use the tag </math>. For example, if you want the formula \displaystyle a+b, in the text box write <math>a+b</math>.

Simple mathematical formulas are written in a straight-forward manner.

Example 1

\displaystyle 1+2-3\quad is written <math>1+2-3</math>
\displaystyle 5/2\quad is written <math>5/2</math>
\displaystyle 4/(2+x)\quad is written <math>4/(2+x)</math>
\displaystyle 4 < 5.3\quad is written <math>4 < 5.3</math>

When you need to use symbols that are not available on the keyboard or construct formulas that are not simple you use special commands that start with a backslash, e.g. \le is a command that gives you \displaystyle \le.

The table below shows some of the most commonly used maths commands in LaTeX.

	Example	LaTeX-code	Comment
Simple operations	a+b	`a+b`
	a-b	`a-b`
	a\pm b	`a\pm b`
	a\times b	`a\times b`
	a/b	`a/b`
	\frac{a}{b}	`\frac{a}{b}`	Use \dfrac{a}{b} for a larger sized fraction
	(a)	`(a)`	Scalable parantheses \left(...\right)
Relation signs	a=b	`a=b`
	a\ne b	`a\ne b`	Alternatively: a\not= b
	a< b	`a< b`	NB: Space after "<"
	a\le b	`a\le b`
	a> b	`a>b`
	a\ge b	`a\ge b`
Powers and roots	x^{n}	`x^{n}`
	\sqrt{x}	`\sqrt{x}`
	\sqrt[n]{x}	`\sqrt[n]{x}`	Write \sqrt[\scriptstyle n]{x} for bigger n
Index	x_n	`x_{n}`
Logarithms	\ln x	`\ln x`
	\log x	`\log x`
	\log_{a} x	`\log_{a} x`
Trigonometry	30^{\circ}	`30^{\circ}`
	\cos x	`\cos x`
	\sin x	`\sin x`
	\tan x	`\tan x`
	\cot x	`\cot x`
Arrows	\Rightarrow	`\Rightarrow`
	\Leftarrow	`\Leftarrow`
	\Leftrightarrow	`\Leftrightarrow`
Various symbols	\pi	`\pi`

Example 2

\displaystyle 1\pm3\times 5\quad is written <math>1\pm 3\times 5</math>
\displaystyle \tfrac{1}{2}y\ne x\le z\quad is written <math>\frac{1}{2}y\ne x\le z</math>
\displaystyle 2^{13}\sqrt{3}+\ln y\quad is written <math>2^{13}\sqrt{3}+\ln y</math>
\displaystyle \tan 30^{\circ}+\cot\pi\quad is written <math>\tan 30^{\circ}+\cot\pi</math>

How to write complex expressions

By combining simple expressions, we may form more complex expressions.

Example 3

\displaystyle \sqrt{x+2}\quad is written <math>\sqrt{x+2}</math>
\displaystyle (a^2)^3=a^6\quad is written <math>(a^2)^3=a^6</math>
\displaystyle 2^{2^2}\quad is written <math>2^{2^2}</math>
\displaystyle \sin\sqrt{x}\quad is written <math>\sin\sqrt{x}</math>

Example 4

\displaystyle \sqrt{x+\sqrt{x}}\quad is written <math>\sqrt{x+\sqrt{x}}</math>
\displaystyle \dfrac{x-x^2}{\sqrt{3}}\quad is written <math>\dfrac{x-x^2}{\sqrt{3}}</math>
\displaystyle \dfrac{x}{x+\dfrac{1}{x}}\quad is written <math>\dfrac{x}{x+\dfrac{1}{x}}</math>
\displaystyle x_{1,2}=-\dfrac{p}{2}\pm\sqrt{\left(\dfrac{p}{2}\right)^2-q}\quad is written <math>x_{1,2}=-\dfrac{p}{2}\pm\sqrt{\left(\dfrac{p}{2}\right)^2-q}</math>

How to avoid common mistakes

One of the most common mistakes when editing math in the wiki is to forget the start <math> tag and the end </math> tag.

Remember also to start commands with a backslash (\) and to add a space after the commands (unless they are followed immediately by a new command).

Another frequent mistake is to use an asterisk (*) instead of a proper multiplication sign \displaystyle \times (\times in TeX).

Example 5

	LaTeX	Result
Don't write	`sin x`	\displaystyle sin x
Don't write	`\sinx`	Error
Do write	`\sin x`	\displaystyle \sin x
Don't write	`4*3`	\displaystyle 4*3
Do write	`4\times 3`	\displaystyle 4\times 3
Don't write	`a\times b`	\displaystyle a\times b
Do write	`ab`	\displaystyle ab

Exponents and indices

When writing exponents you use ^ followed by the exponent and to write indices you use _ followed by the index. If the exponent or index consists of more than one symbol it must be enclosed with braces {}.

A special kind of exponent is the degree sign (°) which is written as ^{\circ}.

Example 6

	LaTeX	Result
Don't write	`a2`	\displaystyle a2
Do write	`a^2`	\displaystyle a^2
Don't write	`x1`	\displaystyle x1
Do write	`x_1`	\displaystyle x_1
Don't write	`a^22`	\displaystyle a^22
Do write	`a^{22}`	\displaystyle a^{22}
Don't write	`30^{o}`	\displaystyle 30^{o}
Don't write	`30^{0}`	\displaystyle 30^{0}
Do write	`30^{\circ}`	\displaystyle 30^{\circ}

Delimiters

In more complex expressions you need to make sure to balance each opening parenthesis ( with a closing parenthesis ).

A pair of parenthesis that delimits a tall expression should be as large as the expression. You should therefore prefix the opening parenthesis with \left and the closing parenthesis with \right to get a pair of extensible parentheses that adjust its height to the expression.

Note also that braces {} and not parentheses () are used in commands to delimits arguments.

Example 7

	LaTeX	Result
Don't write	`(1-(1-x)`	\displaystyle (1-(1-x)
Do write	`(1-(1-x))`	\displaystyle (1-(1-x))
Don't write	`(\dfrac{a}{b}+c)`	\displaystyle (\dfrac{a}{b}+c)
Do write	`\left(\dfrac{a}{b}+c\right)`	\displaystyle \left(\dfrac{a}{b}+c\right)
Don't write	`\frac(1)(2)`	\displaystyle \tfrac(1)(2)
Do write	`\frac{1}{2}`	\displaystyle \tfrac{1}{2}
Don't write	`\sqrt(a+b)`	\displaystyle \sqrt(a+b)
Don't write	`\sqrt{(a+b)}`	\displaystyle \sqrt{(a+b)}
Do write	`\sqrt{a+b}`	\displaystyle \sqrt{a+b}

Fractions

As a rule of thumb you should write fractions where the numerator and denominator consist only of a few digits as a small fraction (i.e. with \frac), while other fractions should be large (i.e. with \dfrac).

If an exponent or index contains a fraction then that fraction should be written in a slashed form (e.g. \displaystyle 5/2 instead of \displaystyle \tfrac{5}{2}) to enhance the legibility.

Example 8

	LaTeX	Result
Don't write	`\dfrac{1}{2}`	\displaystyle \dfrac{1}{2}
Do write	`\frac{1}{2}`	\displaystyle \tfrac{1}{2}
(Exception: If the fraction is next to a large expression you should, however, write the fraction as a large fraction.)
Don't write	`\frac{a}{b}`	\displaystyle \tfrac{a}{b}
Do write	`\dfrac{a}{b}`	\displaystyle \dfrac{a}{b}
Don't write	`\frac{\sqrt{3}}{2}`	\displaystyle \tfrac{\sqrt{3}}{2}
Do write	`\dfrac{\sqrt{3}}{2}`	\displaystyle \dfrac{\sqrt{3}}{2}
Don't write	`a^{\frac{1}{2}}`	\displaystyle a^{\frac{1}{2}}
Do write	`a^{1/2}`	\displaystyle a^{1/2}

Study advice

A tip is to try out your maths formulas in the wiki where you work on your individual assignment.

Useful web sites

A more thorough list of LaTeX maths commands can be found on Wikipedias help page

Two more thorough texts om LaTeX maths can be found in a chapter of the book The LaTeX Companion and a text by Herbert Voss.

If you want to know more about LaTeX you can visit these sites: Wikipedia, The not so Short Introduction to LaTeX and LaTeX Wikibook.

The actual implementation of LaTeX math that is used in the wiki is jsMath.

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3. Roots and logarithms

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