5.1 Skriva matematiska formler i LaTeX

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== Att skriva enkla uttryck i LaTex==
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==How to write basic expressions ==
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För att markera '''starten''' för den matematiska formateringen används taggen '''<nowiki><math></nowiki>'''. För att '''sluta''' den matematiska formateringen används taggen '''<nowiki></math></nowiki>'''.
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Till exempel skrivs formeln <math>a+b</math> så här <nowiki><math></nowiki>a+b<nowiki></math></nowiki>.
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To indicate the '''start''' of math formatting, use the tag '''<nowiki><math></nowiki>'''. To '''end''' math formatting, use the tag '''<nowiki></math></nowiki>'''. For example, if you want the formula <math>a+b</math>, in the text box write <nowiki><math></nowiki>a+b<nowiki></math></nowiki>.
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Matematiska grundekvationer är enkelt uttryckta.
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Simple mathematical formulas are written in a straight-forward manner.
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<div class="exempel">
<div class="exempel">
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''' Example 1'''
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''' Exempel 1'''
<ol type="a">
<ol type="a">
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<li><math>1+2-3\quad</math> is written <tt><nowiki><math></nowiki>1+2-3<nowiki></math></nowiki></tt></li>
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<li><math>1+2-3\quad</math> skrivs <tt><nowiki><math></nowiki>1+2-3<nowiki></math></nowiki></tt></li>
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<li><math>5/2\quad</math> is written <tt><nowiki><math></nowiki>5/2<nowiki></math></nowiki></tt></li>
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<li><math>5/2\quad</math> skrivs <tt><nowiki><math></nowiki>5/2<nowiki></math></nowiki></tt></li>
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<li><math>4/(2+x)\quad</math> is written <tt><nowiki><math></nowiki>4/(2+x)<nowiki></math></nowiki></tt></li>
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<li><math>4/(2+x)\quad</math> skrivs <tt><nowiki><math></nowiki>4/(2+x)<nowiki></math></nowiki></tt></li>
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<li><math>4 < 5\quad</math> is written <tt><nowiki><math></nowiki>4 < 5<nowiki></math></nowiki></tt></li>
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<li><math>4 < 5\quad</math> skrivs <tt><nowiki><math></nowiki>4 < 5<nowiki></math></nowiki></tt></li>
</ol>
</ol>
</div>
</div>
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<td>Logarithms</td>
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<td>Logarithms</td>http://wiki.math.se/wikis/forberedandematte1/skins/mathse/spacer.gif
<td align="center"><span class="math">\ln x</span></td>
<td align="center"><span class="math">\ln x</span></td>
<td align="center"><tt>\ln x</tt></td>
<td align="center"><tt>\ln x</tt></td>
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== How to write complex expressions==
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== Att skriva komplicerade uttryck ==
By combining simple expressions, we may form more complex expressions.
By combining simple expressions, we may form more complex expressions.

Versionen från 26 februari 2009 kl. 09.02

       Teori          Övningar      

Innehåll:

  • LaTeX matematik

Lärandemål:

Efter detta avsnitt ska du ha lärt dig att:

  • Skriva formler i LaTeX
  • Undvika vanliga misstag när man kodar matematik i LaTeX


För att effektivt kunna skriva matematik på din dator i den individuella uppgiften och gruppuppgiften så behöver du koda matematiken med hjälp av LaTeX. I detta avsnitt kommer du få lära dig grunderna i att konstruera LaTeX-kod för att skriva matematiska formler.


Att skriva enkla uttryck i LaTex

För att markera starten för den matematiska formateringen används taggen <math>. För att sluta den matematiska formateringen används taggen </math>. Till exempel skrivs formeln \displaystyle a+b så här <math>a+b</math>.

Matematiska grundekvationer är enkelt uttryckta.

Exempel 1

  1. \displaystyle 1+2-3\quad skrivs <math>1+2-3</math>
  2. \displaystyle 5/2\quad skrivs <math>5/2</math>
  3. \displaystyle 4/(2+x)\quad skrivs <math>4/(2+x)</math>
  4. \displaystyle 4 < 5\quad skrivs <math>4 < 5</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.


http://wiki.math.se/wikis/forberedandematte1/skins/mathse/spacer.gif
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

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


Att skriva komplicerade uttryck

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

Example 3

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

Example 4

  1. \displaystyle \sqrt{x+\sqrt{x}}\quad is written <math>\sqrt{x+\sqrt{x}}</math>
  2. \displaystyle \dfrac{x-x^2}{\sqrt{3}}\quad is written <math>\dfrac{x-x^2}{\sqrt{3}}</math>
  3. \displaystyle \dfrac{x}{x+\dfrac{1}{x}}\quad is written <math>\dfrac{x}{x+\dfrac{1}{x}}</math>
  4. \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
  1. Don't write
sin x \displaystyle sin x
  1. Don't write
\sinx Error
  1. Do write
\sin x \displaystyle \sin x
  1. Don't write
4*3 \displaystyle 4*3
  1. Do write
4\times 3 \displaystyle 4\times 3
  1. Don't write
a\times b \displaystyle a\times b
  1. 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
  1. Don't write
a2 \displaystyle a2
  1. Do write
a^2 \displaystyle a^2
  1. Don't write
x1 \displaystyle x1
  1. Do write
x_1 \displaystyle x_1
  1. Don't write
a^22 \displaystyle a^22
  1. Do write
a^{22} \displaystyle a^{22}
  1. Don't write
30^{o} \displaystyle 30^{o}
  1. Don't write
30^{0} \displaystyle 30^{0}
  1. 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
  1. Don't write
(1-(1-x) \displaystyle (1-(1-x)
  1. Do write
(1-(1-x)) \displaystyle (1-(1-x))
  1. Don't write
(\dfrac{a}{b}+c) \displaystyle (\dfrac{a}{b}+c)
  1. Do write
\left(\dfrac{a}{b}+c\right) \displaystyle \left(\dfrac{a}{b}+c\right)
  1. Don't write
\frac(1)(2) \displaystyle \tfrac(1)(2)
  1. Do write
\frac{1}{2} \displaystyle \tfrac{1}{2}
  1. Don't write
\sqrt(a+b) \displaystyle \sqrt(a+b)
  1. Don't write
\sqrt{(a+b)} \displaystyle \sqrt{(a+b)}
  1. 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
  1. Don't write
\dfrac{1}{2} \displaystyle \dfrac{1}{2}
  1. Do write
\frac{1}{2} \displaystyle \tfrac{1}{2}
  1. (Exception: If the fraction is next to a large expression you should, however, write the fraction as a large fraction.)
  1. Don't write
\frac{a}{b} \displaystyle \tfrac{a}{b}
  1. Do write
\dfrac{a}{b} \displaystyle \dfrac{a}{b}
  1. Don't write
\frac{\sqrt{3}}{2} \displaystyle \tfrac{\sqrt{3}}{2}
  1. Do write
\dfrac{\sqrt{3}}{2} \displaystyle \dfrac{\sqrt{3}}{2}
  1. Don't write
a^{\frac{1}{2}} \displaystyle a^{\frac{1}{2}}
  1. Do write
a^{1/2} \displaystyle a^{1/2}


Study advice

A tip is to try out your maths formulas in the forum or 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.
  • The actual implementation of LaTeX math that is used in the wiki is jsMath.
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