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5.1 Writing formulas in TeX

From Förberedande kurs i matematik 1

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<table cellpadding="6" cellspacing="0" class="normalText" width="70%"
<table cellpadding="6" cellspacing="0" class="normalText" width="70%"
align="center">
align="center">
-
<colgroup>
 
-
<col width="23%">
 
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<col width="13%">
 
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<col width="18%">
 
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<col width="10%">
 
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<col width="36%">
 
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</colgroup>
 
<tr>
<tr>
- 
<td></td>
<td></td>
-
<td align="center"><b><%=lang("_example")%></b></td>
+
<td align="center"><b>Example</b></td>
-
<td align="center"><b><%=lang("txt_latex_code")%></b></td>
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<td align="center"><b>LaTeX-code</b></td>
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<td align="center"><b><%=lang("_button")%></b></td>
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<td align="center"><b>Button</b></td>
-
<td align="left"><b><%=lang("_comment")%></b></td>
+
<td align="left"><b>Comment</b></td>
</tr>
</tr>
<tr style="background:#E6E6E6;">
<tr style="background:#E6E6E6;">
-
<td align="left"><%=lang("txt_simple_operations")%></td>
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<td align="left">Simple operations</td>
<td align="center"><span class="math">a+b</span></td>
<td align="center"><span class="math">a+b</span></td>
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<td align="center"><tt>\frac{a}{b}</tt></td>
<td align="center"><tt>\frac{a}{b}</tt></td>
<td align=center><img src="../images/buttons/frac.gif" /></td>
<td align=center><img src="../images/buttons/frac.gif" /></td>
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<td align="left"><%=lang("txt_bigger_fractions")%></td>
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<td align="left">Use \displaystyle\frac{a}{b} for a larger sized fraction</td>
</tr>
</tr>
<tr style="background:#E6E6E6;">
<tr style="background:#E6E6E6;">
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<td align="center"><tt>(a)</tt></td>
<td align="center"><tt>(a)</tt></td>
<td></td>
<td></td>
-
<td align="left"><%=lang("txt_scalable_parentheses")%></td>
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<td align="left">Scalable parantheses \left(...\right)</td>
</tr>
</tr>
<tr>
<tr>
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<td align="left"><%=lang("txt_relations")%></td>
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<td align="left">Relation signs</td>
<td align="center"><span class="math">a=b</span></td>
<td align="center"><span class="math">a=b</span></td>
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<td align="center"><tt>a\ne b</tt></td>
<td align="center"><tt>a\ne b</tt></td>
<td align=center><img src="../images/buttons/ne.gif" /></td>
<td align=center><img src="../images/buttons/ne.gif" /></td>
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<td><%=lang("txt_alternatively_not")%></td>
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<td>Alternatively: a\not= b</td>
</tr>
</tr>
<tr>
<tr>
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<td align="center"><tt>a< b</tt></td>
<td align="center"><tt>a< b</tt></td>
<td></td>
<td></td>
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<td><%=lang("txt_n_b_space_after")%></td>
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<td>NB: Space after "&lt;"</td>
</tr>
</tr>
<tr style="background:#E6E6E6;">
<tr style="background:#E6E6E6;">
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<tr>
<tr>
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<td><%=lang("txt_powers_and_roots")%></td>
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<td>Powers and roots</td>
<td align="center"><span class="math">x^{n}</span></td>
<td align="center"><span class="math">x^{n}</span></td>
<td align="center"><tt>x^{n}</tt></td>
<td align="center"><tt>x^{n}</tt></td>
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<td align="center"><tt>\sqrt[n]{x}</tt></td>
<td align="center"><tt>\sqrt[n]{x}</tt></td>
<td align=center><img src="../images/buttons/sqrtn.gif" /></td>
<td align=center><img src="../images/buttons/sqrtn.gif" /></td>
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<td><%=lang("txt_bigger_root_index")%></td>
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<td>Write \sqrt[\scriptstyle n]{x} for bigger n</td>
</tr>
</tr>
<tr style="background:#E6E6E6;">
<tr style="background:#E6E6E6;">
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<td><%=lang("txt_logarithms")%></td>
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<td>Logarithms</td>
<td align="center"><span class="math">\ln x</span></td>
<td align="center"><span class="math">\ln x</span></td>
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</tr>
</tr>
<tr>
<tr>
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<td><%=lang("txt_trigonometry")%></td>
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<td>Trigonometry</td>
<td align="center"><span class="math">30^{\circ}</span></td>
<td align="center"><span class="math">30^{\circ}</span></td>
<td align="center"><tt>30^{\circ}</tt></td>
<td align="center"><tt>30^{\circ}</tt></td>
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</tr>
</tr>
<tr style="background:#E6E6E6;">
<tr style="background:#E6E6E6;">
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<td><%=lang("txt_various_symbols")%></td>
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<td>Various symbols</td>
<td align="center"><span class="math">\pi</span></td>
<td align="center"><span class="math">\pi</span></td>
<td align="center"><tt>\pi</tt></td>
<td align="center"><tt>\pi</tt></td>
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</tr>
</tr>
</table>
</table>
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</p>
 
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<p><%=lang("tb_manual_write_math_2")%></p>
 
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<p style="text-align:center">
 
<table cellpadding="6" cellspacing="0" class="normalText" width="70%"
<table cellpadding="6" cellspacing="0" class="normalText" width="70%"
align="center">
align="center">
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<colgroup>
 
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<col width="40%">
 
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<col width="60%">
 
- 
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</colgroup>
 
<tr>
<tr>
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<td align="center"><b><%=lang("_example")%></b></td>
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<td align="center"><b>Example</b></td>
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<td align="center"><b><%=lang("txt_latex_code")%></b></td>
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<td align="center"><b>Latex-code</b></td>
</tr>
</tr>
<tr style="background:#E6E6E6;">
<tr style="background:#E6E6E6;">

Revision as of 13:22, 27 January 2009

       Theory          Exercises      

Contents:

  • What is TeX/LaTeX?
  • Common expressions
  • Common mistakes

Learning outcomes:

After this section you will have learned how to:

  • Write formulas in TeX

What is TeX/LaTeX?

Common expressions

Example LaTeX-code Button Comment
Simple operations a+b a+b
a−b a-b
ab a\pm b <img src="../images/buttons/pm.gif" />
ab a\cdot b <img src="../images/buttons/cdot.gif" />
ab a/b
ba \frac{a}{b} <img src="../images/buttons/frac.gif" /> Use \displaystyle\frac{a}{b} for a larger sized fraction
(a) (a) Scalable parantheses \left(...\right)
Relation signs a=b a=b
a=b a\ne b <img src="../images/buttons/ne.gif" /> Alternatively: a\not= b
ab a< b NB: Space after "<"
ab a\le b <img src="../images/buttons/le.gif" />
ab a>b
ab a\ge b <img src="../images/buttons/ge.gif" />
Powers and roots xn x^{n} <img src="../images/buttons/pow.gif" />
x  \sqrt{x} <img src="../images/buttons/sqrt.gif" />
nx  \sqrt[n]{x} <img src="../images/buttons/sqrtn.gif" /> Write \sqrt[\scriptstyle n]{x} for bigger n
Logarithms \ln x \ln x <img src="../images/buttons/ln.gif" />
\log x \log x
\log_{a} x \log_{a} x <img src="../images/buttons/logn.gif" />
Trigonometry 30^{\circ} 30^{\circ} <img src="../images/buttons/circ.gif" />
\cos x \cos x <img src="../images/buttons/cos.gif" />
\sin x \sin x <img src="../images/buttons/sin.gif" />
\tan x \tan x <img src="../images/buttons/tan.gif" />
\cot x \cot x <img src="../images/buttons/cot.gif" />
Various symbols \pi \pi <img src="../images/buttons/pi.gif" />


Example Latex-code
ax^2+bx+c ax^2+bx+c
(a^2)^3=a^6 (a^2)^3=a^6
\sqrt{x+2} \sqrt{x+2}
\sqrt{x+\sqrt{x}} \sqrt{x+\sqrt{x}}
\displaystyle\frac{a+b}{c-d} \displaystyle\frac{a+b}{c-d}

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

TeX 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

TeX 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

TeX 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 \tfrac), while other fractions should be large (i.e. with \frac).

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

TeX 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

Useful web sites

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