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5.1 Writing formulas in TeX

From Förberedande kurs i matematik 1

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Revision as of 13:34, 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

To write mathematics efficiently on a computer, one uses some sort of coding. We have chosen to use jsMath's LaTeX-code. Below are some basic examples of useful code snippets. For more examples, see for example Wikipedia's help page.

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>.

<colgroup> <col width="25%"> <col width="15%"> <col width="20%"> <col width="40%"> </colgroup> <tr> <td></td> <td align="center">a< b</td> <td align="center">a< b</td> <td>NB: Space after "<" </td> </tr> <tr style="background:#E6E6E6;"> <td></td> <td align="center">a\le b</td> <td align="center">a\le b</td> <td></td> </tr> <tr> <td></td> <td align="center">a> b</td> <td align="center">a>b</td> <td></td> </tr> <tr style="background:#E6E6E6;"> <td></td> <td align="center">a\ge b</td> <td align="center">a\ge b</td> <td></td> </tr> <tr> <td>Powers and roots</td> <td align="center">x^{n}</td> <td align="center">x^{n}</td> <td></td> </tr> <tr style="background:#E6E6E6;"> <td></td> <td align="center">\sqrt{x}</td> <td align="center">\sqrt{x}</td> <td></td> </tr> <tr> <td></td> <td align="center">\sqrt[n]{x}</td> <td align="center">\sqrt[n]{x}</td> <td>Write \sqrt[\scriptstyle n]{x} for bigger n</td> </tr> <tr style="background:#E6E6E6;"> <td>Logarithms</td> <td align="center">\ln x</td> <td align="center">\ln x</td> <td></td> </tr> <tr> <td></td> <td align="center">\log x</td> <td align="center">\log x</td> <td></td> </tr> <tr style="background:#E6E6E6;"> <td></td> <td align="center">\log_{a} x</td> <td align="center">\log_{a} x</td> <td></td> </tr> <tr> <td>Trigonometry</td> <td align="center">30^{\circ}</td> <td align="center">30^{\circ}</td> <td></td> </tr> <tr style="background:#E6E6E6;"> <td></td> <td align="center">\cos x</td> <td align="center">\cos x</td> <td></td> </tr> <tr> <td></td> <td align="center">\sin x</td> <td align="center">\sin x</td> <td></td> </tr> <tr style="background:#E6E6E6;"> <td></td> <td align="center">\tan x</td> <td align="center">\tan x</td> <td></td> </tr> <tr> <td></td> <td align="center">\cot x</td> <td align="center">\cot x</td> <td></td> </tr> <tr style="background:#E6E6E6;"> <td>Various symbolsr</td> <td align="center">\pi</td> <td align="center">\pi</td> <td></td> </tr> </table> By combining these simple expressions, we may form more complex expressions. The table below shows some examples.

	Example	LaTeX-code	Comment
Simple operations	a+b	`a+b`
	a-b	`a-b`
	a\pm b	`a\pm b`
	a\cdot b	`a\cdot b`
	a/b	`a/b`
	\frac{a}{b}	`\frac{a}{b}`	Use \displaystyle\frac{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</tt>

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
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

	TeX	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

	TeX	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 \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
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

Useful web sites

A video course in mathematical writing by Donald Knuth (A compendium accompaning the course is avalable in source form or in excerpts from Google books).

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3. Roots and logarithms

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5.1 Writing formulas in TeX

From Förberedande kurs i matematik 1

Revision as of 13:34, 27 January 2009

What is TeX/LaTeX?

Common expressions

Common mistakes

Exponents and indices

Delimiters

Fractions