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5.1 Writing formulas in TeX

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Revision as of 12:28, 27 January 2009

Theory

Exercises

Contents:

Learning outcomes:

After this section you will have learned how to:

Express mathematics
Explain mathematics

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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5.1 Writing formulas in TeX

From Förberedande kurs i matematik 1

Revision as of 12:28, 27 January 2009

Common mistakes

Exponents and indices

Delimiters

Fractions