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5.1 Writing formulas in TeX

From Förberedande kurs i matematik 1

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Revision as of 14:57, 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 a+b, in the text box write <math>a+b</math>.

	Example	LaTeX-code	Comment
Simple operations	a+b	`a+b`
	a−b	`a-b`
	ab	`a\pm b`
	ab	`a\cdot b`
	ab	`a/b`
	ba	`\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=b	`a\ne b`	Alternatively: a\not= b
	ab	`a< b`	NB: Space after "<"
	ab	`a\le b`
	ab	`a>b`
	ab	`a\ge b`
Powers and roots	xn	`x^{n}`
	x	`\sqrt{x}`
	nx	`\sqrt[n]{x}`	Write \sqrt[\scriptstyle n]{x} for bigger n
Logarithms	lnx	`\ln x`
	logx	`\log x`
	logax	`\log_{a} x`
Trigonometry	30	`30^{\circ}`
	cosx	`\cos x`
	sinx	`\sin x`
	tanx	`\tan x`
	cotx	`\cot x`
Various symbolsr		`\pi`

By combining these simple expressions, we may form more complex expressions. The table below shows some examples.

Example	Latex-code
ax2+bx+c	`ax^2+bx+c`
(a2)3=a6	`(a^2)^3=a^6`
x+2	`\sqrt{x+2}`
x+x	`\sqrt{x+\sqrt{x}}`
c−da+b	`\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 (\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}