5.1 Writing formulas in TeX
From Förberedande kurs i matematik 1
| 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 | |||
| a\pm b | a\pm b | <img src="../images/buttons/pm.gif" /> | ||
| a\cdot b | a\cdot b | <img src="../images/buttons/cdot.gif" /> | ||
| a/b | a/b | |||
| \frac{a}{b} | \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\ne b | a\ne b | <img src="../images/buttons/ne.gif" /> | Alternatively: a\not= b | |
| a< b | a< b | NB: Space after "<" | ||
| a\le b | a\le b | <img src="../images/buttons/le.gif" /> | ||
| a> b | a>b | |||
| a\ge b | a\ge b | <img src="../images/buttons/ge.gif" /> | ||
| Powers and roots | x^{n} | x^{n} | <img src="../images/buttons/pow.gif" /> | |
| \sqrt{x} | \sqrt{x} | <img src="../images/buttons/sqrt.gif" /> | ||
| \sqrt[n]{x} | \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 | |
| sin x | \displaystyle sin x |
| \sinx | Error |
| \sin x | \displaystyle \sin x |
| 4*3 | \displaystyle 4*3 |
| 4\times 3 | \displaystyle 4\times 3 |
| a\times b | \displaystyle a\times b |
| 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 | |
| a2 | \displaystyle a2 |
| a^2 | \displaystyle a^2 |
| x1 | \displaystyle x1 |
| x_1 | \displaystyle x_1 |
| a^22 | \displaystyle a^22 |
| a^{22} | \displaystyle a^{22} |
| 30^{o} | \displaystyle 30^{o} |
| 30^{0} | \displaystyle 30^{0} |
| 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-(1-x) | \displaystyle (1-(1-x) |
| (1-(1-x)) | \displaystyle (1-(1-x)) |
| (\dfrac{a}{b}+c) | \displaystyle (\dfrac{a}{b}+c) |
| \left(\dfrac{a}{b}+c\right) | \displaystyle \left(\dfrac{a}{b}+c\right) |
| \frac(1)(2) | \displaystyle \tfrac(1)(2) |
| \frac{1}{2} | \displaystyle \tfrac{1}{2} |
| \sqrt(a+b) | \displaystyle \sqrt(a+b) |
| \sqrt{(a+b)} | \displaystyle \sqrt{(a+b)} |
| \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 | |
| \dfrac{1}{2} | \displaystyle \dfrac{1}{2} |
| \frac{1}{2} | \displaystyle \tfrac{1}{2} |
| ||
| \frac{a}{b} | \displaystyle \tfrac{a}{b} |
| \dfrac{a}{b} | \displaystyle \dfrac{a}{b} |
| \frac{\sqrt{3}}{2} | \displaystyle \tfrac{\sqrt{3}}{2} |
| \dfrac{\sqrt{3}}{2} | \displaystyle \dfrac{\sqrt{3}}{2} |
| a^{\frac{1}{2}} | \displaystyle a^{\frac{1}{2}} |
| 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).
