Math LaTeX Crash Course

LaTeX for Math Crash Course

(It’s easy, don’t worry)

CodeCogs

CodeCogs is a website that’ll allow you to test your LaTeX math code in real time. A stable internet connection is required for the ‘real time’ part.

I highly recommend following along with this tutorial.

Note that LaTeX is not only for math, so if you google “how to… latex,” you might see results for non-math related stuff.

What is LaTeX for Math?

It’s a way to let you type math as code, and make it look pretty.

Typing operators

$+$, $-$ and $=$ are intuitive. Just type +, -, or =.

Example
1 + 1 - 1 = 1
$1 + 1 - 1 = 1$

Multiply and divide use symbols that you can’t normally type on the keyboard, so instead, you type \times or \div instead.

Don’t forget the \ at the beginning! This is the ‘escape character’ and is how you type most symbols.

Example
4 \times 2 \div 3 = 2.6666667...
$4 \times 2 \div 3 = 2.666666...$

Note that you won’t be using $\div$ much, as most of the time you use fractions. We’ll show fractions later in this document.

Superscript and subscript

This is pretty intuitive too – you probably already use these symbols.

^ for ^superscript

_ for _subscript

Example
y = v_i t + a_g t^2 \div 2
$y = v_i t + a_g t^2 \div 2$

You can combine them too. Order doesn’t matter.

Example
v^2_1 and v_1^2 are the same.
$v^2_1$ and $v_1^2$ are the same.

Note that LaTeX doesn’t care about spaces.

Example
x = v_1t and x = v_1 t are the same.
$x = v_1t$ and $x = v_1 t$ are the same.

Example (bad)
v^42
$v^42$

If your superscript or subscript is longer than 1 character, you must use { curly braces } to surround them.

Example (fixed)
v^{42}
$v^{42}$

Example
v_{1 f}
$v_{1 f}$

Example
v^{42}_{final\ of\ the\ first\ object}
$v^{42}_{final\ of\ the\ first\ object}$

Notice the \ before the spaces. Inserting a backslash before a space tells LaTeX that you want to insert the space character.

Fractions

Fractions use \frac, and require 2 parameters (a numerator and denominator).

Example
\frac 12
$\frac 12$

If you want more than 1 character in the fraction, you need to surround them in curly braces.

Example
\frac{42}{18}
$\frac{42}{18}$

Example
\frac{x^2 - 1}{(x + 1)(x - 4)} = \frac{x - 1}{x - 4}
$$\frac{x^2 - 1}{(x + 1)(x - 4)} = \frac{x - 1}{x - 4}$$

Exercise 1

Try to copy this equation exactly:

$$m_1\frac{v_{1i}^2}{r} = qv \times B - m_1g$$

See answer

Square root

Uses \sqrt

Example
\sqrt{x^2 + y^2}
$\sqrt{x^2 + y^2}$

You can also do cube root (or any root) using \sqrt[n]{...}

Example
\sqrt[3]{x^2 + y^2 + z^2}
$\sqrt[3]{x^2 + y^2 + z^2}$

Dot multiply

People don’t really use $\times$ that much either… you tend to see $\cdot$ instead.

You can type that thing with \cdot. (center dot)

Example
4 N \cdot m
$4 N \cdot m$

Vectors

You can add \vec to add a vector arrow above your $\vec {\textup{variables}}$

Example
\vec F = q \vec v \times \vec B
$\vec F = q \vec v \times \vec B$

Other symbols

You can type other symbols by remembering their (greek) names.

Note that if you capitalize the code, you will get the capitalized letter.

Symbol	Code
$\delta$	\delta
$\Delta$	\Delta
$\theta$	\theta
$\Theta$	\Theta
$\mu$	\mu
$\Mu$	\Mu
$\nu$	\nu
$\varepsilon$	\varepsilon
$\omega$	\omega
$\alpha$	\alpha

etc…

Other math symbols you might find useful:

Symbol	Code	Mnemonic
$\approx$	\approx	approximately equal
$\sum$	\sum
$\neq$	\neq	not equal
$\pm$	\pm	plus or minus
$\int$	\int	integral
$\therefore$	\therefore

Exercise 2

Copy this equation exactly:

$$v = \pm \sqrt{\frac{2mg_{Earth}h - k_{sp}x^2}{m}}$$

See answer

Trig functions

While you can just type sin, it’ll look slightly better if you type \sin or \cos or \tan, etc.

Example (bad)
sin \theta = \frac{opp}{adj}
$sin \theta = \frac{opp}{adj}$

Example (fixed)
\sin \theta = \frac{opp}{adj}
$\sin \theta = \frac{opp}{adj}$

Adding \ before trig functions removes the italics that LaTeX applies on variables.

Without \	With \
$sin$	$\sin$
$tan$	$\tan$
$arctan$	$\arctan$

Big brackets

Sometimes, you just need big brackets.

Example (bad)
x \cdot (\frac{a}{d} + v_i)
$$x \cdot (\frac{a}{d} + v_i)$$

LaTeX will auto-size brackets for you if you do \left ( ... \right )

Example
x \cdot \left ( \frac{a}{d} + v_i \right )
$$x \cdot \left ( \frac{a}{d} + v_i \right )$$

Units

Units aren’t variables, and therefore are usually not in italics. You can remove italics yourself using \textup

Example (bad)
4 N \cdot m
$4 N \cdot m$

_{yes that is the same example for dot multiply}

Example (fixed)
4 \textup N \cdot \textup m
$4 \textup N \cdot \textup m$

Colors

Colors are nice sometimes.

Some escape codes have already been defined for you.

Result	Code
$\red{red}$	\red{red}
$\green{green}$	\green{green}
$\blue{blue}$	\blue{blue}

There are lots more you can discover yourself.

Exercise 3

Copy this equation exactly:

$$\red{\textup E} \green{\tan \left [ \blue{\sin \left ( \frac \Mu \alpha \right )} \right ]}$$

See answer

Cancel

You can cross out stuff to show cancelling out.

Example
\frac{1}{\cancel{22}} \times \cancel{22} = 1
$\frac{1}{\cancel{22}} \times \cancel{22} = 1$

Appendix

Deriving exercise 2

I made up a question in my head where you’re asked to calculate the velocity of some object on a vertical spring. (These equations don’t come from thin air, you know!)

$$mg_{Earth}h = \frac 1 2 k_{sp}x^2 + \frac 1 2 mv^2$$
$$mg_{Earth}h - \frac 1 2 k_{sp}x^2 = \frac 1 2 mv^2$$
$$2mg_{Earth}h - k_{sp}x^2 = mv^2$$
$$\frac{2mg_{Earth}h - k_{sp}x^2}{m} = v^2$$
$$\pm\sqrt{ \frac{2mg_{Earth}h - k_{sp}x^2}{m}} = v$$
$$v = \pm \sqrt{\frac{2mg_{Earth}h - k_{sp}x^2}{m}}$$

Answers to exercises

Answer 1

$$m_1\frac{v_{1i}^2}{r} = qv \times B - m_1g$$

m_1\frac{v_{1i}^2}{r} = qv \times B - m_1g

Go back to exercise 1

Answer 2

$$v = \pm \sqrt{\frac{2mg_{Earth}h - k_{sp}x^2}{m}}$$

v = \pm \sqrt{\frac{2mg_{Earth}h - k_{sp}x^2}{m}}

Go back to exercise 2

Answer 3

$$\red{\textup E} \green{\tan \left [ \blue{\sin \left ( \frac \Mu \alpha \right )} \right ]}$$

\red{\textup E} \green{\tan \left [ \blue{\sin \left ( \frac \Mu \alpha \right )} \right ]}

Go back to exercise 3