Overview of Formula Formatting with TeX

In the Note editor (CKedit) : 

• Use the Math plugin to enter formulas in the notes
• Later, if desired, go into Source mode and add  style="font-size:20px" , or whatever desired size, to the  span class="math-tex" element.

Examples:

\(F(\xi) \triangleq \left\{ \{x = \log_{10}{\int_{-\infty}^{\pi} {-b \pm \sqrt{b^2-4ac \sin(\xi)} \over 2a}}\otimes\partial f/\partial t\}\Rightarrow\{\lim_{\delta \rightarrow \infty}[\arcsin(\delta)] = \oint_a^b\det\begin{bmatrix}\frac{\text{d}x}{\text{d}y} & \sum_a^b f''(x) \\\frac{\partial a}{\partial b} & \sqrt[n/t]{ab} \end{bmatrix}\} \right\}\)

 

\(f = \underbrace {x^3} _ \textrm {text 1} + \underbrace {2 + sin(x)} _ \textrm {text 2} \oplus \mathbf{V_0}\)

Useful TeX - the basics

\       blank space

\quad    a space equal to the current font size

 

Normal text:

\text{count of samples with } T=x     \(\text{count of samples with } T= x\)

 

Boldface (e.g., vectors):

\mathbf{V}       \(\mathbf{V}\)

 

Greek:

\varphi \phi \gamma\Gamma          \(\varphi \phi \gamma\Gamma\)

Note: Uppercase letters that are identical to latin, such as A, aren't available.
Lowercase epsilon, theta, kappa, phi, pi, rho, and sigma are provided in two different versions; the alternate, or variant, version is created by adding "var" before the name of the letter

 

Calligraphy:

\mathcal{AC}    \(\mathcal{AC}\)

\mathscr{AC}   \(\mathscr{AC}\)

 

Subscript/Superscript (use curly brackets for groups):

k_i    k_i

k^s     k^s

\alpha'   \( \alpha'\)

{\huge\varphi}_{A,B} \ \circ \ {\huge\alpha}'_{X,A}    \({\huge\varphi}_{A,B} \ \circ \ {\huge\alpha}'_{X,A} \)             (could also use \large in lieu of \huge)

Commom symbols and more complex constructs

\triangleq  \(\triangleq\)

\approx   \(\approx\)

\otimes   \(\otimes\)

\bigotimes  \(\bigotimes\)

\oplus  \(\oplus\)

\bigoplus \(\bigoplus\)

\circ   \(f \circ g\)

\sqrt{x}    \(\sqrt{x}\)

\sqrt[n]{x}     \(\sqrt[n]{x}\)

 

Arrows:

\longrightarrow    \(X \longrightarrow Y\)

\Longrightarrow    \(\Longrightarrow\)

\leadsto            \(A \leadsto B\)

\leq     \(a \leq b\)

 

\in      \(\in\)

Empty set  \emptyset    \( \emptyset \)

Curly brackets  \{ x+y \}       \(\{ x+y \} \)

 

Summations:

\sum_{i=1}^{10} t_i                 \(\sum_{i=1}^{10} t_i\)

\displaystyle\sum_{i=1}^{10} t_i      \(\displaystyle\sum_{i=1}^{10} t_i\)

 

Calculus:

\int_{a}^{b}    \(\int_{a}^{b} \)

\nabla   \(\nabla\)

 

Large brackets:

To make parentheses, etc, larger (automatic sizing), use pairs of  \left  and  \right  .  If one side is not paired up, use a period as an invisible placeholder  .   Can also use  \middle

\left( \frac{x^2}{y^2} \right)      \(\left(\frac{x^2}{y^2}\right)\)

If using curly brackets, they must be preceded by a \ , because curly brackets have a special meaning:

\left\{ \frac{x^2}{y^2} \right\}    \(\left\{ \frac{x^2}{y^2} \right\}\)

 

Large fractions:

A \over B       \(A \over B\)

 

Binomial:

\left(\begin{array}{c}a\\ b\end{array}\right)     \(\left(\begin{array}{c}a\\ b\end{array}\right)\)

 

BINARY OPERATORS

\pm     \(\pm\)

\cdot      \(\mathbf{V} \cdot \mathbf{W}\)       Dot (inner) product:

\times     \(\mathbf{V} \times \mathbf{W}\)     Cross product

2-D Layouts

Matrices:

\( \begin{pmatrix} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \end{pmatrix}\)

For determinants, use  vmatrix  instead of  pmatrix

 

---

Definitions by case:

\(f(i, j) = \begin{cases} T \quad \text{if} \ \left({a_i},{b_j}\right) \in R \\ F \quad \text{if} \ \left({a_i},{b_j}\right) \notin R \end{cases}\)

 

---

Systems of equations:

\(\begin{cases}      3x + 5y = 2 \\     x – y =10 \end{cases}\)

 

To align (here we use 2 columns, and align the signs and equals.   The &{}  specifies a small spacing; only need to specify it once):

\(\begin{alignat*}{2}     3 x   & +   5y &{}  & =  2 \\        x  & -   y  &    & = 10 \end{alignat*}\)

 

\(\begin{cases}     3 x   & +   5y &{} & =  2 \\         x  & -   y     &   & = 10 \end{cases} \) 

Alignment and Complex layouts

The \\  indicates new lines.

The  &  positions determine what gets aligned horizontally.

\(\begin{align}f \colon A &\to B \\x &\mapsto f(x)\end{align}\)

Another example:

 \(\begin{align} C(x_i \ ,\ t_{\mu+1}) = \ &C(x_i \ , \ t_\mu ) \\ &+ D \ {\Delta t \over (\Delta x)^2 } \end{align}\)

Note:  split  works equally well in lieu of align.   Both are provided by the by included amsmath package.

Matrix in running text:

\(\text{In other words}: \bigl(\begin{smallmatrix} a&b \\ c&d \end{smallmatrix} \bigr)\)

 

yields:     \(X \begin {smallmatrix} \phi \\ \longrightarrow \\ \\ \\ \\ \\ \\ \\ \end{smallmatrix} Y\)

In this case, the simpler  X \xrightarrow{\phi} Y  will do a similar job:  \(X \xrightarrow{\phi} Y\)

 

yields:

$$
\begin{array}{ccccccccc}
0 & \xrightarrow{i} & A & \xrightarrow{f} & B & \xrightarrow{q} & C & \xrightarrow{d} & 0 \\
\downarrow & \searrow & \downarrow & \nearrow & \downarrow & \searrow & \downarrow & \nearrow & \downarrow \\
0 & \xrightarrow{j} & D & \xrightarrow{g} & E & \xrightarrow{r} & F & \xrightarrow{e} & 0
\end{array}
$$

Color

\color{red}{x + y}     \(\color{red}{x + y} \)

 

Available colors

To define one's own custom commands

\def  and  \newcommand  are available.

EXAMPLES

yields:

$$ \def\myHearts{\color{purple}{\heartsuit}\kern-2.5pt\color{green}{\heartsuit}} \myHearts $$

More info on \def

 

---

yields:
$$ \newcommand\myHearts[2] {\color{#1}{\heartsuit}\kern-2.5pt\color{#2}{\heartsuit}}
\myHearts{red}{blue}
$$

 

yields:
$$
\newcommand{\bra}[1]{\left<#1\right|}
\newcommand{\ket}[1]{\left|#1\right>}
\newcommand{\bk}[2]{\left<#1\middle|#2\right>}
\newcommand{\bke}[3]{\left<#1\middle|#2\middle|#3\right>}

\bra{x}
\ket{y}
\bk{x}{y}
\bke{x}{y}{z}
$$

 

yields

$$
\newcommand{\ra}[1]{\!\!\!\!\!\!\!\!\!\!\!\!\xrightarrow{\quad#1\quad}\!\!\!\!\!\!\!\!}
\newcommand{\da}[1]{\left\downarrow{\scriptstyle#1}\vphantom{\displaystyle\int_0^1}\right.}
%
\begin{array}{llllllllllll} 0 & \ra{f_1} & A & \ra{f_2} & B & \ra{f_3} & C & \ra{f_4} & D & \ra{f_5} & 0 \\
\da{g_1} & & \da{g_2} & & \da{g_3} & & \da{g_4} & & \da{g_5} & & \da{g_6} \\
0 & \ra{h_1} & 0 & \ra{h_2} & E & \ra{h_3} & F & \ra{h_4} & 0 & \ra{h_5} & 0 \\
\end{array}
$$

More info on \newcommand

Complex expressions with 3-rd party extensions (packages)

One way (not the only one) to load these extensions from within a math expression using the non-standard \require{extension} macro, which allows SKIPPING CONFIGURATION CHANGES / PRE-LOADING (i.e. "Loading Extensions at Run Time".)  For example:

\(\require{\AMScd} \begin{CD} A @<<< B @>>> X\\ @. @| @AAA\\ @. P @= E \end{CD}\)

 

 

Note: if the begin/end statements are left out, the size disparity is reduced!  If \require{\AMScd} is not included, it still works on the webpage, but not in the CK editor!

\(\require{\AMScd} \begin{CD} Normal: \sum_{i=0}^n\int_{a_i}^{b_i}f(x) \quad Large: {\large \sum_{i=0}^n\int_{a_i}^{b_i}f(x) } \quad HUGE: {\huge \sum_{i=0}^n\int_{a_i}^{b_i}f(x) } \end{CD}\)

 

Chemistry

Note:  \ce  stands for "chemical equation"

\(\require{\mhchem} \ce{aA +bB <=> cC + dD}\)

 

 \(\require{\mhchem} \ce{aA +bB <=>[kF][kR] cC + dD}\)

 

\(\require{\mhchem} \ce{CO2 + C ->[k_F] 2 CO}\)

 

\(\require{\mhchem} \ce{Zn^2+  <=>[+ 2OH-][+ 2H+]   $\underset{\text{zinc hydroxide}}{\ce{Zn(OH)2 v}} $  <=>[+ 2OH-][+ 2H+] $\underset{\text{tetrahydroxozincate(II)}}{\ce{[Zn(OH)4]^2-}}$}\)

More info on mhchem