Formula examples

From DIYWiki

Examples of how to use mathematical expressions, and formula in this wiki.


Chemical Equations

<ce>C6H5-CHO</ce>

<ce>\mathit{A} ->[\ce{+H2O}] \mathit{B}</ce>

<ce>{SO4^{2-}} + Ba^2+ -> BaSO4 v</ce>

<math chem>A \ce{->[\ce{+H2O}]} B</math>

<ce>H2O</ce>

<ce>Sb2O3</ce>

<ce>H+</ce>

<ce>CrO4^2-</ce>

<ce>AgCl2-</ce>

<ce>[AgCl2]-</ce>

<ce>Y^{99}+</ce>

<ce>Y^{99+}</ce>

<ce>H2_{(aq)}</ce>

<ce>NO3-</ce>

<ce>(NH4)2S</ce>

Quadratic Polynomial



<math>ax^2 + bx + c = 0</math>

Quadratic Polynomial (Force PNG Rendering)



<math>ax^2 + bx + c = 0\,</math>

Quadratic Formula



<math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>

Tall Parentheses and Fractions



<math>2 = \left(
 \frac{\left(3-x\right) \times 2}{3-x}
 \right)</math>

 <math>S_{\text{new}} = S_{\text{old}} - \frac{ \left( 5-T \right) ^2} {2}</math>
 

Integrals



<math>\int_a^x \!\!\!\int_a^s f(y)\,dy\,ds
 = \int_a^x f(y)(x-y)\,dy</math>

Summation



<math>\sum_{m=1}^\infty\sum_{n=1}^\infty\frac{m^2\,n}
 {3^m\left(m\,3^n+n\,3^m\right)}</math>

Differential Equation



<math>u'' + p(x)u' + q(x)u=f(x),\quad x>a</math>

Complex numbers



<math>|\bar{z}| = |z|,
 |(\bar{z})^n| = |z|^n,
 \arg(z^n) = n \arg(z)</math>

Limits



<math>\lim_{z\rightarrow z_0} f(z)=f(z_0)</math>

Integral Equation



<math>\phi_n(\kappa) =
 \frac{1}{4\pi^2\kappa^2} \int_0^\infty
 \frac{\sin(\kappa R)}{\kappa R}
 \frac{\partial}{\partial R}
 \left[R^2\frac{\partial D_n(R)}{\partial R}\right]\,dR</math>

Example



<math>\phi_n(\kappa) = 
 0.033C_n^2\kappa^{-11/3},\quad
 \frac{1}{L_0}\ll\kappa\ll\frac{1}{l_0}</math>

Continuation and cases



<math>
 f(x) =
 \begin{cases}
 1 & -1 \le x < 0 \\
 \frac{1}{2} & x = 0 \\
 1 - x^2 & \mbox{otherwise}
 \end{cases}
 </math>

Prefixed subscript



 <math>{}_pF_q(a_1,\dots,a_p;c_1,\dots,c_q;z)
 = \sum_{n=0}^\infty
 \frac{(a_1)_n\cdots(a_p)_n}{(c_1)_n\cdots(c_q)_n}
 \frac{z^n}{n!}</math>

Fraction and small fraction


<math> \frac {a}{b}\  \tfrac {a}{b} </math>

Alternate layout for expressions using math Template

This layout renders simpler expressions using HTML rather than the full blown rendering of the <math> tag. E.g:

xn + yn = 1
{{math|1=''x''<sup>''n''</sup> + ''y''<sup>''n''</sup> {{=}} 1}}