Fractions in equation mode

equationsmath-mode

I don't want to double up other questions and this is probably a quick one for somebody that uses math mode more often than me (I pretty much started today)

Can someone help me understand what is wrong with the syntax here?

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{equation} \label{eqn:x}
$\Delta$C$_{i}$ = $(\frac{m^{a}/m^{o}}{C_{i}^{a}/C_{i}^{o}}-1) C_{i}^{o}$   
\end{equation}

\end{document}

The above produces this preview in Sublime Text 3, which is fine and just how I need the equation to look.

But with it came a series of errors, which I assume is because I'm mixing \frac with the equation environment in a bad way somehow or being uneconomic with my notation.

"Display math should end with $$. [ $\Delta]"
"Missing $ inserted. [  $\Delta]"
"LaTeX Error: Bad math environment delimiter. [ \end{equation}]"
"You can't use `\eqno' in horizontal mode. [    \end{equation}]"
"Missing $ inserted. [  \end{equation}]"
"Display math should end with $$. [ \end{equation}]"

I tried for some time to understand where delimiters should go to no avail

Could someone please spare a second to help me learn to do this more sensibly?

Best Answer

TeX has two fundamental ways of processing material. The material can be processed either in text mode or in math mode. TeX's math mode has two main subcategories: inline math mode and display math mode.

One can use $ tokens to initiate and terminate inline math mode while in text mode. However, after \begin{equation}, TeX is in display math mode automatically; while in display math mode, it's an error to try to initiate (or terminate) inline text mode.

What to do? Easy! Just get rid of all six instances of $ in the equation. In addition, I would also tell TeX to enlarge the parentheses, by prefixing \Bigl to ( and \Bigr to ).

Moral of the story? Don't ever ignore TeX's error messages. Just because the program somehow manages to struggle through to the end without crashing completely doesn't mean that it's ok to ignore the error messages.

\documentclass{article}
\usepackage{amsmath}
\begin{document}

\begin{equation} \label{eqn:x}
\Delta C_{i} = \Bigl(\frac{m^{a}/m^{o}}{C_{i}^{a}/C_{i}^{o}}-1\Bigr) C_{i}^{o}   
\end{equation}

\end{document}

Related Solutions

[Tex/LaTex] LatexIt not rendering properly

Latexit will have a preamble and a postamble of its own which you can access through its preferences (Edit > Preferences)

enter image description here

The standard preamble contains a \begin{displaymath} and the postamble \end{displaymath}:

enter image description here

Hence if you add \begin{equation} and \end{equation} in your code, you will get an error:

! LaTeX Error: \begin{document} ended by \end{displaymath}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              

l.11 \end{displaymath}

! Extra \endgroup.
<recently read> \endgroup 

l.11 \end{displaymath}

Remove \begin{equation} and \end{equation}, you get the result:

enter image description here

PS: Since the equations are exported as images from latexit and inserted elsewhere, I feel that it is not a good idea to use equation number (which is inserted by equation environment) and a label. It is better if they are included in the main document. However, for your own reasons if you want them, replace \begin{displaymath} with \begin{equation} in the preamble and \end{displaymath} with \end{equation} in the postamble of latexit.

[Tex/LaTex] Why there is an “missing $ inserted error” in the equation* environment

You shouldn't be using either \begin{equation*} ... \end{equation*} or \[ ... \] inside the columns of a tabular environment. Instead, simply change the column definition of the right-hand column from c to >{$\displaystyle}c<{$}; this will ensure that all cells in the second column will automatically be in math mode.

You have several (syntax) errors in the equations. Also, write \exp and \ln instead of just exp and ln; that way, "exp" and "ln" will be typeset using upright letters.

Also, where possible, avoid using fractional expressions using \frac in the second column; instead, using "inline-style" fractions, e.g., a/b instead of \frac{a}{b}.

\documentclass{article}
\usepackage{mathtools,array}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\newcommand\FWHM{\mathrm{FWHM}}
\begin{document}
\begin{table}[!htb]
\centering
\renewcommand{\arraystretch}{2.75}
\begin{tabular}{|l|>{$\displaystyle}l<{$}|}
\hline
\multicolumn{2}{|c|}{Square Pulse} \\
\hline
Pulse & 
I(t)=
\begin{cases}
1; & \abs{t}\le\tfrac{1}{2}\Delta t_{p}^{\FWHM}\\[1.5ex]
0; & \abs{t}>  \tfrac{1}{2}\Delta t_{p}^{\FWHM}
\end{cases}
 \\
\hline
Autocorrelation & 
A^{(2)}(\tau)=
\begin{cases}
1-\abs*{\tau\big/\Delta\tau_{A}^{\FWHM}}; 
& \abs{\tau}\le\Delta\tau_{A}^{\FWHM}\\[2ex]
0;  & \abs{\tau}>\Delta\tau_{A}^{\FWHM}
\end{cases}
 \\
\hline
Relationship & {\Delta}t_{p}^{\FWHM}=\Delta\tau_{A}^{\FWHM} \\
\hline
 \multicolumn{2}{|c|}{Gaussian Pulse} \\
 \hline
 Pulse & I(t)=\exp\Bigl[-\bigl(2\sqrt{\ln2t}/{\Delta}t_{p}^{\FWHM}\bigr)^2\Bigr] \\ 
\hline
Autocorrelation & 
A^{(2)}(\tau)=\exp\Bigl[-\bigl(2\sqrt{\ln2\tau}/\Delta\tau_{A}^{\FWHM}\bigr)^2\Bigr] \\
\hline
Relationship & 
{\Delta}t_{p}^{\FWHM}=\Delta\tau_{A}^{\FWHM} \\
\hline
 \end{tabular}
\caption{The relationship between the initial pulse and autocorrelation of square pulse and Gaussian pulse}
\label{table AC1}
\end{table}

\end{document}

Addendum: Your table contains lots of vertical and horizontal lines, which actually don't enhance the readability of its contents. You may want to give some thought to giving the table a more "open" look, e.g., by getting rid all vertical lines and most horizontal lines. I hope you will agree that the following table is much more "inviting" to the readers' eye (and brain...).

\documentclass{article}
\usepackage{mathtools,array,booktabs}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}  % "absolute value" macro
\newcommand\FWHM{\mathrm{FWHM}}
\begin{document}
\begin{table}[!htb]
\centering
\renewcommand{\arraystretch}{1.25}
\begin{tabular}{@{}l>{$\displaystyle}l<{$}@{}}
\toprule
\multicolumn{2}{@{}l}{\bfseries Square Pulse} \\
\addlinespace
Pulse & 
I(t)=
\begin{cases}
1; & \abs{t}\le\tfrac{1}{2}\Delta t_{p}^{\FWHM}\\[1ex]
0; & \abs{t}>  \tfrac{1}{2}\Delta t_{p}^{\FWHM}
\end{cases}
 \\
\addlinespace
Autocorrelation & 
A^{(2)}(\tau)=
\begin{cases}
1-\abs*{\tau\big/\Delta\tau_{A}^{\FWHM}}; 
& \abs{\tau}\le\Delta\tau_{A}^{\FWHM}\\[1ex]
0;  & \abs{\tau}>\Delta\tau_{A}^{\FWHM}
\end{cases}
 \\
\addlinespace
Relationship & {\Delta}t_{p}^{\FWHM}=\Delta\tau_{A}^{\FWHM} \\
\midrule
\multicolumn{2}{@{}l}{\bfseries Gaussian Pulse} \\
\addlinespace
Pulse & I(t)=\exp\bigl[-\bigl(2\sqrt{\ln2t}\big/{\Delta}t_{p}^{\FWHM}\bigr)^2\,\bigr] \\ 
\addlinespace
Autocorrelation & 
A^{(2)}(\tau)=\exp\bigl[-\bigl(2\sqrt{\ln2\tau}\big/\Delta\tau_{A}^{\FWHM}\bigr)^2\,\bigr] \\
\addlinespace
Relationship & 
{\Delta}t_{p}^{\FWHM}=\Delta\tau_{A}^{\FWHM} \\
\bottomrule
 \end{tabular}
\caption{Relationship between initial pulse and autocorrelation for square and Gaussian pulses}
\label{table AC1}
\end{table}

\end{document}

Best Answer

Related Solutions

[Tex/LaTex] LatexIt not rendering properly

[Tex/LaTex] Why there is an “missing $ inserted error” in the equation* environment

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