[Tex/LaTex] Begin Array in LaTex

equations

enter image description here

Tried the equation in the image below with the following codes, but was encountering errors. Please can anybody be kind enough to help. Thanks.

\begin{array}
{p^'}_0\left( t \right) =  - \lambda {p_0}\left( t \right) + \mu {p_1}\left( t \right),\\
{p^'}_j\left( t \right) = \lambda {p_{j - 1}}\left( t \right) - \left( {\lambda  + j\mu } \right){p_j}\left( t \right) + \mu \left( {j + 1} \right){p_{j + 1}}\left( t \right)
\end{array}

Best Answer

there are several problems with the code used:

array must be inside a math environment; this could be fixed by enclosing it in \[ ... \]
the alignment within the array must be specified; for this, \begin{array}{l} would work.
the primes (input as apostrophes) are defined to be superscripts, so the explicit ^ is unwanted.
the \left ... \right for the parentheses isn't needed anywhere, since everything within them is "normal" size
extra grouping with braces isn't needed except around the multi-element subscripts

it would be equally appropriate, and perhaps simpler, to use the align* environment from amsmath:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{align*}
p'_0 (t) &= -\lambda p_0 (t) + \mu p_1 (t),\\
p'_j (t) &=  \lambda p_{j-1} (t) - (\lambda + j\mu) p_j (t) + \mu (j+1) p_{j+1} (t)
\end{align*}
\end{document}

output of example code

Related Solutions

[Tex/LaTex] Multi-line Equations

Besides the balancing issue associated to the use of \left, \right, your expression can be improved introducing some modifications:

Using \left( ... \right) for the inner expressions produces delimiters that are too big and introduce some additional horizontal space that it's superfluous in this particular case, so I think that it's better to use just (...).
You need to use +{} so that the ending plus sign in the first line is correctly trated as an operator; analogously, you need to use {}+ for the first plus sign in the second line.
Instead of using \left[, \right. in the first line and \right., \left] in the second line, I would suggest you to use \bigl[, \bigr] which don't need to be balanced in each line and produce better sized delimiters in most cases.
The plus sign in the second line must be (according to some standard typographical rules for displayed math expressions) two-ems to the right of the alignment point.

In the following code I include, for comparison, your code (with the balancing problem solved) and then the code implementing my suggestions:

\documentclass[12pt]{article}
\usepackage[margin=2cm]{geometry}% just for the example
\usepackage{amsmath}

\begin{document}

\begin{equation}
\begin{split}
MSE_{II}(\overline{y}_{CST}) &= MSE_{I}(\overline{y}_{CST})
  +\overline{Y}^{2}\left[ \left( c_{2}^{2}+2c_{1}c_{3} \right)V_{4,\, 0}+2c_{1}c_{2}V_{3,\,0}
  +2\left(2c_{1}c_{2}+c_{3}\right)V_{3,\, 1} + \right. \\ 
& \left. + 2 \left(c_{1}^{2}+c_{2} \right)V_{2,\, 1}+ \left(c_{1}^{2}+2c_{2} \right)V_{2,\, 2} 
 + {2c_{1}V_{1,\, 2}}  \right]
\end{split}
\end{equation}

\begin{equation}
\begin{split}
MSE_{II} ( \overline{y}_{CST} ) &= MSE_{I} ( \overline{y}_{CST} )
  + \overline{Y}^{2} \bigl[ (c_{2}^{2} + 2c_{1}c_{3} ) V_{4,\, 0} + 2c_{1}c_{2} V_{3,\,0}
  + 2 ( 2c_{1}c_{2} + c_{3} ) V_{3,\, 1} +{} \\ 
&\qquad {}+ 2 ( c_{1}^{2} + c_{2} )V_{2,\, 1} + ( c_{1}^{2} + 2c_{2} ) V_{2,\, 2} 
 + {2c_{1}V_{1,\, 2}} \bigr]
\end{split}
\end{equation}

\end{document}

enter image description here

[Tex/LaTex] mathpazo package and changing font within \begin{equation} … \end{equation}

Just reset \rmdefault to the definition it had before mathpazo was loaded.

\documentclass{article}

\let\temp\rmdefault
\usepackage{mathpazo}
\let\rmdefault\temp

\begin{document}
The quick brown fox jumps over the lazy dog.
\[
\int_a^b f(x) dx
\]
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] Multi-line Equations

[Tex/LaTex] mathpazo package and changing font within \begin{equation} … \end{equation}

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