Text Formatting ⇒ managing long equation

[teddy0625]

I have this one very long equation which can not be displayed on one page as it can be seen from the attachment. I want to know how I can display it properly.
Thanks!

Code: Select all

\documentclass[a4paper,12pt,twoside]{book}
\usepackage{amsmath,amssymb,amsfonts,geometry} % Typical maths resource packages
\usepackage{xcolor}                    % For creating coloured text and background
\usepackage{hyperref}                 % For creating hyperlinks in cross references
\usepackage{graphicx}


\newtheorem{theorem}{Theorem}[section]
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{teo}{Theorem}[section]

\usepackage{fancyhdr}
\pagestyle{fancy}
  \renewcommand{\chaptermark}[1]{\markboth{\MakeUppercase{\chaptername \ \thechapter \ \ #1}}{}}
  \fancyhf{}%clear all header and footer fields
    \fancyhead[LO]{\nouppercase{\rightmark}}
    \fancyhead[RE]{\nouppercase{\leftmark}}
       \fancyhead[RO,LE]{\thepage}
\def\chem#1#2{ {{\scriptscriptstyle#1\atop\longrightarrow}\atop{\longleftarrow\atop \scriptscriptstyle#2}} }


\begin{document}
.
.
.
\subsection{Linearization stability parallel flow (Rayleigh equation)}
.
.
.
Now, seek the solution with form $ \overline{\psi}=\phi(y)e^{i\alpha(x-ct)} $ where $ \alpha $ and c are constants (c is complex in general) so continue derivation 
\begin{align*}
\\-\dfrac{\partial}{\partial t}{[-\alpha^{2}\phi(y)+\phi_{yy}(y)]e^{{\textrm{i}}\alpha(x-ct)}}+U(y)\dfrac{\partial}{\partial x}{[-\alpha^{2}\phi(y)+\phi_{yy}(y)e^{{\textrm{i}}\alpha(x-ct)}]}+U_{yy}(y)\dfrac{\partial}{\partial x}[\phi(y)e^{{\textrm{i}}\alpha(x-ct)}]&=0,\\
\end{align*}
\begin{align*}
\\ \alpha c{\textrm{i}}[\phi_{yy}(y)-\alpha^{2}\phi(y)]e^{{\textrm{i}}\alpha(x-ct)}-\alpha {\textrm{i}}U(y)[\phi_{yy}(y)-\alpha^{2}\phi(y)]e^{{\textrm{i}}\alpha(x-ct)}+\alpha {\textrm{i}}U_{yy} (y)\phi(y)e^{{\textrm{i}}\alpha(x-ct)}&=0,\\
\end{align*}
\begin{align*}
\\(c-U(y))(\phi_{yy}(y)-\alpha^{2}\phi(y))+U_{yy}(y)\phi(y)&=0,\\
\end{align*}
\begin{align*}
\\\phi_{yy}(y)-\alpha^{2}\phi(y)+\frac{U_{yy}(y)}{c-U(y)}\phi(y)&=0.\\
\end{align*}
\begin{align*}
\therefore \ \phi_{yy}(y)-\alpha^{2}\phi(y)-\frac{U_{yy}(y)}{U(y)-c}\phi(y)&=0 \\
\end{align*}
With boundary condition it can be written as
\[\left\{ 
\begin{array}{l l}
\phi''(y)-\alpha^{2}\phi(y)-\dfrac{U''(y)}{U(y)-c}\phi(y) \\ \\
\phi(0)=\phi(h)=1\\ 
\end{array} \right. \]
Which is Rayleigh's stability equation where h is usually given as 1.\\

[localghost]

First of all, when using the align* environment, you should use it correctly. Typesetting the equations as shown in the image the equation* environment would be sufficient. In case of too long equations you can decrease the font size temporarily.

Code: Select all

\small
\begin{align*}
  -\frac{\partial}{\partial t}{[-\alpha^{2}\phi(y)+\phi_{yy}(y)]e^{{\text{i}}\alpha(x-ct)}}+U(y)\frac{\partial}{\partial x}{[-\alpha^{2}\phi(y)+\phi_{yy}(y)e^{{\text{i}}\alpha(x-ct)}]}+U_{yy}(y)\frac{\partial}{\partial x}[\phi(y)e^{{\text{i}}\alpha(x-ct)}]&=0,\\
  \alpha c{\textrm{i}}[\phi_{yy}(y)-\alpha^{2}\phi(y)]e^{{\text{i}}\alpha(x-ct)}-\alpha {\text{i}}U(y)[\phi_{yy}(y)-\alpha^{2}\phi(y)]e^{{\textrm{i}}\alpha(x-ct)}+\alpha {\textrm{i}}U_{yy} (y)\phi(y)e^{{\textrm{i}}\alpha(x-ct)}&=0,\\
  (c-U(y))(\phi_{yy}(y)-\alpha^{2}\phi(y))+U_{yy}(y)\phi(y)&=0,
\end{align*}
\normalsize

Best regards
Thorsten¹