% master: main % format: latex %%-------------------------------------------------------------------------- \part{Mathematical Equations, Figures and Tables} %%-------------------------------------------------------------------------- In a thesis, one may need to write many more equations than simple in-text formula and display formula. In this part, some more involved formula are included and they will be put in the equation like environments. The user should also pay attention to the way the equations being numbered, labeled and cross-referenced. %%-------------------------------------------------------------------------- \chapter{EQUATIONS AND EQUATION ARRAYS} %%-------------------------------------------------------------------------- The following equation (\ref{eq:1}) is in the \textbf{equation} environment and it is labeled, \begin{equation} \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+x}}}}}}} = ? \label{eq:1} \end{equation} \LaTeX\ numbers the equation as long as it is in the equation or eqnarray environment. The following is an un-labeled equation, \LaTeX\ still numbers it \ifAMS \begin{equation} A= \begin{pmatrix} a_{11}&a_{12}&\ldots&a_{1n}\\ a_{21}&a_{22}&\ldots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{m1}&a_{m2}&\ldots&a_{mn} \end{pmatrix} \end{equation} \else \begin{equation} A= \left( \begin{array}{cccc} a_{11}&a_{12}&\ldots&a_{1n}\\ a_{21}&a_{22}&\ldots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{m1}&a_{m2}&\ldots&a_{mn} \end{array} \right) \end{equation} \fi If one does not need to number and label a equation, he can place it inside the math display environment or delimiters, i.e., \textbf{displaymath} environment and \begin{verbatim} \[ ... \] \end{verbatim} or \begin{verbatim} $$ ... $$ \end{verbatim} delimiter pairs, e.g., $$ \left(\frac{\partial^2}{\partial x^2}+ \frac{\partial^2}{\partial y^2}\right)\left|\varphi(x+iy)\right|^2 = 0 $$ and \begin{displaymath} 2\uparrow\uparrow k\mathrel{\mathop=^{\rm def}} 2^{2^{2^{\cdot^{\cdot^{\cdot^2}}}}} \vbox{\hbox{$\Bigr\}\scriptstyle k$}\kern0pt} \end{displaymath} or \[ \prod_{j\ge0}\left(\sum_{k\ge0}a_{jk}z^k\right) =\sum_{n\ge0}z^n\,\left(\sum_ {\stackrel{\scriptstyle k_0,k_1,\ldots\ge0} {\scriptstyle k_0+k_1+\cdots=n}} a_{0k_0}a_{1k_1}\ldots\,\right) \] If there are more than one equation in a group or there are many lines in an equation, one can use the \textbf{eqnarray} environment, but he should pay special attention to those multi-line equations (otherwise all the lines will be numbered) by using \textbf{nonumber} command as shown below, \begin{eqnarray} \left(\int_{-\infty}^\infty e^{-x^2}\,dx\right)^2 & =& \int_{-\infty}^\infty\int_{-\infty}^\infty e^{-(x^2+y^2)}\,dx\,dy \nonumber \\ & =& \int_0^{2\pi}\int_0^\infty e^{-r^2}r\,dr\,d\theta \nonumber \\ & =& \int_0^{2\pi}\left(\left. -\frac{e^{-r^2}}{2} \right|_{r=0}^{\infty}\,\right)\,d\theta \nonumber \\ & =& \pi \end{eqnarray} otherwise \begin{eqnarray} \textstyle\sin18^\circ={\frac{1}{4}}(\sqrt5-1)\\ k=1.38\times10^{-23}\rm\,J/^\circ K. \end{eqnarray} %%-------------------------------------------------------------------------- \chapter{FIGURES AND TABLES} %%-------------------------------------------------------------------------- Figures and tables are essential ingredients in a non-trivial engineering or science thesis. Before the computer typesetting became good enough, these things took authors lots of time to hand-draw. Nowadays, the computer seems to be able to draw any kind of simple and fancy figures and tables. Many users are still computer-generating figures and tables separately from typesetting the thesis, and then cut-and-paste. However, with good packages such as \TeX/\LaTeX, one can avoid this type of waste most of times. In the following, we will see how the figures can be inserted into the thesis. The figure itself is generated otherwise, and the table is produced by \LaTeX\ commands. \section{Figures--Inserting, Captioning and Importing} Shown in Figure~\ref{fig:1} is a figure (Pitt Engineering Thesis Guide Manual has a good definition as for what is called a figure). This Figure is generated by: \begin{verbatim} \begin{figure} \centering \includegraphics[width=3in]{bridge.eps} \caption{The ``Bridge'' image} \label{fig:1} \end{figure} \end{verbatim} \begin{figure}[h] \centering \includegraphics[width=4in]{bridge.eps} \caption{The ``Bridge'' image} \label{fig:1} \end{figure} \texttt{bridge.eps} is a postscript file converted from an image file. Note that figure \ref{fig:1} is also labeled and cross-referenced here. For more details about graphics file inclusion, please refer to \texttt{graphics} package of \LaTeXe. \LaTeXe\ has a few commands to draw simple pictures. Figure \ref{fig:2} shows a picture drawn with \LaTeXe\ commands in the \texttt{picture} environment. The user can read \cite{lp:latex} for details. \begin{figure} \centering \unitlength 0.8in % make unit length to be 0.8 inch \begin{picture}(6,4)(0,0) % picture coordinates 6 in width, 4 in height, % origin 0,0 \put(1.4,2.6){\line(3,-1){3.0}} % draw a straight line at slope -1/3 % starting at (1.4,2.6) of length 3.0 \put(0,0){\vector(1,0){5.5}} \put(0,0){\vector(0,1){3}} \end{picture} \caption{A Picture Drawn with \LaTeX\ Commands}\label{fig:2} \end{figure} \section{Tables-Inserting and Drawing} Tables and figures are inserted labeled and so on in rather similar ways except the caption for a table usually appears on top of the table instead of below that. An example of table is given in Table~\ref{tab:1}. Note also that this table is written in \textbf{minipage} environment. \begin{table} \begin{minipage}[t]{6in} \caption{Text Formatting and Word Processing Packages}\label{tab:1} \begin{center} \begin{tabular}{|l|l|l|} \hline & Scribe \\ \cline{2-2} & \TeX \\ \cline{2-2} Text Formatters\footnote{All the text formatters listed are command-driven}% & \LaTeX \\ \cline{2-2} & troff \\ \hline & WordStar \\ \cline{2-2} Word processors \footnote{All the word processors listed are menu-driven}% & Word Perfect \\ \cline{2-2} & Ms Word \\ \cline{2-2} & MacWrite \\ \hline \end{tabular} \end{center} \end{minipage} \end{table} Note also that Table~\ref{tab:1} is labeled and referenced. It will be listed in the LIST OF TABLES. %%-------------------------------------------------------------------------- \chapter{SPECIAL SYMBOLS} %%-------------------------------------------------------------------------- \TeX\ has pre-defined many useful special symbols, such as the Greek letters, mathematical symbols, accented European letters. The newer version of \TeX\ has even introduced some sets of fonts for some foreign languages. For a thesis writer, the most essential knowledge he needs about the special symbols is Greek letters and mathematical symbols. \section{Greek Letters} In \TeX\ and \LaTeXe\ Greek letters are called by their English names, e.g., alpha, beta. If the first letter is in capital, then \TeX\ outputs a capital Greek letter (but many capital Greek letters coincide with English letters, and hence no commands are designed for them). The commands for all the Greek letters are listed in Table \ref{tab:greek}. Note that Greek letters have to be in math mode, e.g., $\alpha$. \section{Other Mathematical Symbols} Beside the Greek letters there are many more math symbols, for example the Calligraphic letter $\cal F$ which may used for Fourier and $\cal L$ for Laplace. The user can refer to the \LaTeXe\ Manual\cite{lp:latex} pp. 41--50 for more information. Many mathematical symbols are listed in Appendix \ref{sec:mathsym}. \section{Accented European Letters} In the \LaTeXe\ Manual\cite{lp:latex} pp. 38--39, one can find some help as for how typeset accented European letters.