%%% %%% This is the beginning of the actual thesis. If you don't know latex %%% then start with the LaTeX manual by Lamport and another easy %%% reference, like the paperback by Jane Hahn, LaTeX for Everyone, PTI, %%% 1991. See also /sample.tex %%% % Start this dissertation.... % \chapter{Introduction}\label{introduction} % This is a sample LaTeX chapter file as part of our sample thesis. (Version of 2003) % % A '%' character causes TeX to ignore all remaining text on the line, % and is used for comments like this one. \begin{comment} you may also you the comment environment if you include the verbatim package. Then everything contained within the tags is a comment. This is great for commenting out large sections. But is annoying in emacs in that it is not color code as a comment. \end{comment} % % \section{The Sample.tex file} % Produces section heading. % level 2 % % Lower -level sections are begun with similar % \subsection and \subsubsection commands. This sample is {\bf not} meant to be a \LaTeX tutorial, but demonstrate the use of the msudoc.cls and associated style files. Help on \LaTeX, emacs, and many of the packages mentioned within this sample are available at: www.math.montana.edu/help/. \begin{comment} One more note on emacs use: if you 'right-click' on the '(LaTeX Fill)' in the minor menu, you can select 'flyspell', which turns on the on the fly spell correcting. \end{comment} In order to use this class file you will need, as a minimum, to copy the following files from this directory to your own thesis directory: \begin{verbatim} msudoc.cls mystyle.sty thesis.tex \end{verbatim} and probably the following to follow all the examples: \begin{verbatim} chap1.tex chap2.tex chap3.tex abstract.tex acknowledgements.tex thesis.bib \end{verbatim} and the {\it figs} subdirectory. You should then edit the {\it graphicspath} in thesis.tex accordingly. Issue the following commands: \begin{verbatim} >latex thesis (this creates the .dvi file) >bibtex thesis (followed by two more 'latex thesis' will create the dvi and the bibliography.) \end{verbatim} If you wish to create a .pdf file then: \begin{verbatim} > dvips -Ppdf thesis.dvi -o thesis.ps (followed by) > ps2pdf -dPDFsettings=/prepress thesis.ps \end{verbatim} This will create a .pdf file with all level one fonts and clean .eps files. This is certainly not the only way of creating a .pdf file (one may also use pdflatex) but is one method that does work. One may also issue commands from within emacs, if that is the text editor you choose to use to edit the .tex files. Please note the many comments in all the various .tex files for further information. \subsection{Ordinary Text} % level 3 The ends of words and sentences are marked by spaces. It doesn't matter how many spaces you type; one is as good as 100. The end of a line counts as a space.\footnote{ This is a sample input file. Comparing it with the output it generates can show you how to produce a simple document of your own. } One or more blank lines denote the end of a paragraph. Since any number of consecutive spaces are treated like a single one, the formatting of the input file makes no difference to \LaTeX, but it makes a difference to you. When you use \LaTeX, % The \LaTeX command generates the LaTeX logo. making your input file as easy to read as possible will be a great help as you write your document and when you change it. This sample file shows how you can add comments to your own input file. Because printing is different from typewriting, there are a number of things that you have to do differently when preparing an input file than if you were just typing the document directly. Quotation marks like ``this'' have to be handled specially, as do quotes within quotes: ``\,`this' % \, separates the double and single quote. is what I just wrote, not `that'\,.'' Dashes come in three sizes: an intra-word dash, a medium dash for number ranges like 1--2, and a punctuation dash---like this. A sentence-ending space should be larger than the space between words within a sentence. You sometimes have to type special commands in conjunction with punctuation characters to get this right, as in the following sentence. Gnats, gnus, etc.\ % `\ ' makes an inter-word space. all begin with G\@. % \@ marks end-of-sentence punctuation. You should check the spaces after periods when reading your output to make sure you haven't forgotten any special cases. Generating an ellipsis \ldots\ % `\ ' needed because TeX ignores spaces after % command names like \ldots made from \ + letters. % % Note how a `%' character causes TeX to ignore the % end of the input line, so these blank lines do not % start a new paragraph. with the right spacing around the periods requires a special command. \LaTeX\ interprets some common characters as commands, so you must type special commands to generate them. These characters include the following: \$ \& \% \# \{~and~\}. In printing, text is emphasized by using an {\em italic\/} % The \/ command produces the tiny extra space that % should be added between a slanted and a following % unslanted letter. type style. \begin{em} A long segment of text can also be emphasized in this way. Text within such a segment given additional emphasis with\/ {\em Roman} type. Italic type loses its ability to emphasize and become simply distracting when used excessively. \end{em} It is sometimes necessary to prevent \LaTeX\ from breaking a line where it might otherwise do so. This may be at a space, as between the ``Mr.'' and ``Jones'' in ``Mr.~Jones,'' % ~ produces an unbreakable interword space. or within a word---especially when the word is a symbol like \mbox{\em itemnum\/} that makes little sense when hyphenated across lines. Footnotes\footnote{This is an example of a footnote.} pose no problem. \LaTeX\ is good at typesetting mathematical formulas like $ x-3y = 7 $ or $$ a_{1} > x^{2n} / y^{2n} > x'. $$ Remember that a letter like $x$ % $ ... $ and \( ... \) are equivalent is a formula when it denotes a mathematical symbol, and should be treated as one. \subsection{Displayed Text} Text is displayed by indenting it from the left margin. \subsubsection{Quotations} Quotations are commonly displayed. There are short quotations \begin{quote} This is a short a quotation. It consists of a single paragraph of text. There is no paragraph indentation. \end{quote} and longer ones. \begin{quotation} This is a longer quotation. It consists of two paragraphs of text. The beginning of each paragraph is indicated by an extra indentation. This is the second paragraph of the quotation. It is just as dull as the first paragraph. \end{quotation} \subsubsection{Lists} Another frequently-displayed structure is a list. The following is an example of an {\em itemized} list. \begin{quote} \begin{itemize} \item This is the first item of an itemized list. Each item in the list is marked with a ``tick''. The document style determines what kind of tick mark is used. \item This is the second item of the list. It contains another list nested inside it. The inner list is an {\em enumerated} list. \begin{enumerate} \item This is the first item of an enumerated list that is nested within the itemized list. \item This is the second item of the inner list. \LaTeX\ allows you to nest lists deeper than you really should. \end{enumerate} This is the rest of the second item of the outer list. It is no more interesting than any other part of the item. \item This is the third item of the list. \end{itemize} \end{quote} You can even display poetry. \begin{quote} \begin{quote} \begin{verse} There is an environment for verse \\ % The \\ command separates lines Whose features some poets will curse. % within a stanza. % One or more blank lines separate stanzas. For instead of making\\ Them do {\em all\/} line breaking, \\ It allows them to put too many words on a line when they'd rather be forced to be terse. \end{verse} \end{quote} \end{quote} \subsubsection{Mathematics} Mathematical formulas may also be displayed. A displayed formula is one-line long; multiline formulas require special formatting instructions. \[ x' + y^{2} = z_{i}^{2}\] Don't start a paragraph with a displayed equation, nor make one a paragraph by itself. \section{More examples} Equations like $\gamma = 0$ that don't need numbering may be set inline by the coding \verb"$\gamma = 0$" or displayed by \par \begin{verbatim} $$ \gamma = 0. $$ \end{verbatim} \par Numbered equations are set as shown in the next paragraph. They use the theorem environments defined in \verb"thesis.sty": \par \begin{verbatim} \newtheorem{thrm}{Theorem} \newtheorem{lem}[thrm]{Lemma} \newtheorem{cor}[thrm]{Corollary} \newtheorem{rem}[thrm]{Remark} \newtheorem{defn}[thrm]{Definition} \newtheorem{exmpl}[thrm]{Example} \end{verbatim} \par The Gelfand problem is the following elliptic boundary value problem: % % The equation-array feature in LaTeX is a bad idea. For centered % numbers you should set your own equations and arrays as follows: % \def\dd{\displaystyle} \begin{equation}\label{gelfand} \begin{array}{rl} \dd \Delta u + \lambda e^u = 0, & \dd u\in \Omega,\\[8pt] % add 8pt extra vertical space. 1 line=23pt \dd u=0, & \dd u\in\partial\Omega. \end{array} \end{equation} The previous equation had a label. It may be referenced as equation~(\ref{gelfand}). % % \section{History of the Gelfand problem} % % According to Bebernes and Eberly \cite[p.46]{bebernes:mpc89}, Gelfand was ``the first to make an in-depth study'' of (\ref{gelfand}). Following this statement they briefly outline the history of the Gelfand problem. \par % Quotes need to forced single space: \begin{singlespace} \begin{quote} For dimension $n=1$, Liouville~\cite{liouville:edp53} first studied and found an explicit solution in 1853. For $n=2$, Bratu~\cite{bratu:ein14} found an explicit solution in 1914. Frank-Kamenetski~\cite{frank:dhe55} rediscovered these results in his development of thermal explosion theory. Joseph and Lundgren~\cite{joseph:qdp73} gave an elementary proof via phase plane analysis of the multiple existence of solutions for dimensions $n\geq 3$. \end{quote} \end{singlespace} \par % Several things to note here. Latex sometimes breaks equations, this % can be restricted by the samepage command. The spacing in the array % mode is also important for some structures. From Zeidler~\cite{zeidler:nfa88IIa}: {\samepage \begin{equation}\label{station} \begin{array}{rcll} \dd\mbox{div } j& = &\dd f, &\dd x\in\Omega ,\\[8pt] \dd u& = & \dd g_1, & \dd x\in\partial\Omega_1 , \\[8pt] \dd j\nu & = & \dd g_2, & \dd x\in\partial\Omega_2 , \end{array} \end{equation} } where \begin{equation}\label{current} j = h(|\nabla u|^2)\nabla u \end{equation} and $\Omega$ is a bounded domain in ${\Bbb R}^n$ with smooth boundary $\partial\Omega = \overline{\partial\Omega_1}\cup \overline{\partial\Omega_2}$, $\partial\Omega_1 \cap \partial\Omega_2 = \emptyset$ and $\nu$ is the normal vector to $\partial\Omega$. % There is a lot of shorthand set up for structures, for example a % lemma: \begin{lemma} Assuming that $\partial\Omega_2 = \emptyset$ and that $h(t) = 1$, we have $$ \begin{array}{lr} \dd\Delta u = f, & \dd x\in\Omega ,\\[8pt] \dd u = g_1, & \dd x\in\partial\Omega . \end{array} $$ \end{lemma} % another ... \begin{cor} If $g_2 = 0$ then $$ \begin{array}{lr} \dd \Delta u = f, & \dd x\in\Omega ,\\[8pt] \dd u = 0, & \dd x\in\partial\Omega . \end{array} $$ \end{cor} % Look in thesis.sty for more structures. \section{Fundamental results} The investigation of the Gelfand problem begins with examining the ..... (this paragraph continues for many lines). % % This is an example of a big ugly technical theorem. It has two % levels of lists, referencing, citations and names. % \begin{thm}[Joseph-Lundgren~\cite{joseph:qdp73}] Boundary value problem (\ref{gelfand}) has positive radial solutions $u$ on the unit ball which depend on $n$ and $\lambda$ in the following manner. \begin{enumerate} \item For $n=1,2$, there exists $\lambda^* >0$ such that \begin{enumerate} \item for $0< \lambda < \lambda^*$ there are two positive solutions, \item for $\lambda =\lambda^*$ there is a unique solution, and \item for $\lambda > \lambda^*$ there are no solutions. \end{enumerate} \item For $3\leq n \leq 9$, let $\overline{\lambda}=2(n-2)$; then there exist positive constants $\lambda_*$, $\lambda^*$ with $0< \lambda_* < \overline{\lambda} < \lambda^*$, such that \begin{enumerate} \item for $\lambda = \lambda^*$ there is a unique solution, \item for $\lambda > \lambda^*$ there are no solutions, \item for $\lambda = \overline{\lambda}$ there is a countably infinite number of solutions, \item for $\lambda \in (\lambda_*,\lambda^*)$, $\lambda \neq \overline{\lambda}$, there is a finite number of solutions, \item for $\lambda < \lambda_*$ there is a unique solution. \end{enumerate} \item For $n\geq 10$, let $\lambda^* = 2(n-2)$ then \begin{enumerate} \item for $\lambda \geq \lambda^*$ there are no solutions, \item for $\lambda \in (0,\lambda^*)$ there is a unique solution. \end{enumerate} \end{enumerate} \end{thm}