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January 3, 2014 09:12
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| ----tex---- | |
| %Start, font settings, packages | |
| %!TEX TS-program = xelatex | |
| %!TEX encoding = UTF-8 Unicode | |
| \documentclass[a4paper]{report} | |
| \usepackage{amsmath,amsfonts,amssymb,mathtools,mathdots,mathptmx} | |
| \usepackage{letltxmacro,nicefrac,xfrac} | |
| \usepackage{fontspec,xltxtra,xunicode,color,textcomp,hyperref,graphicx} | |
| \usepackage[italian]{babel} | |
| \usepackage{marginnote,thmtools} | |
| \usepackage[top=2cm, bottom=3.5cm, outer=4cm, inner=4cm, marginparsep=0.7cm, marginparwidth=1.5cm]{geometry} | |
| \setmathrm{Times New Roman} | |
| \setmathsf{Times New Roman} | |
| \setmathtt{Times New Roman} | |
| \setboldmathrm[BoldFont={Optima ExtraBlack}]{Optima Bold} | |
| \defaultfontfeatures{Mapping=tex-text} | |
| \setromanfont{Times New Roman} | |
| \setsansfont{Times New Roman} | |
| \setmonofont{Helvetica} | |
| \newfontfamily{\vrb}{Helvetica} | |
| \newfontfamily{\Ak}{Akkadian}% | |
| \newfontfamily{\mapu}{Arial Unicode MS} | |
| \newfontfamily{\Ar}{Geeza Pro} | |
| \newfontfamily{\Chs}{STSong} | |
| \newfontfamily{\Cht}{PMingLiU} | |
| \newfontfamily{\Ja}{MS Mincho} | |
| \newfontfamily{\Ru}{Times New Roman} | |
| \newfontfamily{\Gr}{Times New Roman} | |
| \newfontfamily{\He}{Times New Roman} | |
| \newfontfamily{\Ko}{Batang} | |
| \newfontfamily{\Ind}{Devanagari MT} | |
| \newfontfamily{\Mal}{Malayalam MN} | |
| \newfontfamily{\Sinh}{Free Sans} | |
| \newfontfamily{\Thai}{Free Serif} | |
| \newcommand{\€}{\Gr{ }} | |
| \newcommand{\mbold}{\mathbf} | |
| \newcommand{\tbold}{\textbf} | |
| \newcommand{\ital}{\textit} | |
| \newcommand{\CAPS}{\textsc} | |
| \newcommand{\slant}{\textsl} | |
| \newcommand{\bemph}[1]{\tbold{\emph{#1}}} | |
| %All-notes commands | |
| %%Greek letters | |
| \newcommand{\bag}{\alpha} | |
| \newcommand{\ag}{\scb{0.85}[0.85]{$\alpha$}} | |
| \newcommand{\eag}{\expsc{\ag}} | |
| \newcommand{\bbg}{\beta} | |
| \newcommand{\bg}{\tallsc{\bbg}} | |
| \newcommand{\ebg}{\expsc{\bbg}} | |
| \newcommand{\bgg}{\gamma} | |
| \let\oldgg\gg% | |
| \renewcommand{\gg}{\normsc{\bgg}} | |
| \newcommand{\egg}{\expsc{\bgg}} | |
| \newcommand{\bdg}{\delta} | |
| \newcommand{\dg}{\tallsc{\bdg}} | |
| \newcommand{\edg}{\expsc{\bdg}} | |
| \newcommand{\beg}{\varepsilon} | |
| \newcommand{\eg}{\normsc{\beg}} | |
| \newcommand{\eeg}{\expsc{\beg}} | |
| \newcommand{\bzg}{\zeta} | |
| \newcommand{\zg}{\tallsc{\bzg}} | |
| \newcommand{\ezg}{\expsc{\bzg}} | |
| \newcommand{\bhg}{\eta} | |
| \newcommand{\hg}{\normsc{\bhg}} | |
| \newcommand{\ehg}{\expsc{\bhg}} | |
| \newcommand{\bqg}{\theta} | |
| \newcommand{\qg}{\scb{0.95}[0.95]{$\bqg$}} | |
| \newcommand{\eqg}{\scb{0.7}[0.7]{$\bqg$}} | |
| \newcommand{\biog}{\iota} | |
| \newcommand{\ig}{\normsc{\biog}} | |
| \newcommand{\eig}{\expsc{\biog}} | |
| \newcommand{\bkg}{\kappa} | |
| \newcommand{\kg}{\normsc{\bkg}} | |
| \newcommand{\ekg}{\expsc{\bkg}} | |
| \let\oldlg\lg% | |
| \newcommand{\blg}{\lambda} | |
| \renewcommand{\lg}{\tallsc{\blg}} | |
| \newcommand{\elg}{\expsc{\blg}} | |
| \newcommand{\bmg}{\mu} | |
| \newcommand{\mg}{\normsc{\bmg}} | |
| \newcommand{\emg}{\expsc{\bmg}} | |
| \let\oldng\ng% | |
| \newcommand{\bng}{\nu} | |
| \renewcommand{\ng}{\normsc{\bng}} | |
| \newcommand{\eng}{\expsc{\bng}} | |
| \newcommand{\bjg}{\xi} | |
| \newcommand{\jg}{\tallsc{\jg}} | |
| \newcommand{\ejg}{\expsc{\jg}} | |
| \newcommand{\bog}{\omicron} | |
| \newcommand{\og}{\scb{0.96}[0.96]{$\bog$}} | |
| \newcommand{\eog}{\scb{0.72}[0.72]{$\bog$}} | |
| \newcommand{\bpg}{\pi} | |
| \newcommand{\pg}{\normsc{\bpg}} | |
| \newcommand{\epg}{\expsc{\bpg}} | |
| \newcommand{\brg}{\rho} | |
| \newcommand{\rg}{\normsc{\brg}} | |
| \newcommand{\erg}{\expsc{\brg}} | |
| \newcommand{\bsg}{\sigma} | |
| \newcommand{\sg}{\normsc{\bsg}} | |
| \newcommand{\esg}{\expsc{\bsg}} | |
| \newcommand{\btg}{\tau} | |
| \newcommand{\tg}{\tallsc{\btg}} | |
| \newcommand{\etg}{\expsc{\btg}} | |
| \newcommand{\bug}{\upsilon} | |
| \newcommand{\ug}{\normsc{\bug}} | |
| \newcommand{\eug}{\expsc{\bug}} | |
| \newcommand{\bfg}{\varphi} | |
| \newcommand{\fg}{\normsc{\bfg}} | |
| \newcommand{\efg}{\expsc{\bfg}} | |
| \newcommand{\bxg}{\chi} | |
| \newcommand{\xg}{\normsc{\bxg}} | |
| \newcommand{\exg}{\expsc{\bxg}} | |
| \newcommand{\byg}{\psi} | |
| \newcommand{\yg}{\normsc{\byg}} | |
| \newcommand{\eyg}{\expsc{\byg}} | |
| \newcommand{\bwg}{\omega} | |
| \newcommand{\wg}{\normsc{\bwg}} | |
| \newcommand{\ewg}{\expsc{\bwg}} | |
| \newcommand{\vr}{\varrho} | |
| \newcommand{\vs}{\varsigma} | |
| \newcommand{\vq}{\vartheta} | |
| \newcommand{\luneps}{\epsilon}%Apparently there is no difference between varepsilon and epsilon which IS strange as I had seen it before. | |
| %A good scaling for Greek CAPS is 0.96. | |
| \newcommand{\Gg}{\Gamma} | |
| \newcommand{\Dg}{\Delta} | |
| \newcommand{\Qg}{\Theta} | |
| \newcommand{\Lg}{\Lambda} | |
| \newcommand{\Jg}{\Xi} | |
| \newcommand{\Pg}{\Pi} | |
| \newcommand{\Sg}{\Sigma} | |
| \newcommand{\Fg}{\Phi} | |
| \newcommand{\Yg}{\Psi} | |
| \newcommand{\Wg}{\Omega} | |
| \newcommand{\dig}{\digamma} | |
| %%Mathbb letters | |
| \newcommand{\A}{\mathbb A} | |
| \newcommand{\Bm}{\mathbb B} % | |
| \newcommand{\Cm}{\mathbb C} | |
| \newcommand{\D}{\mathbb D} | |
| \newcommand{\E}{\mathbb E} | |
| \newcommand{\F}{\mathbb F} | |
| \newcommand{\Gm}{\mathbb G} % | |
| \newcommand{\Hm}{\mathbb H} % | |
| \newcommand{\I}{\mathbb I} | |
| \newcommand{\J}{\mathbb J} | |
| \newcommand{\K}{\mathbb K} | |
| \newcommand{\Lm}{\mathbb L} % | |
| \newcommand{\Mm}{\mathbb M} % | |
| \newcommand{\N}{\mathbb N} | |
| \newcommand{\Om}{\mathbb O} % | |
| \newcommand{\Pm}{\mathbb P} % | |
| \newcommand{\Q}{\mathbb Q} | |
| \newcommand{\R}{\mathbb R} | |
| \newcommand{\Sm}{\mathbb S} % | |
| \newcommand{\Tm}{\mathbb T} % | |
| \newcommand{\Um}{\mathbb U} % | |
| \newcommand{\V}{\mathbb V} | |
| \newcommand{\W}{\mathbb W} | |
| \newcommand{\X}{\mathbb X} | |
| \newcommand{\Y}{\mathbb Y} | |
| \newcommand{\Z}{\mathbb Z} | |
| %%Hebrew | |
| \newcommand{\alef}{\aleph} | |
| \newcommand{\bet}{\beth} | |
| %%Set theory | |
| \newcommand{\sps}{\supset} | |
| \newcommand{\spse}{\supseteq} | |
| \newcommand{\sbs}{\subset} | |
| \newcommand{\sbse}{\subseteq} | |
| \newcommand{\nsps}{\not\supset} | |
| \newcommand{\nspse}{\not\supseteq} | |
| \newcommand{\nsbs}{\not\subset} | |
| \newcommand{\nsbse}{\not\subseteq} | |
| \newcommand{\nin}{\not \in} | |
| \newcommand{\nni}{\not \ni} | |
| \newcommand{\bun}{\displaystyle\bigcup} | |
| \newcommand{\bint}{\displaystyle\bigcap} | |
| %%Operators | |
| \DeclareMathOperator{\spam}{span} | |
| \newcommand{\spn}{\spam} | |
| \DeclareMathOperator{\re}{Re} | |
| \DeclareMathOperator{\im}{Im} | |
| \DeclareMathOperator{\sgn}{sgn} | |
| \DeclareMathOperator{\cof}{cof} | |
| \DeclareMathOperator{\graf}{graf} | |
| \newcommand{\Graf}[1]{\graf\pa{#1}} | |
| \DeclareMathOperator{\Mat}{Mat} | |
| \DeclareMathOperator{\mis}{mis}% | |
| \DeclareMathOperator{\diam}{diam}% | |
| \DeclareMathOperator{\MCDo}{M.C.D.} | |
| \newcommand{\MCD}[1]{\MCDo\pa{#1}} | |
| \DeclareMathOperator{\mcmo}{m.c.m.} | |
| \newcommand{\mcm}[1]{\mcmo\pa{#1}} | |
| \DeclareMathOperator{\mcdo}{m.c.d.} | |
| \newcommand{\mcd}[1]{\mcdo\pa{#1}} | |
| \DeclareMathOperator{\kerr}{ker} | |
| %%General Maths | |
| %%%[Fractions and similar | |
| \newcommand{\fr}{\dfrac} | |
| \newcommand{\bnm}{\binom} | |
| \newcommand{\of}[2]{\nicefrac{^{#1}}{_{#2}}} | |
| \newcommand{\mf}[2]{^{#1}\scb{0.5}[1]{/}_{#2}} | |
| \newcommand{\dfr}[2]{\dsi{\fr{#1}{#2}}} | |
| \newcommand{\dbfr}[2]{\dsib{\fr{#1}{#2}}} | |
| %] | |
| %%%[Relational Operators and other undeclared Operators | |
| \newcommand{\grad}{\nabla} | |
| \newcommand{\pd}{\partial} | |
| \renewcommand{\~}{\sim} | |
| \newcommand{\dsim}{\approx} | |
| \newcommand{\per}{\cdot} | |
| \newcommand{\rad}{\sqrt} | |
| \newcommand{\cng}{\equiv} | |
| \newcommand{\ncng}{\not\equiv} | |
| \newcommand{\omeo}{\cong} | |
| \newcommand{\nomeo}{\ncong} | |
| \newcommand{\prop}{\propto} | |
| \newcommand{\dsum}{\displaystyle\sum} | |
| \newcommand{\dprod}{\displaystyle\prod} | |
| \newcommand{\dlim}{\displaystyle\lim} | |
| \newcommand{\dint}{\displaystyle\int\limits} | |
| \newcommand{\diint}{\displaystyle\iint\limits} | |
| \newcommand{\diiint}{\displaystyle\iiint\limits} | |
| \newcommand{\diiiint}{\displaystyle\iiiint\limits} | |
| \newcommand{\didotsiint}{\displaystyle\idotsint\limits} | |
| \newcommand{\dmin}{\displaystyle\min} | |
| \newcommand{\dmax}{\displaystyle\max} | |
| \newcommand{\dsup}{\displaystyle\sup} | |
| \newcommand{\dinf}{\displaystyle\inf} | |
| \newcommand{\x}{\times} | |
| \newcommand{\ssm}{\smallsetminus} | |
| \newcommand{\xint}{\dint\limits} | |
| \newcommand{\xints}[2]{\xint_{#1}^{#2}} | |
| \newcommand{\xiint}{\di\iint\limits} | |
| \newcommand{\xiints}[2]{\xiint_{#1}^{#2}} | |
| \newcommand{\xiiint}{\di\iiint\limits} | |
| \newcommand{\xiiints}[2]{\xiiint_{#1}^{#2}} | |
| \newcommand{\xiiiint}{\di\iiiint\limits} | |
| \newcommand{\xiiiints}[2]{\xiiiint_{#1}^{#2}} | |
| \newcommand{\xidotsint}{\di\idotsint\limits} | |
| \newcommand{\xidotsints}[2]{\xidotsint_{#1}^{#2}} | |
| \newcommand{\eval}[2]{\scb{0.5}[1]{$\fvb$}_{#1}^{#2}} | |
| \newcommand{\dd}{\mathrm{d}} | |
| \LetLtxMacro{\oldsqrt}{\sqrt} % makes all sqrts closed | |
| \renewcommand{\sqrt}[1][\ ]{% | |
| \def\DHLindex{#1}\mathpalette\DHLhksqrt} | |
| \def\DHLhksqrt#1#2{% | |
| \setbox0=\hbox{$#1\oldsqrt[\DHLindex]{#2\,}$}\dimen0=\ht0 | |
| \advance\dimen0-0.2\ht0 | |
| \setbox2=\hbox{\vrule height\ht0 depth -\dimen0}% | |
| {\box0\lower0.71pt\box2}} | |
| %%%[Arrows above, below and beside | |
| \newcommand{\vct}{\overrightarrow} | |
| \newcommand{\sv}{\underrightarrow} | |
| \newcommand{\iv}{\overleftarrow} | |
| \newcommand{\isv}{\underleftarrow} | |
| \newcommand{\sse}{\Longleftrightarrow} | |
| \newcommand{\slse}{\Longleftarrow} | |
| \newcommand{\hla}{\hookleftarrow} | |
| \newcommand{\hra}{\hookrightarrow} | |
| \newcommand{\ra}{\xrightarrow} | |
| \newcommand{\la}{\xleftarrow} | |
| \newcommand{\bra}{\xRightarrow} | |
| \newcommand{\bla}{\xLeftrightarrow} | |
| \newcommand{\xhla}{\xhookleftarrow} | |
| \newcommand{\xhra}{\xhookrightarrow} | |
| \newcommand{\xmaps}{\xmapsto} | |
| %] | |
| %%%[Logical symbols and quantifiers | |
| \newcommand{\3}{\exists} | |
| \newcommand{\ex}{\exists} | |
| \newcommand{\nex}{\nexists} | |
| \newcommand{\et}{\wedge} | |
| \newcommand{\vel}{\vee} | |
| \newcommand{\VA}{\forall} | |
| %] | |
| \newcommand{\s}{\mathcal} | |
| \newcommand{\f}{\mathfrak} | |
| \newcommand{\8}{\infty} | |
| \newcommand{\0}{\varnothing} | |
| \newcommand{\cl}[2]{[ #1 ]_#2} | |
| \newcommand{\ubar}{\underline} | |
| %%%[Bracketing | |
| \newcommand{\ang}[1]{\left\langle#1\right\rangle} | |
| \newcommand{\pa}[1]{\left(#1\right)} | |
| \newcommand{\sq}[1]{\left[#1\right]} | |
| \newcommand{\br}[1]{\left\lbrace#1\rightrbrace} | |
| \newcommand{\pasq}[1]{\left(#1\right]} | |
| \newcommand{\sqpa}[1]{\left[#1\right)} | |
| \newcommand{\pabr}[1]{\left(#1\right\rbrace} | |
| \newcommand{\brpa}[1]{\left\lbrace#1\right)} | |
| \newcommand{\sqbr}[1]{\left[#1\right\rbrace} | |
| \newcommand{\brsq}[1]{\leftlbrace#1\right]} | |
| \newcommand{\paang}[1]{\left(#1\right\rangle} | |
| \newcommand{\angpa}[1]{\left\langle#1\right)} | |
| \newcommand{\sqang}[1]{\left[#1\right\rangle} | |
| \newcommand{\angsq}[1]{\left\langle#1\right]} | |
| \newcommand{\brang}[1]{\left\rbrace#1\right\rangle} | |
| \newcommand{\angbr}[1]{\left\langle#1\right\rbrace} | |
| \newcommand{\lf}{\left} | |
| \newcommand{\rt}{\right} | |
| \newcommand{\abs}[1]{\lb#1\rb} | |
| \newcommand{\norm}[1]{\ldb#1\rdb} | |
| %] | |
| %%%[Display modifiers | |
| \newcommand{\us}[2]{\underset{#2}{#1}} | |
| \newcommand{\os}[2]{\overset{#2}{#1}} | |
| \newcommand{\ous}[3]{\os{\us{#1}{#2}}{#3}} | |
| \newcommand{\uos}[3]{\us{\os{#1}{#3}}{#2}} | |
| \newcommand{\di}{\displaystyle} | |
| \newcommand{\pusher}{\scb{0}[1]{{\color{white}$\fr{}{}_\whitea$}}} | |
| \newcommand{\dpusher}{\scb{0}[1]{{\color{white}$\fr{}{}^\whitea$}}} | |
| \newcommand{\mcl}{\mathclap} | |
| \newcommand{\sstack}{\substack} | |
| \newcommand{\ubr}{\underbrace} | |
| \newcommand{\ubrk}{\underbracket} | |
| %] | |
| %%%[Accents and dots | |
| \newcommand{\lbar}{\overline} | |
| \newcommand{\sdot}[1]{\underset{^{^{^{^{\scb{1.3}[1.3]{\,.}}}}}}{#1}} | |
| \newcommand{\sddot}[1]{\underset{^{^{^{^{\scb{1.3}[1.3]{\,..}}}}}}{#1}} | |
| \newcommand{\stdot}[1]{\underset{^{^{^{^{\scb{1.3}[1.3]{\,...}}}}}}{#1}} | |
| \newcommand{\tdot}[1]{\overset{_{\scb{1.1}[1.1]{...}}}{#1}} | |
| \newcommand{\tupdot}[1]{$\dot{\hbox{#1}}$} | |
| \newcommand{\tddot}[1]{$\ddot{\hbox{#1}}$} | |
| \newcommand{\ttdot}[1]{$\tdot{\hbox{#1}}$} | |
| \newcommand{\tsdot}[1]{$\sdot{\hbox{#1}}$} | |
| \newcommand{\tsddot}[1]{$\sddot{\hbox{#1}}$} | |
| \newcommand{\tstdot}[1]{$\stdot{\hbox{#1}}$} | |
| \newcommand{\pint}[1]{\mathaccent23{#1}} | |
| \newcommand{\dvect}[1]{\dot{\vct{#1}}} | |
| \newcommand{\dlbar}[1]{\lbar{\lbar{#1}}} | |
| \newcommand{\dubar}[1]{\ubar{\ubar{#1}}} | |
| %%%[Miscellanea | |
| \newcommand{\olvb}{\,\,\scalebox{1}[1.2]{$\left|\scalebox{0.1}[1]{{\color{white}$^a_b$}}\right.$}} | |
| \newcommand{\fvb}{\,\,\left|\scalebox{0.1}[1]{{\color{white}$\fr{^a}{_b}$}}\right.} | |
| \newcommand{\1}{\prime} | |
| \newcommand{\sistbis}[4]{\left\lbrace\begin{array}{cl} #1 & #2 \\ #3 & #4 \\\end{array}\right.} | |
| \newcommand{\sistbisdue}[6]{\left\lbrace\begin{array}{cl} #1 & #2 \\ #3 & #4 \\ #5 & #6 \\\end{array}\right.} | |
| \newcommand{\sistbistre}[8]{\left\lbrace\begin{array}{cl} #1 & #2 \\ #3 & #4 \\ #5 & #6 \\ #7 & #8 \\\end{array}\right.} | |
| \newcommand{\mat}{\begin{array}} | |
| \newcommand{\emat}{\end{array}} | |
| \newcommand{\blockmatLineVColVLetter}[8]{\scb{0.1}[1]{$\mat{c}% | |
| \scb{10}[1]{$\mat{cccc}#1\\\emat$} \\% | |
| \mat{ll}% | |
| \scb{10}[1]{$\mat{l}#5\\#6\\#7\\\emat$}\scb{10}[1]{\hsp{0.3cm}} & \scb{0.625}[0.0625]{$\mat{l}\\\scalebox{48}[48]{$^{#8}$\hsp{0.2cm}}\\\emat$}\\% | |
| \emat% | |
| \emat$}} %Makes a block matrix much like the A at the beginning of page 62, with parameters #1 through #4 in the line vector which is the first line of the matrix, parameters #5 through #7 in the column vector which contains the three v^i in that A, and parameter #8 in the place of the maxi R of that A. It is advisable to use parameters similar to that of the A matrix above mentioned, because using parameters wider that those of that matrix may cause decentering and an ugly resulting output of the matrix. | |
| %] | |
| %%Footnotes and associated | |
| \newcommand{\fn}{\footnote} | |
| \newcommand{\fnt}{\footnotetext} | |
| \newcommand{\fnm}{\footnotemark} | |
| \newcommand{\ic}{\addtocounter} | |
| \newcommand{\ifnc}{\ic{footnote}} | |
| \makeatletter | |
| \def\blfn{\xdef\@thefnmark{}\@footnotetext} | |
| \makeatother | |
| \newcommand{\rmfn}{\renewcommand{\thefootnote}{\roman{footnote}}} | |
| \newcommand{\Rmfn}{\renewcommand{\thefootnote}{\Roman{footnote}}} | |
| \newcommand{\afn}{\renewcommand{\thefootnote}{\alph{footnote}}} | |
| \newcommand{\Afn}{\renewcommand{\thefootnote}{\Alph{footnote}}} | |
| \newcommand{\symbfn}{\renewcommand{\thefootnote}{\fnsymbol{footnote}}} | |
| \newcommand{\setfnm}{\renewcommand{\thefootnote}} | |
| \newcommand{\fnmreset}{\renewcommand{\thefootnote}{\arabic{footnote}}} | |
| %%Text sectioning, lists | |
| \newcommand{\sect}{\section} | |
| \newcommand{\ssect}{\subsection} | |
| \newcommand{\sssect}{\subsubsection} | |
| \newcommand{\secta}{\section*} | |
| \newcommand{\ssecta}{\subsection*} | |
| \newcommand{\sssecta}{\subsubsection*} | |
| \newcommand{\ben}{\begin{enumerate}} | |
| \newcommand{\een}{\end{enumerate}} | |
| \newcommand{\bde}{\begin{description}} | |
| \newcommand{\ede}{\end{description}} | |
| \newcommand{\bi}{\begin{itemize}} | |
| \newcommand{\ei}{\end{itemize}} | |
| \newcommand{\spar}{\hsp{0.55cm}} | |
| \newcommand{\whitea}{{\color{white}a}} | |
| \newcommand{\lfeed}{\hsp{0cm}\\} | |
| %%Environments | |
| \newenvironment{sistema}% | |
| {\left \lbrace \begin{array}{@{}l@{}}}%l | |
| {\end{array}\right.} | |
| \newtheorem{defi}{Definizione} | |
| \newtheorem{teor}{Teorema} | |
| \newtheorem{es}{Esempio} | |
| \newtheorem{ese}{Esercizio} | |
| \newtheorem{pt}{Punto} | |
| \newtheorem{riass}{Riassunto} | |
| \newtheorem{propo}{Proposizione} | |
| \newtheorem{oss}{Osservazione} | |
| \newtheorem{cor}{Corollario} | |
| \newtheorem{esecasa}{Esercizio svolto da me} | |
| \newtheorem{lemma}{Lemma} | |
| \newtheorem{fatto}{Fatto} | |
| \newtheorem{eseese}{Esercizio Ortenziano}% to be adapted to the notes' subject, naturally | |
| %%Graphic scalings | |
| \newcommand{\scb}{\scalebox} | |
| \newcommand{\scbtt}{\scb{0.1}[1]} | |
| \newcommand{\scbt}{\scb{10}[1]} | |
| \newcommand{\ta}[2]{\scbtt{$\left.\begin{array}{c} \scbt{$#1$} \\ \scbt{$#2$} \\ \end{array}\right.$}} | |
| \newcommand{\dsi}[1]{\scalebox{0.7}[0.7]{$#1$}} | |
| \newcommand{\dsib}[1]{\scb{0.5}[0.5]{$#1$}} | |
| \newcommand{\scaleOpointnine}[1]{\scalebox{0.9}[0.9]{$#1$}} | |
| \newcommand{\expsc}[1]{\scb{0.65}[0.65]{$#1$}} | |
| \newcommand{\normsc}[1]{\scb{0.85}[0.85]{$#1$}} | |
| \newcommand{\tallsc}[1]{\scb{0.88}[0.88]{$#1$}} | |
| %%Text positioning | |
| \newcommand{\tsup}[1]{$^{\hbox{#1}}$} | |
| \newcommand{\tsub}[1]{$_{\hbox{#1}}$} | |
| \newcommand{\tus}[2]{$\us{\hbox{#1}}{\hbox{#2}}$} | |
| \newcommand{\tos}[2]{$\os{\hbox{#1}}{\hbox{#2}}$} | |
| \newcommand{\tous}[3]{$\ous{\hbox{#1}}{\hbox{#2}}{\hbox{3}}$} | |
| \newcommand{\tuos}[3]{$\uos{\hbox{#1}}{\hbox{#2}}{\hbox{#3}}$} | |
| \newcommand{\centre}[1]{$$\hbox{\ital{#1}}$$} | |
| \newcommand{\hsp}{\hspace} | |
| \newcommand{\vsp}{\vspace} | |
| %%Other | |
| \newcommand{\tick}{\checkmark} | |
| \newcommand{\crux}{\dagger} | |
| \newcommand{\dcrux}{\ddagger} | |
| \newcommand{\hs}{\heartsuit} | |
| \newcommand{\ds}{\diamondsuit} | |
| \newcommand{\cs}{\clubsuit} | |
| \renewcommand{\ss}{\spadesuit} | |
| \let\sz\ss | |
| \newcommand{\tcrux}{$\dagger$} | |
| \newcommand{\tdcrux}{$\ddagger$} | |
| \newcommand{\ths}{$\heartsuit$} | |
| \newcommand{\tds}{$\diamondsuit$} | |
| \newcommand{\tcs}{$\clubsuit$} | |
| \newcommand{\tss}{$\spadesuit$} | |
| \newcommand{\bs}{\backslash} | |
| \newcommand{\tbs}{$\bs$} | |
| \newcommand{\6}{'} | |
| \newcommand{\bk}{\Gr{ }} | |
| \def\mapu#1#2#3{\overset{#1}{\underset{#2}{#3}}} | |
| %Pseudo-shorthands: commands that are shorthands disguised as commands to avoid problems with the shorthand characters | |
| %Naturally need to be devised at need and are subject-specific | |
| %Tabbing environment: the first line defines the number of tab positions; every \= is a potential position which becomes effective only if there is something after it and before it. Then to align with one or another \= you put as many \> as there are \= to the desired position. The first line is considered to end with the \kill, whereas other lines are considered to end with \\. Of course, if you forget a \\ or the \kill or you put more \>s than the \=s of the first line, you won't be able to typeset anything. The last line needs not be ended with a \\, as the \end{tabbing} is sufficient for that. A LaTeX tab is about 0.26cm. If you exceed that with the text at one tab position, whatever you write at the next one will overlap with that text, so be careful. | |
| \begin{document} | |
| \chapter*{Introduzione} | |
| \addcontentsline{toc}{chapter}{Introduzione} | |
| Questo documento, che si pone come completamento necessario della guida \emph{\LaTeX\Gr{ }for dummies}, vuole proporre un preambolo che secondo me può considerarsi ben fatto, e spiegarlo in ogni dettaglio, sia per aiutare i lettori a comprenderne il funzionamento e l'utilità, sia per permettermi di mettere giù varie cose che ho imparato questi giorni senza dover ulteriormente rivoluzionare la summenzionata guida. \\[1em] | |
| Il preambolo che consiglio è proprio quello di questo documento, e la divisione della spiegazioni discende dall'organizzazione logica del preambolo stesso, che potete vedere nelle righe commentate che dividono il preambolo stesso in sezioni. I titoli delle sezioni sono proprio quelle righe commentate, opportunamente tradotte in Italiano. \\[1em] | |
| Molti pacchetti io non li so usare al meglio delle loro potenzialità, quindi spiegherò solo quello che so fare con essi. Per ulteriori informazioni, ogni pacchetto ha la sua documentazione, scaricabile presumibilmente da Internet, o, nel caso di un computer Mac con TeXShop, leggibile col comando \verb"Show help for package" (Mostrare aiuto per pacchetto, tradotto letteralmente) nel menù \verb"Help" (Aiuto), raggiungibile tramite il comando Command+Option+I (Mela+Alt+I). \\[1em] | |
| Questo documento, insieme alla guida summenzionata, mirano a fornire ai lettori un approccio soprattutto pratico, che li aiuti a capire come usare \LaTeX\Gr{ }per i loro scopi, e a dare un'infarinatura teorica del funzionamento di \LaTeX. Per ulteriori informazioni, si può leggere \href{http://en.wikibooks.org/wiki/LaTeX}{\emph{il libro \LaTeX\Gr{ } su Wikibooks}}, una guida molto più dettagliata fatta da editori che ne sanno più di me, e anche \href{ftp://ftp.tex.ac.uk/ctan\%3A/info/texbytopic/TeXbyTopic.pdf}{\emph{\TeX\Gr{ }by topic}}, che mi sembra fornisca anche dettagli più teorici e programmativi. Per chi poi volesse addentrarsi nel magico mondo della programmazione in \LaTeX, un ottimo inizio possono essere \href{http://profs.sci.univr.it/~gregorio/introtex.pdf}{\emph{gli appunti di Enrico Gregorio}}, che forniscono una chiara spiegazione di molti aspetti programmativi del sistema \TeX\Gr{ }e di \LaTeX. \\[1em] | |
| Per un po' di troubleshooting (soluzione di problemi), consiglio vivamente di creare un account su \href{tex.stackexchange.com}{\emph{\TeX\Gr{ }stack exchange}}, e porre direttamente le domande che si desidera per poi attendere con fiducia che altri utenti vi rispondano. Per chi ha Facebook, praticamente l'account è già definito, basta entrare con Facebook. Come avrete notato, l'Inglese si fa molto utile in questo contesto, anche perché \TeX\Gr{ }e \LaTeX\Gr{ }sono entrambi scritti in Inglese sostanzialmente, quindi è bene impararselo. Ora vi metto un elenco di domande che ho trovato utili. quando vedete l'utente \emph{MickG}, sono io. | |
| \bi | |
| \item \href{http://tex.stackexchange.com/questions/8351/what-do-makeatletter-and-makeatother-do}{\emph{\tbs makeatletter e \tbs makeatother, una questione di programamzione}}; | |
| \item \href{http://tex.stackexchange.com/questions/148862/strange-error-generated-after-another-error-and-related-to-aux-files-xelatex\#}{\emph{Problema di compilazione dopo un errore}}; | |
| \item \href{http://tex.stackexchange.com/questions/107967/need-to-typeset-twice-for-correct-compile}{\emph{Devo compilare due volte: perché?}}; | |
| \item \href{http://tex.stackexchange.com/questions/35832/what-are-the-situations-where-you-have-to-compile-a-document-more-than-once}{\emph{Quando bisogna compilare due volte?}}; | |
| \item \href{http://tex.stackexchange.com/questions/151686/removing-marks-any-tex-in-my-case-xelatex}{\emph{Come togliere i numeri di pagina e simili}}; | |
| \item \href{http://tex.stackexchange.com/questions/35433/creating-unnumbered-chapters-sections-plus-adding-them-to-the-toc-and-or-header/35436\#35436}{\emph{Creare sezioni ecc. senza numero ed aggiungerli all'indice}}; | |
| \item \href{http://tex.stackexchange.com/questions/151780/strange-error-related-to-theorem-name-xetex}{\emph{Errore legato ai nomi di theorem}}; | |
| \item \href{http://tex.stackexchange.com/questions/4736/what-is-the-difference-between-fragile-and-robust-commands}{\emph{Comandi fragili e robusti: differenze}}; | |
| \item \href{http://tex.stackexchange.com/questions/151794/texshop-console-messages-xetex\#}{\emph{Console di TeXShop: Avvertimenti}}; | |
| \item \href{http://tex.stackexchange.com/questions/138/what-are-underfull-hboxes-and-vboxes-and-how-can-i-get-rid-of-them}{\emph{Underfull hbox e vbox}}; | |
| \item \href{http://tex.stackexchange.com/questions/148858/shorthand-characters-in-section-titles-xelatex\#}{\emph{Caratteri di abbreviazione nei titoli di sezione}}; | |
| \item \href{http://tex.stackexchange.com/questions/152023/extra-blank-page-mysteriously-being-made-to-appear-xetex\#}{\emph{Pagina bianca di troppo che appare misteriosamente}}; | |
| \item \href{http://tex.stackexchange.com/questions/503/why-is-preferable-to}{\emph{Perché preferire \tbs[...\tbs] a \$\$...\$\$ per il modo matematico?}}; | |
| \ei | |
| Confesso che ho alquanto scassato le balle su quel sito :). Per chi si stesse chiedendo come trovare i supposti link di sopra, provi a cliccare sul corsivo: quasi sicuramente troverà un link ad una pagina Internet. | |
| \chapter{Inizio, impostazioni di fonts, pacchetti} | |
| \sect{Inizio} | |
| Cominciamo dalle prime due righe: \\[0.5em] | |
| \verb"%!TEX TS-program = xelatex" \\ | |
| \verb"%!TEX encoding = UTF-8 Unicode" \\[0.5em] | |
| Queste due righe servono la prima a dire a TeXShop di compilare con \XeLaTeX, che è un compilatore diverso che estende il support dei caratteri, consente la scelta della font, e assume ciecamente che il documento sia salvato secondo la codifica Unicode UTF-8, la seconda a dire a TeXShop di salvare il documento appunto con la codifica suddetta. Se non si usa \XeLaTeX, per assumere che il documento sia salvato in UTF-8 e quindi poter visualizzare le lettere accentate come è o ò, bisogna aggiungere l'istruzione: \\[0.5em] | |
| \verb"\usepackage[utf8]{inputenc}". \\[0.5em] | |
| Quest'ultima chiama il pacchetto \verb"inputenc", che serve a cambiare la codifica del documento agli occhi del compilatore, che sarà pdf\TeX, visto che anche Lua\TeX\Gr{ }assume che la codifica sia UTF-8. Tenere le codifiche del documento in TeXShop e per il compilatore diverse può generare stranezze quali ``√®'' che compilato diventa ``è''. Questa avviene perché la sequenza ``√®'' corrisponde, nella codifica standard di TeXShop, che è Mac-Roman, a una certa sequenza di byte, che in UTF-8 corrisponde invece a ``è''. È quindi consigliabile mantenere l'unità delle codifiche. Come dire all'editore di usare \XeLaTeX\Gr{ }piuttosto che Lua\LaTeX, o di cambiare la codifica del documento, dipende dall'editore. Io ho spiegato come si fa in TeXShop, come si faccia altrove dovete scoprirlo voi. \\[1em] | |
| A questo punto inizia il preambolo vero e proprio, con la classificazione del documento. Questa si fa mediante il comando: \\[0.5em] | |
| \verb"\documentclass[a4paper]{report}" \\[0.5em] | |
| Cosa significa classificare il documento? Significa sostanzialmente dire che tipo di documento è. Questo ha come implicazioni delle particolari formattazioni del testo, per le quali invito caldamente i lettori a leggere \href{http://en.wikibooks.org/wiki/LaTeX/Document_Structure}{\emph{la sezione} Document Structure \emph{(Struttura del Documento) sul libro di Wikibooks sopra citato}}, che dà un elenco delle classi standard (di cui menziono solo \verb"article", \verb"report" (la mia, consigliata per le tesi su Stack Exchange) e \verb"book", nonché \verb"beamer" per le presentazioni (v. \emph{\LaTeX\Gr{ }for dummies}), e inoltre spiega i parametri opzionali che vanno tra quadre. | |
| \sect{Pacchetti} | |
| A questo punto si invocano i pacchetti. Cosa sono i pacchetti? Sono una serie di macro, ovvero di comandi aggiuntivi, che si possono invocare solo una volta caricato un pacchetto. È come se, scrivendo un programma Java, io volessi semplificare l'input da tastiera con una classe come la SavitchIn, o la Scanner. Per poter usare i pacchetti, si procede in due modi. Un modo, stile SavitchIn, prevede che il file del pacchetto (.sty, file di stile, o .cls, file di classe) sia piazzato \emph{nella stessa cartella} del file .tex. L'altro modo, stile Scanner, prevede che il pacchetto si trovi in una directory apposta dove il compilatore va a cercare i pacchetti invocati per default. Entrambi i metodi prevedono, per l'invocazione, l'istruzione: \\[0.5em] | |
| \verb"\usepackage[<argomenti opzionali>]{<nome del pacchetto>}", \\[0.5em] | |
| simile all'\verb"import java.util.Scanner" richiesto per usare la classe Scanner. Un esempio l'abbia-mo già visto sopra: il pacchetto \verb"inputenc". Alcuni pacchetti, come questo, permettono di fornire al compilatore dei \emph{parametri opzionali}, che regolano, diciamo, l'uso del pacchetto. Ad esempio \verb"inputenc" come parametro accetta la codifica del documento, nel caso sopra UTF-8. Si possono raggruppare i pacchetti con un'istruzione del tipo: \\[0.5em] | |
| \verb"\usepackage{pacchetto1,pacchetto2,...}", \\[0.5em] | |
| tenendo però presente che i parametri opzionali si possono specificare \emph{SOLO} con \emph{UN} pacchetto tra graffe, altrimenti il compilatore dà errore perché non se a quale pacchetto si riferiscono le opzioni. Ora vediamo i pacchetti che uso io e cosa mi permettono di fare. | |
| \ssecta{\verb"amsmath,amsfonts,amssymb"} | |
| \addcontentsline{toc}{subsection}{\vrb{amsmath,amsfonts,amssymb}} | |
| Questi sono pacchetti per il modo matematico, che forniscono una serie di simboli matematici o font matematiche. Non so di preciso cosa forniscano. Una cosa che so è che la classe \verb"\mathbb" (Blackboard Bold), che fa le lettere con spessore (ad es. \verb"\mathbb{R}" restituisce $\mathbb{R}$), viene da uno di questi pacchetti, mi sembra \verb"amssymb", ma non ricordo con certezza. Suppongo che anche \verb"\mathcal" (corsivo maiuscolo) e \verb"\mathfrac" (Fraktur, come $\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$) vengono da lì. Per il corsivo minuscolo serve un'altro pacchetto, il pacchetto \verb"unicode-math". NB con tutte queste classi NON usate il minuscolo, perché porta a risultati del tutto imprevedibili (provate per credere!). | |
| \ssecta{\verb"mathtools"} | |
| \addcontentsline{toc}{subsection}{\vrb{mathtools}} | |
| Il pacchetto \verb"mathtools" fornisce molti utili strumenti da usarsi in modo matematico. Quelli che uso principalmente sono \verb"\underset, \overset, \underbrace, \overbrace". Questi servono per scrivere cose sopra o sotto ad una formula. La sintassi del primo è: \\[0.5em] | |
| \verb"\underset{cosa sotto}{formula}". \\[0.5em] | |
| Per esempio, \verb"\underset{\leq0}{\alpha+\beta}" restituisce $\underset{\leq0}{\alpha+\beta}$. Sintassi analoga si usa per \verb"\overset", dove al posto della \verb"cosa sotto" si scrive la \verb"cosa sopra". Riprendendo l'esempio di prima, sostituire \verb"\underset" con \verb"\overset" restituisce $\overset{\leq0}{\alpha+\beta}$. Entrambi vanno usati rigorosamente nel modo matematico, altrimenti si incorre in un errore: \verb"Command \overset only allowed in math mode". È ovviamente possibile ``barare'': basta definire un comando che incorpori i dollari del modo matematico. In tal caso consiglio di inserire nel comando i comandi \verb"\hbox" e \verb"\text". Il primo, disponibile per default e indipendente da \verb"mathtools", esce dal modo matematico all'interno dei dollari, dalla graffa dopo \verb"\hbox" alla graffa chiusa. Il secondo, fornito da \verb"mathtools", fa una cosa analoga, in più adattando lo stile alla posizione. Esistono 4 stili: dispayed math, math, script e scriptscript. Il testo normale, se non erro, è script, le formule tra dollari singoli o \verb"\(\)" sono in math, le formule tra doppi dollari o \verb"\[\]" sono in displayed math (che si può forzare anche tra dollari singoli con \verb"\displaystyle" che vedremo poi), mentre Pedici e Apici ad ogni livello dovrebbero essere in scriptscript. Avere dello script in mezzo allo scriptscript significa che sotto alla formula appare un testo troppo grosso. \verb"\text", per come lo uso io, serve sostanzialmente a scalare il testo. Lo stesso effetto si ottiene con un'opportuno \verb"\scalebox", che vedremo sotto nel pacchetto \verb"graphicx", ma ciò comporterebbe una necessità di studio del fattore di scala opportuno, e inoltre \verb"\text" segue meglio il principio WYSIWYM (What You See Is What You Mean, Quello che Vedi È Quello che Intendi), base di un sistema di composizione tipografica come \LaTeX. Per farsi un'idea di questa scala necessaria, si confronti \verb"\underset{\hbox{abc}}{\alpha}" con \verb"\underset{\text{abc}}{\alpha}": il primo restituisce $\underset{\hbox{abc}}{\alpha}$, il secondo $\underset{\text{abc}}{\alpha}$. Un'effetto simile si ottiene mettendo al posto di \verb"\text" uno \verb"\scalebox{0.7}[0.7]": $\underset{\scb{0.7}[0.7]{abc}}{\alpha}$. Il codice però è notevolmente più complicato e meno intuitivo. \\[0.5em] | |
| Gli altri sono simili, ma aggiungono una graffa sopra o sotto la formula. La sintassi di \verb"\underbrace" è: \\[0.5em] | |
| \verb"\underbrace{formula}_{cosa sotto}", \\[0.5em] | |
| e quello che si ottiene è: $\underbrace{formula}_{cosa sotto}$. Con overbrace la sintassi è la stessa, salvo che è bene usare \verb"^" anziché \verb"_". Infatti con \verb"^" si ottiene $\overbrace{formula}^{cosa sopra}$, mentre con \verb"_" abbiamo $\overbrace{formula}_{cosa sotto}$. Di fatto si può usare \verb"^" anche con \verb"\underbrace", ottenendo $\underbrace{formula}^{cosa sotto}$. Naturalmente si può combinare \verb"_" con \verb"_", ottenendo $\underbrace{formula}_{cosa sotto}^{cosa sopra}$. Come avrete certamente notato, gli spazi in modo matematico vengono ignorati, e così anche una sequenza di più di uno spazio in modo testo o una qualsiasi sequenza di spazi dopo un comando. Per ovviare a questo, si veda la sezione dei comandi di \LaTeX\Gr{ }for dummies, dove ci sono i comandi \verb"\,,\:,\;,\!" che ovviano a questo come ivi descritto. Un altro comando di \verb"mathtools" che uso spesso è \verb"\substack", che permette di fare \verb"\underset" e analoghi su più righe, semplicemente circondando tutto con un \verb"\substack{...}", dove \verb"..." è il tutto, e andando a capo con \verb"\\". Abbiamo poi anche \verb"\mathclap", che fa sì che un \verb"\underset" od analogo non si espanda troppo. Per capire cosa intendo, si confronti \verb"\underset{qweqweqweqwe}{=}" con \verb"\underset{\mathclap{qweqweqweqwe}}{=}": il primo restituisce $\underset{qweqweqweqwe}{=}$, il secondo $\underset{\mathclap{qweqweqweqwe}}{=}$. Per combinare \verb"\substack" con \verb"\mathclap" si mette l'ultimo dentro al primo, ossia \verb"\substack{\mathclap{qweqwe}\\\mathclap{qweqwe}}", che combinato con \verb"\underset{...}{a}" restituisce $\underset{\substack{\mathclap{qweqwe}\\\mathclap{qweqwe}}}{a}$. Ovviamente è bene usare \verb"\text" per inserire del testo nel \verb"\substack", e quindi \verb"\text" va inserito nel \verb"\mathclap" ogni volta che sia necessario. Altri due comandi di cui sono a conoscenza, ma che non uso, sono \verb"\overbracket" e \verb"\underbracket". Come suggerisce il nome, sono gemelli di \verb"\overbrace" e \verb"\underbrace", ma al posto della graffa mettono una quadra. La sintassi è del tutto analoga, con in più che prima della \verb"formula" si possono mettere due parametri opzionali tra quadre, che, prendendo un numero in pt (punti, unità di misura di Word per le font), regolano il primo lo spessore della quadra, e il secondo la sua altezza. Così ad esempio \verb"\overbracket[1pt][10pt]{formula}^{cosa sopra}" restituisce $\overbracket[1pt][10pt]{formula}^{cosa sopra}$, mentre invertendo i numeri si ottiene $\overbracket[10pt][1pt]{formula}^{cosa sopra}$. Come potete vedere fare una parentesi più spessa che alta dà qualche problemino a \LaTeX, che si vede costretto a bypassare l'altezza per lo spessore. | |
| \ssecta{\verb"mathdots"} | |
| \addcontentsline{toc}{subsection}{\vrb{mathdots}} | |
| Questo pacchetto, per l'uso che ne faccio, serve solo ed esclusivamente per avere il comando \verb"\iddots", che restituisce i punti diagonali invertiti $\iddots$, laddove senza i si ha un comando già disponibile senza \verb"mathdots" che restituisce $\ddots$. L'ho aggiunto quando dovevo scrivere un blocco di matrice, che richiedeva quei punti: | |
| $$\mat{cccc}\ddots&\vdots&\vdots&\iddots\\\dots&e^{at}\cos bt&-e^{at}\sin bt&\dots\\\dots&e^{at}\sin bt&e^{at}\cos bt&\dots\\\iddots&\vdots&\vdots&\ddots\emat.$$ | |
| \ssecta{\verb"mathptmx"} | |
| \addcontentsline{toc}{subsection}{\vrb{mathptmx}} | |
| Anche di questo pacchetto non so molto. In teoria dovrebbe servire a cambiare le font di default, sia in modo testo, sia in modo matematico, a qualcosa di più simile a Times della (a mio parere brutta) font di default di \LaTeX. Tuttavia visti i comandi sotto (\verb"\setmonofont" e simili) che vedremo poi, forse non è necessario. Quei comandi sono però, credo, solo di \XeLaTeX, quindi con pdf\LaTeX consiglio \verb"mathptmx". Un altro pacchetto che dovrebbe avere lo stesso effetto è \verb"mathpazo". Non ho usato quello perché se non erro confliggeva con altri pacchetti, forse \verb"fontspec", che mi servivano per usare al meglio \XeLaTeX. Sì, stando alla documentazione di \verb"fontspec", \verb"mathpazo" confligge proprio con \verb"fontspec" | |
| \ssecta{\verb"letltxmacro"} | |
| \addcontentsline{toc}{subsection}{\vrb{letltxmacro}} | |
| Anche di questo pacchetto non so molto. Vista l'omonima macro, potrebbe essere un pacchetto volto a facilitare la definizione di comandi o ambienti. Tutto quello che so è che consente il comando \verb"\letltxmacro", variante dl \verb"\let" che vedremo dopo, che serve ad assegnare comandi predefiniti a sequenze nuove in modo da non perdere niente nel caso di assegnamento delle vecchie sequenze a qualcos'altro. Cosa significa questa assai contorta frase? Vediamo l'esempio su cui lo uso io. La radice quadrata \verb"\sqrt", che prende in ingresso un gruppo (quindi quanto racchiuso tra graffe o il primo token, semplificando ``il primo carattere'', che trova dopo), di default viene senza il trattino verticale che chiude, ossia come $\oldsqrt{abc}$ piuttosto che $\rad{abc}$. A noi piace di usare sempre quella chiusa, ma vogliamo riservarci la scelta. Vogliamo però che sia \verb"\sqrt" a fare la radice chiusa, quindi vorremmo salvare quella aperta su qualcosa, per esempio \verb"\oldsqrt", e poi ridefinire la \verb"\sqrt". Un modo è: \\[0.5em] | |
| \verb"\let\oldsqrt\sqrt"\\ | |
| \verb"% it defines the new \sqrt in terms of the old one"\\ | |
| \verb"\def\sqrt{\mathpalette\DHLhksqrt}"\\ | |
| \verb"\def\DHLhksqrt#1#2{%"\\ | |
| \verb"\setbox0=\hbox{$#1\oldsqrt{#2\,}$}\dimen0=\ht0"\\ | |
| \verb"\advance\dimen0-0.2\ht0"\\ | |
| \verb"\setbox2=\hbox{\vrule height\ht0 depth -\dimen0}%"\\ | |
| \verb"{\box0\lower0.4pt\box2}}". \\[0.5em] | |
| Non chiedetemi di spiegarvi i dettagli di questo arabo perché non sono assolutamente capace :). Semplicemente posso dirvi che \verb"\let comando1 comando 2" passa \verb"comando 2" a \verb"comando 1" secondo la definizione al momento del \verb"\let", sicché se dopo si ridefinisce \verb"coman-" \verb"do 2" non si altera in alcun modo \verb"comando 1". Il resto è un codice copiato da Wikibooks che permette di definire la radice chiusa. Posso però aggiungere che \verb"\def" è un comando primitivo di \TeX\Gr{ }che corrisponde al \verb"\newcommand" di \LaTeX, colla differenza che non controlla se il comando assegnato è già definito, ma lo ripeteremo meglio sotto. A quanto pare però questo non permette le radici con indice, come $\rad[3]{2}$. Il risultato di quel codice applicato a una radice con indice, come \verb"\sqrt[3]{2}", è una schifezza come $\sqrt{[}3]2$. Per risolvere questo problema entra in scena il comando \verb"\LetLtxMacro", nel codice: \\[0.5em] | |
| \verb"\LetLtxMacro{\oldsqrt}{\sqrt} % makes all sqrts closed"\\ | |
| \verb"\renewcommand{\sqrt}[1][\ ]{%"\\ | |
| \verb" \def\DHLindex{#1}\mathpalette\DHLhksqrt}"\\ | |
| \verb"\def\DHLhksqrt#1#2{%"\\ | |
| \verb" \setbox0=\hbox{$#1\oldsqrt[\DHLindex]{#2\,}$}\dimen0=\ht0"\\ | |
| \verb" \advance\dimen0-0.2\ht0"\\ | |
| \verb" \setbox2=\hbox{\vrule height\ht0 depth -\dimen0}%"\\ | |
| \verb" {\box0\lower0.71pt\box2}}"\\[0.5em] | |
| Ancora una volta è arabo, però appare chiaro che \verb"\LetLtxMacro" e \verb"\let" fanno cose simili. Guardando più da vicino il codice, sembra che la vera differenza sia quel \verb"DHLindex" che si vede vicino al \verb"\setbox0". Infatti prendendo questo arabo e mettendo un normale \verb"\let" al posto di \verb"\LetLtxMacro", il tutto sembra funzionare. Io intanto vi ho segnalato un pacchetto, poi chiederò su Stack Exchange perché Wikibooks consiglia di far così invece che usare il normale \verb"\let". Forse alcune cose del pacchetto rendono in qualche modo più sicura questa maniera. Diamo un'occhiata alla documentazione di \verb"letltxmacro", chissà mai che. Stando all'inizio della documentazione, usare \verb"\let" con un comando dichiarato con \verb"\DeclareRobustCommand" (vedi sotto) darebbe problemi. Effettivamente boh, qua non so se sia robusto. Comunque se funziona, potete usare il \verb"\let". Io uso l'altro modo, vuoi per sicurezza, vuoi perché non ho voglia di tapusciare ancora col preambolo a meno di stretta necessità :). | |
| \ssecta{\verb"nicefrac,xfrac"} | |
| \addcontentsline{toc}{subsection}{\vrb{nicefrac,xfrac}} | |
| Il pacchetto \verb"nicefrac", per quanto ne so, offre il comando \verb"\nicefrac" per le frazioni oblique: \verb"\nicefrac{a}{b}" restituisce $\nicefrac{a}{b}$. Questa fratino secondo me non è molto nice, ma con un paio di apici si sistema. Io scriverei $\nicefrac{^a}{_b}$, cioè \verb"\nicefrac{^a}{_b}". Invece \verb"xfrac" probabilmente offre \verb"\cfrac" per le frazioni continue. Ah no, offre \verb"\sfrac", gemello di \verb"\nicefrac". Vediamo come risulta. $\sfrac{a}{b}$. Mi sembra uguale al suo gemello. Quindi lo eliminerò, questo pacchetto. \verb"\cfrac" viene da altrove, e serve per andare a capo a metà frazione quando si ha una frazione come $\cfrac{1}{a+\cfrac{1}{a+\cfrac{1}{a+\cfrac{1}{a}}}}$. Io non penso che lo userò, perché di solito tengo tutto su una riga. Può però essere utile per render più leggibile il codice. Proviamo a vedere come viene con una normale \verb"\frac": $\frac{1}{a+\frac{1}{a+\frac{1}{a+\frac{1}{a}}}}$. A quanto pare \verb"\cfrac" forza il display math style, mentre \verb"\frac" no. Proviamo a forzarlo noi: $\di\frac{1}{\di a+\frac{1}{\di a+\frac{1}{\di a+\frac{1}{a}}}}$. Identico, tranne che quegli uni sbattono contro le linee di frazione sopra. | |
| \ssecta{\verb"fontspec,xltxtra,xunicode,textcomp"} | |
| \addcontentsline{toc}{subsection}{\vrb{fontspec,xltxtra,xunicode,textcomp}} | |
| Questi sono pacchetti associati ad \XeTeX, che ho adottato senza sapere cosa facciano perché il file delle istruzioni per il \emph{General Typesetting} diceva di usarli. Sicuramente uno di questi, probabilmente \verb"fontspec", fornisce i comandi che vedremo tra poco per modificare le font. State attenti a \verb"xltxtra", che si sbaglia a scrivere con estrema facilità: è x-l-txt-ra, non per esempio x-l-xtra. Attenti a scriverlo bene che se scrivete male poi vi fa Package Not Found o qualcosa del genere. | |
| \ssecta{\verb"color"} | |
| \addcontentsline{toc}{subsection}{\vrb{color}} | |
| Questo pacchetto, come dice il nome, permette di regolare il colore del testo mediante il comando \verb"\color". La sintassi è un po' diversa dal solito: \\[0.5em] | |
| \verb"{\color{colore}testo}". \\[0.5em] | |
| Questa strana sintassi probabilmente si spiega dicendo che \verb"\color" modifica un parametro interno a \TeX, ma solo localmente, e le graffe quindi servono a delimitare il gruppo in cui la modifica ha effetto. Stesso discorso per \verb"\itshape", che fa il corsivo. Può essere una buona idea definirsi un comando che sfrutti \verb"\color" ma abbia la solita sintassi che vedremo sotto, ci proverò. \verb"colore" è o un colore predefinito (red, blue, white, ecc.) oppure un colore dato tramite numeri, come si può leggere in \emph{\LaTeX\Gr{ }for dummies}. | |
| \ssecta{\verb"hyperref"} | |
| \addcontentsline{toc}{subsection}{\vrb{hyperref}} | |
| Questo pacchetto serve per i link esterni, come ne avete visti tanti di sopra. La sintassi è: \\[0.5em] | |
| \verb"\href{link esterno}{testo da fare apparire}". \\[0.5em] | |
| Il \verb"link esterno" è l'indirizzo della pagina web che si vuole linkare, che va riportato per esteso. Attenti ai caratteri speciali: \verb"%" va sostituito con \verb"\%", e analogamente \verb"#,$,&". Per \verb"^" non so cosa si debba fare. Il \verb"testo da fare apparire" è in realtà opzionale, ed è quello che deve apparire nel pdf al posto del link. Per esempio, \verb"\href{www.wikipedia.org}{Wikipedia}" restituisce \href{www.wikipedia.org}{Wikipedia}, link cliccabile sul pdf che rimanda esattamente a www.wikipedia.org. | |
| \ssecta{\verb"graphicx"} | |
| \addcontentsline{toc}{subsection}{\vrb{graphicx}} | |
| Questo pacchetto lo uso fondamentalmente per due scopi: scalare il testo e inserire figure. Per la prima cosa, il comando è: \\[0.5em] | |
| \verb"\scalebox{so}[sv]{testo da scalare}". \\[0.5em] | |
| Le graffe racchiudono un numero, il fattore di scala orizzontale, che rappresenta il rapporto tra la dimensione del testo scalato e quella normale in orizzontale. Ad esempio, \verb"\scalebox{0.5}" \verb"[1]{testo}" restituisce un testo con lunghezza dimezzata, come \scb{0.5}[1]{testo}. Invece metterci 2 raddoppia la lunghezza: \scb{2}[1]{testo}. Posso anche metterci fattori negativi, nel qual caso si riflette lungo un asse verticale il testo e poi lo si scala. Gli stessi numeri di prima col meno dànno \scb{-0.5}[1]{testo} e \scb{-2}[1]{testo}. Analogo è il discorso per le quadre, che scalano in verticale, quindi l'altezza. Riporto gli esempi di prima con i numeri scambiati: \scb{1}[0.5]{testo}, \scb{1}[2]{testo}, \scb{1}[-0.5]{testo} e \scb{1}[-2]{testo}. Esiste peraltro anche il comando \verb"\reflectbox", che abbrevia \verb"\scalebox{-1}[1]": \reflectbox{testo}. Sempre giocando col testo, scopro ora \verb"\rotatebox", che accetta come parametro un angolo in gradi e ruota il testo di quell'angolo in senso antiorario. Guardiamo ad esempio cosa succede con 30, 60, 120, 340: \rotatebox{30}{testo}, \rotatebox{60}{testo}, \rotatebox{120}{testo} e \rotatebox{340}{testo}. Come parametro opzionale si può specificare il centro di rotazione, che di default è l'angolo in basso a sinistra del testo, per ruotarlo in maniera diversa. Specifichiamo \verb"x=a,y=b", dapprima con (a,b)=(3mm,4mm), poi (6mm,30mm), infine (-1mm,-20mm): \rotatebox[x=3mm,y=4mm]{30}{testo}, \rotatebox[x=6mm,y=30mm]{30}{testo}, \rotatebox[x=-1mm,y=-20mm]{30}{testo}, ruotando sempre di 30 gradi. A questo punto l'altro scopo: le figure. Il comando è: \\[0.5em] | |
| \verb"\includegraphics[width=xcm]{nome file.estensione}". \\[0.5em] | |
| Il parametro opzionale specifica la larghezza dell'immagine, che verrà opportunamente scalata dal compilatore. Si può specificare anche l'altezza (\verb"height"), sempre con un numero in cm. Altri parametri sono \verb"trim", seguito da quattro numeri che specificano di quanti bp ritagliare la foto a sinistra, in basso, a destra ed in alto rispettivamente, \verb"angle" l'angolo di rotazione e \verb"origin" l'origine, come in \verb"\rotatebox", e molti altri per cui si veda la documentazione. L'ultima cosa che scopro è che i modelli di colore rgb e simili sono di \verb"graphicx", che fornisce anche \verb"\textcolor{colore}{testo}" che equivale a \verb"{\color{colore}testo}". Inoltre fornisce \verb"\pagecolor" che, con gli stessi parametri di \verb"\textcolor", cambia il colore della pagina. Per esempio \verb"\pagecolor{yellow}" restituisce la pagina come la vedete colorata. \pagecolor{yellow} Proviamo ora a vedere cosa succede con \verb"\includegraphics[width=5cm,origin={x=6mm,y=-20mm},angle=40]" confrontandolo con un normale \verb"\includegraphics[width=5cm]": \\ | |
| \includegraphics[width=4.9cm,origin={x=6mm,y=-20mm},angle=40]{mapu.jpg}, \includegraphics[width=4.9cm]{mapu.jpg}. \\ | |
| Piccola nota: \verb"graphicx" è la versione estesa di \verb"graphics", che sostanzialmente aveva meno parametri opzionali possibili. | |
| \ssecta{\verb"babel"} | |
| \addcontentsline{toc}{subsection}{\vrb{babel}} | |
| \pagecolor{white} | |
| Questo è il pacchetto del multilinguismo. Io lo uso principalmente per far sì che appaia Indice, Capitolo, e non Contents (generato col comando \verb"\tableofcontents") e Chapter (comando \verb"\chapter{titolo}"). Un'altra cosa che fa è di regolare la sillabazione delle parole, mandando a capo a "li-sta" invece che a "lis-ta" per esempio. Altre features non ne ho esplorate. Un parametro opzionale che accetta il pacchetto \verb"babel" è la lingua. Questo spiega perché \\[0.5em] | |
| \verb"\usepackage[italian]{babel}": \\[0.5em] | |
| sto scrivendo in Italiano. La documentazione di \verb"fontspec" suggerisce di sostituirlo con \verb"poly-" \verb"glossia": io non so come usare quello, non ho voglia di leggerne la documentazione e non ho mai avuto problemi con questo, quindi perché mai cambiare? | |
| \ssecta{\verb"marginnote"} | |
| \addcontentsline{toc}{subsection}{\vrb{marginnote}} | |
| Questo pacchetto riguarda le note a margine come quella che vedete sulla destra della pagina\marginpar{Ecco una nota a margine.}. {Normalmente queste si inseriscono con il comando \verb"\marginpar", che non richiede \verb"marginnote" né alcun pacchetto extra, e se accoppiate a \verb"\reversemarginpar" appaiono a sinistra. \reversemarginpar\marginpar{Ecco appunto.}}\marginpar{Ora torniamo a destra.} Tuttavia nelle note a piè di pagina (footnotes) si hanno problemi. Con il comando \verb"\marginnote" del medesimo pacchetto il problema è risolto\fn{Come potete vedere qua.\marginnote{Ecco appunto.}{\reversemarginpar\marginnote{E a sinistra?}}\marginnote{Come già visto.}}. Come potete vedere, il \verb"\reversemarginpar" sembra non funzionare che sulle \verb"\marginnote". Inoltre queste ultime rischiano di sovrapporsi se non si fa attenzione, come il ``Come già visto'' con ``Ecco appunto''. Notare che \verb"\reversemarginpar" è globale, quindi per agire solo su \emph{alcune} note bisogna fare in modo di circondarle con delle graffe, sicché all'interno vale il riverse, poi si chiude la graffa e sparisce l'effetto. Inoltre, ma non potete vederlo, un \verb"\reversemarginpar" globale agisce anche sulle \verb"\marginnote", ma non si può raddoppiare, pare, col risultato che tutto va a sinistra, e un'altra note si sovrappone alle due che vedete sovrapposte. {A questo punto proviamo una \verb"\marginnote" a sinistra fuori da una nota a piè di pagina\reversemarginpar\marginnote{Eccola qua.}} In definitiva, abbandonate \verb"\marginpar" in favore di \verb"\marginnote". Manca solo una \verb"\marginnote" fuori da una nota a piè di pagina\marginnote{Eccola! Tutto OK no?}. Perfetto. Noto che alla prima compilazione le note a margine possono finire a sovrapporsi col testo, ma non vi preoccupate: ricompilate, e tutto si sistema. | |
| \ssecta{\verb"geometry"} | |
| \addcontentsline{toc}{subsection}{\verb"geometry"} | |
| Questo è il pacchetto che serve a regolare i margini. Le opzioni sono: | |
| \ben | |
| \item \verb"top", che specifica il margine superiore, la distanza del testo dalla cima della pagina; | |
| \item \verb"bottom", che specifica quello inferiore, la distanza dal fondo della pagina; | |
| \item \verb"outer", che specifica il margine destro, la distanza del testo dal bordo destro della pagina; | |
| \item \verb"inner" che specifica il margine sinistro, la distanza del testo dal bordo sinistro della pagina; | |
| \item \verb"marginparsep", che specifica la distanza tra il testo e le note a margine; | |
| \item \verb"marginparwidth", che specifica la larghezza delle note a margine. | |
| \een | |
| Queste almeno son quelle che uso io, poi se ce ne sono altre non lo so, guardatevi la documentazione. Io lo chiamo così: \\[0.5em] | |
| \verb"\usepackage[top=2cm, bottom=3.5cm, outer=4cm, inner=4cm," \\ | |
| \verb"marginparsep=0.7cm, marginparwidth=1.5cm]{geometry}", \\[0.5em] | |
| ottenendo il risultato che avete sotto i vostri occhi. Penso che specificare in in (pollici, inches) vada altrettanto bene: potete provare. Forse anche i pt (punti) vanno bene, chissà. | |
| \ssecta{\verb"thmtools"} | |
| \addtocontents{toc}{subsection}{\verb"thmtools"} | |
| Questa è una scoperta recente, tutta dovuta a \TeX\Gr{ }Stack Exchange. Sostanzialmente lo uso per fare liste di \emph{theorems}, che vedremo poi come dichiarare. Il comando base è \verb"\listoftheorems", che causa un'interruzione di pagina prima di essa. Il titolo automatico è ``List of Theorems'', ma si può cambiare: è sufficiente inserire: \\[0.5em] | |
| \verb"\renewcommand{\listtheoremname}{Titolo alternativo}". \\[0.5em] | |
| Inoltre si può anche opzionalmente specificare quali tipi di theorem includere e quali escludere dalla lista. Il parametro opzionale sarà: \\[0.5em] | |
| \verb"[ignoreall,show={lista dei tipi da includere}]", \\[0.5em] | |
| dove vanno elencati i nomi che si inseriscono nei \verb"\begin", non quelli che appaiono nel pdf (v. sotto per saperne di più). Ora dò un'occhiata alla documentazione per vedere se c'è qualcosa di molto interessante che val la pena copiare, o che mi son dimenticato ma già uso. Per esempio mi son dimenticato i parametri opzionali post-\verb"\begin". Quando si inizia un theorem con \verb"\begin{nomeTheorem}", si può aggiungere dopo le graffe delle quadre. Queste possono contenere 4 parametri opzionali: | |
| \ben | |
| \item\verb"name=", che è un nome che viene dato al teorema, appare tra graffe dopo l'apertura (Teorema 1 (titolo), ad esempio), e nella lista di teoremi; è anche possibile far sì che siano distinti: si racchiude tra graffe la dichiarazione del \verb"name", e dopo l'uguale si mette tra quadre quello che va nella lista, e fuori da esse quello che invece deve apparire dopo l'apertura del teorema; attenti alle virgole: se avete una virgola in un qualsiasi parametro, \bemph{racchiudetelo tra graffe}, altrimenti vi vengono ogni sorta di problemi, da errori strani a pezzi di \verb"name" che spariscono, perché lui dopo la virgola cerca un altro parametro opzionale; | |
| \item\verb"label=", che etichetta il teorema con una stringa cui ci si può riferire dopo col comando \verb"\ref", che tra graffe prende l'etichetta; questo sostanzialmente riprende il comando \verb"\label", che fa la stessa cosa e si può mettere anche in un titolo di sezione, e credo anche in un'equazione; usare \verb"\ref" farà apparire solo il numero, il nome è bene mettercelo a mano davanti al \verb"\ref"; | |
| \item\verb"continues=", che tramite l'etichetta permette di fare una continuazione di un precedente theorem; | |
| \item\verb"restates", che ancora usa l'etichetta, e dal nome dovrebbe ripetere il teorema, accettando peraltro come extra quadra (presumibilmente da mettere tra graffe come col doppio \verb"name" prima) un nuovo \verb"name" da dare al teorema. | |
| \een | |
| Un'altra feature potenzialmente interessante di \verb"thmtools" è \verb"\declaretheorem", che prende il nome del teorema tra graffe, e prima, come opzionali, tutta una serie di parametri sullo stile del teorema (numerazione, riquadranti, evidenziature, ecc.). Io non l'ho mai usato, quindi provate voi. | |
| \sect{Impostazioni di font} | |
| Qui parliamo di due tipi di regolazioni: font di default e font families. | |
| \ssect{Font di default} | |
| Le font di default sono usate nel documento a meno di cambiamenti fatti intervenire dall'utente. Si regolano mediante i seguenti comandi: | |
| \ben | |
| \item\verb"\setmathrm{Times New Roman}" definisce la font della classe \verb"\mathrm", una cosa da modo matematica; | |
| \item\verb"\setmathsf{Times New Roman}" regola la \verb"\mathsf" (font sans-serif, senza grazie, teoricamente almeno); | |
| \item\verb"\setmathtt{Times New Roman}" regola la \verb"\mathtt", teoricamente monospaced, cioè tale per cui ogni carattere occupa lo stesso spazio orizzontale, tipo macchina da scrivere; | |
| \item\verb"\setboldmathrm[BoldFont={Optima ExtraBlack}]{Optima Bold}" regola la \verb"\mathrm" versione grassetto, per esempio in \verb"\mathbold"; | |
| \item\verb"\defaultfontfeatures{Mapping=tex-text}" è un comando consigliato dal mio coso sul General Typesetting, che non so cosa faccia; | |
| \item\verb"\setromanfont{Times New Roman}" regola la font di default del testo, ed equivale a \verb"\setmainfont"; | |
| \item\verb"\setsansfont{Times New Roman}" regola la font sans del testo; | |
| \item\verb"\setmonofont{Helvetica}" regola la font monospaziata del testo, quella per esempio del \verb"\verb", che continuo ad usare per distinguere il codice dal testo. | |
| \een | |
| Tutti questi comandi prendono come parametro opzionale le \emph{font features}, come bold (grassetto), italic (corsivo) o bold italic (grassetto corsivo), che dipendono dalla font che si chiama in causa. | |
| \tableofcontents | |
| \end{document} | |
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| ................................................. | |
| ................................................. | |
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| . | |
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| ................................................. | |
| ................................................. | |
| . fontspec info: "defining-font" | |
| . | |
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| . | |
| . This font family consists of the following shapes: | |
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| \g_fontspec_family_MS Mincho_int=\count160 | |
| ................................................. | |
| . fontspec info: "no-font-shape" | |
| . | |
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| ................................................. | |
| ................................................. | |
| . fontspec info: "no-font-shape" | |
| . | |
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| ................................................. | |
| ................................................. | |
| . fontspec info: "no-font-shape" | |
| . | |
| . Could not resolve font MS Mincho/BI (it probably doesn't exist). | |
| ................................................. | |
| ................................................. | |
| . fontspec info: "defining-font" | |
| . | |
| . Font family 'MSMincho(0)' created for font 'MS Mincho' with options | |
| . [Mapping=tex-text,]. | |
| . | |
| . This font family consists of the following shapes: | |
| . | |
| . * 'normal' with NFSS spec.: | |
| . <->"MS Mincho/ICU:script=latn;language=DFLT;mapping=tex-text;" | |
| ................................................. | |
| ................................................. | |
| . fontspec info: "defining-font" | |
| . | |
| . Font family 'TimesNewRoman(1)' created for font 'Times New Roman' with | |
| . options [Mapping=tex-text,]. | |
| . | |
| . This font family consists of the following shapes: | |
| ................................................. | |
| ................................................. | |
| . fontspec info: "defining-font" | |
| . | |
| . Font family 'TimesNewRoman(1)' created for font 'Times New Roman' with | |
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| . | |
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| ................................................. | |
| ................................................. | |
| . fontspec info: "defining-font" | |
| . | |
| . Font family 'TimesNewRoman(1)' created for font 'Times New Roman' with | |
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| \g_fontspec_family_Batang_int=\count161 | |
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| . fontspec info: "no-font-shape" | |
| . | |
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| ................................................. | |
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| . fontspec info: "no-font-shape" | |
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| ................................................. | |
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| . fontspec info: "no-font-shape" | |
| . | |
| . Could not resolve font Batang/BI (it probably doesn't exist). | |
| ................................................. | |
| ................................................. | |
| . fontspec info: "defining-font" | |
| . | |
| . Font family 'Batang(0)' created for font 'Batang' with options | |
| . [Mapping=tex-text,]. | |
| . | |
| . This font family consists of the following shapes: | |
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| . | |
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| \g_fontspec_family_Devanagari MT_int=\count162 | |
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| . fontspec info: "no-font-shape" | |
| . | |
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| ................................................. | |
| ................................................. | |
| . fontspec info: "defining-font" | |
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| . * 'bold' with NFSS spec.: | |
| . <->"Devanagari MT/B/AAT:mapping=tex-text;" | |
| . | |
| . * 'bold italic' with NFSS spec.: | |
| . <->"Devanagari MT/BI/AAT:mapping=tex-text;" | |
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| ................................................. | |
| . fontspec info: "no-scripts" | |
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| . fontspec info: "no-font-shape" | |
| . | |
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| ................................................. | |
| ................................................. | |
| . fontspec info: "defining-font" | |
| . | |
| . Font family 'MalayalamMN(0)' created for font 'Malayalam MN' with options | |
| . [Mapping=tex-text,]. | |
| . | |
| . This font family consists of the following shapes: | |
| . | |
| . * 'normal' with NFSS spec.: | |
| . <->"Malayalam MN/ICU:mapping=tex-text;" | |
| . | |
| . * 'bold' with NFSS spec.: | |
| . <->"Malayalam MN/B/ICU:mapping=tex-text;" | |
| . | |
| . * 'bold italic' with NFSS spec.: | |
| . <->"Malayalam MN/BI/ICU:mapping=tex-text;" | |
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| \g_fontspec_family_Free Sans_int=\count164 | |
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| ................................................. | |
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| . fontspec info: "no-font-shape" | |
| . | |
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| ................................................. | |
| ................................................. | |
| . fontspec info: "no-font-shape" | |
| . | |
| . Could not resolve font Free Sans/BI (it probably doesn't exist). | |
| ................................................. | |
| ................................................. | |
| . fontspec info: "defining-font" | |
| . | |
| . Font family 'FreeSans(0)' created for font 'Free Sans' with options | |
| . [Mapping=tex-text,]. | |
| . | |
| . This font family consists of the following shapes: | |
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| . <->"Free Sans/ICU:script=latn;language=DFLT;mapping=tex-text;" | |
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| \g_fontspec_family_Free Serif_int=\count165 | |
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| . fontspec info: "defining-font" | |
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| . <->"Free Serif/ICU:script=latn;language=DFLT;mapping=tex-text;" | |
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| . * 'bold' with NFSS spec.: | |
| . <->"Free Serif/B/ICU:script=latn;language=DFLT;mapping=tex-text;" | |
| . | |
| . * 'italic' with NFSS spec.: | |
| . <->"Free Serif/I/ICU:script=latn;language=DFLT;mapping=tex-text;" | |
| . | |
| . * 'bold italic' with NFSS spec.: | |
| . <->"Free Serif/BI/ICU:script=latn;language=DFLT;mapping=tex-text;" | |
| ................................................. | |
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| (./app_An_2.aux) | |
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| [1 | |
| ] [0] | |
| Capitolo 1. | |
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| []\EU1/TimesNewRoman(1)/m/n/10 poi Barutello-Conti-Ferrario-Terracini (Ferrario | |
| è QUEL Ferrario) Analisi Ma- | |
| [] | |
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| ine 492. | |
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| [1 | |
| ] | |
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| e 501. | |
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| \EU1/TimesNewRoman(1)/m/it/10 il più piccolo chiuso che contiene $\OML/ztmcm/m/ | |
| it/10 A$\EU1/TimesNewRoman(1)/m/it/10 , e si indica con $[] \OT1/ztmcm/m/n/10 = | |
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| [] | |
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| OML/ztmcm/m/it/10 A \OMS/ztmcm/m/n/10 ^^R \OML/ztmcm/m/it/10 X$ \EU1/TimesNewRo | |
| man(1)/m/it/10 è $\OML/ztmcm/m/it/10 @A \OT1/ztmcm/m/n/10 = [] \OMS/ztmcm/m/n/1 | |
| 0 \ []$\EU1/TimesNewRoman(1)/m/it/10 . | |
| [] | |
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| mcm/m/n/10 ([]\OML/ztmcm/m/it/10 ; \OT1/ztmcm/m/n/10 1)$ \EU1/TimesNewRoman(1)/ | |
| m/it/10 ri- | |
| [] | |
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| [] | |
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| [] | |
| [] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 a[] []a[] | |
| [] | |
| [4] [5] [6] | |
| Capitolo 2. | |
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| []\EU1/TimesNewRoman(1)/m/it/10 È cruciale che | |
| [] | |
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| [7 | |
| ] [8] | |
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| [] | |
| [9] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Le funzioni $\OML/ztmcm/m/it/10 ^^Y[] \OT1/ztmc | |
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| Roman(1)/m/it/10 de- | |
| [] | |
| [10] | |
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| []$\OML/ztmcm/m/it/10 f$ \EU1/TimesNewRoman(1)/m/it/10 è continua | |
| [] | |
| [11] | |
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| Capitolo 3. | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Dati []a[] | |
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| [13 | |
| ] | |
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| 1)/m/it/10 conver- | |
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| [] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Consideriamo []a[] | |
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| [14] | |
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| \EU1/TimesNewRoman(1)/m/n/10 Il ragionamento è identico[][][]. []a[] | |
| [] | |
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| [15] | |
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| [17] | |
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| mcm/m/n/10 1])$ | |
| [] | |
| [19] | |
| Capitolo 4. | |
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| zione positiva è positivo, e l’integranda | |
| [] | |
| [20 | |
| ] | |
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| [21] [22] | |
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| mcm/m/n/10 1])\OML/ztmcm/m/it/10 ; d[]$ \EU1/TimesNewRoman(1)/m/it/10 ove $\OML | |
| /ztmcm/m/it/10 d[]\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 f; g\OT1/ztmcm/m/n/10 ) | |
| = [][] \OMS/ztmcm/m/n/10 j\OML/ztmcm/m/it/10 f\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/ | |
| it/10 x\OT1/ztmcm/m/n/10 )\OML/ztmcm/m/it/10 g\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/i | |
| t/10 x\OT1/ztmcm/m/n/10 )\OMS/ztmcm/m/n/10 j\OML/ztmcm/m/it/10 dx$ | |
| [] | |
| [23] | |
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| Capitolo 5. | |
| [25 | |
| ] | |
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| [26] | |
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| [] | |
| [27] | |
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| [] | |
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| Capitolo 6. | |
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| [] | |
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| [] | |
| [34 | |
| ] | |
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| \OT1/ztmcm/m/n/10 )$ \EU1/TimesNewRoman(1)/m/it/10 è uno spazio normato e $\OT1 | |
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| [] | |
| [35] | |
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| [] | |
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| [] | |
| [36] | |
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| [] | |
| [37] [38] | |
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| (1)/m/it/10 uno spa- | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Dimostrare la proposizio- | |
| [] | |
| [39] [40] | |
| Capitolo 7. | |
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| (1)/m/it/10 una suc- | |
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| [41 | |
| ] | |
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| [] | |
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| [42] | |
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| [] | |
| [43] | |
| Capitolo 8. | |
| [44 | |
| ] [45] [46] [47] | |
| Capitolo 9. | |
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| /it/10 x; z\OT1/ztmcm/m/n/10 ) = | |
| [] | |
| [48 | |
| ] | |
| Capitolo 10. | |
| [49 | |
| ] [50] [51] | |
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| [54] [55] | |
| Capitolo 11. | |
| [56 | |
| ] [57] [58] | |
| Capitolo 12. | |
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| [] [] \OMS/ztmcm/m/n/10 ^^T [] \OML/ztmcm/m/it/10 g[]\OT1/ztmcm/m/n/10 (\OML/zt | |
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| /ztmcm/m/n/10 (\OML/ztmcm/m/it/10 x\OT1/ztmcm/m/n/10 ) \OMS/ztmcm/m/n/10 ! \OT1 | |
| /ztmcm/m/n/10 0 \OML/ztmcm/m/it/10 uniformemente \OT1/ztmcm/m/n/10 =[]\OMS/ | |
| ztmcm/m/n/10 ) \OML/ztmcm/m/it/10 f[] \OMS/ztmcm/m/n/10 ! \OT1/ztmcm/m/n/10 0 | |
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| [] | |
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| ) = \OMS/ztmcm/m/n/10 ^^@[] [] \OT1/ztmcm/m/n/10 = \OMS/ztmcm/m/n/10 ^^@[] [] \ | |
| OML/ztmcm/m/it/10 : | |
| [] | |
| [59 | |
| ] [60] | |
| Overfull \hbox (32577.95602pt too wide) in paragraph at lines 2048--2050 | |
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| [] | |
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| [][] | |
| [] | |
| [64] [65] [66] | |
| Capitolo 13. | |
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| [68] | |
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| []$\OML/ztmcm/m/it/10 f\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 x\OT1/ztmcm/m/n/10 | |
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| [69] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Dirò che $\OML/ztmcm/m/it/10 f$ \EU1/TimesNewRo | |
| man(1)/m/it/10 è con- | |
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| n- | |
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| [71] [72] | |
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| n(1)/m/n/10 coefficien- | |
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| [] | |
| [73] [74] | |
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| [76] [77] | |
| Capitolo 14. | |
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| [] | |
| [78 | |
| ] [79] [80] | |
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| [81] | |
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| [] | |
| [82] [83] [84] [85] | |
| Capitolo 15. | |
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| [90] | |
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| [91] [92] | |
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| 8 , e la seconda per | |
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| [93] [94] [95] | |
| Capitolo 16. | |
| [96 | |
| ] [97] | |
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| [98] [99] [100] | |
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| [101] | |
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| [102] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Si studino la convergenza puntuale ed uniforme | |
| della suc- | |
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| [103] | |
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| [104] | |
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| m/m/it/10 e[]dx \OT1/ztmcm/m/n/10 = \OMS/ztmcm/m/n/10 ^^@1$\EU1/TimesNewRoman(1 | |
| )/m/n/10 , e questo valore dell’inte- | |
| [] | |
| [105] [106] | |
| Capitolo 17. | |
| [107 | |
| ] [108] [109] [110] [111] [112] [113] | |
| Capitolo 18. | |
| [114 | |
| ] | |
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| \OMS/ztmcm/m/n/10 ^^R \U/msb/m/n/10 R[]$ | |
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| [116] | |
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| f\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 P \OT1/ztmcm/m/n/10 + \OML/ztmcm/m/it/10 | |
| H\OT1/ztmcm/m/n/10 ) \OMS/ztmcm/m/n/10 ^^@ \OML/ztmcm/m/it/10 f\OT1/ztmcm/m/n/ | |
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| /n/10 (\OML/ztmcm/m/it/10 f\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 P\OT1/ztmcm/m/ | |
| n/10 )) + \OML/ztmcm/m/it/10 dg\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 f\OT1/ztmc | |
| m/m/n/10 (\OML/ztmcm/m/it/10 P\OT1/ztmcm/m/n/10 ))(\OML/ztmcm/m/it/10 df\OT1/zt | |
| mcm/m/n/10 (\OML/ztmcm/m/it/10 P\OT1/ztmcm/m/n/10 )(\OML/ztmcm/m/it/10 H\OT1/zt | |
| mcm/m/n/10 ) + \OML/ztmcm/m/it/10 R\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 H\OT1/ | |
| ztmcm/m/n/10 )) + \OML/ztmcm/m/it/10 ^^Z\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 f | |
| \OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 P \OT1/ztmcm/m/n/10 + \OML/ztmcm/m/it/10 | |
| H\OT1/ztmcm/m/n/10 ) \OMS/ztmcm/m/n/10 ^^@ \OML/ztmcm/m/it/10 f\OT1/ztmcm/m/n/1 | |
| 0 (\OML/ztmcm/m/it/10 P\OT1/ztmcm/m/n/10 )) = | |
| [] | |
| [117] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Supponiamo di []a[] | |
| [] | |
| [118] [119] | |
| Capitolo 19. | |
| [120 | |
| ] [121] [122] | |
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| [] | |
| [123] [124] [125] [126] | |
| Capitolo 20. | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Siano $\OML/ztmcm/m/it/10 f \OT1/ztmcm/m/n/10 : | |
| \OMS/ztmcm/m/n/10 ! | |
| [] | |
| [127 | |
| ] [128] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Sia $\OML/ztmcm/m/it/10 f \OT1/ztmcm/m/n/10 : | |
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| [] | |
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| \OMS/ztmcm/m/n/10 ^^R \U/msb/m/n/10 R[]$ \EU1/TimesNewRoman(1)/m/it/10 aperto | |
| e $\OML/ztmcm/m/it/10 P \OMS/ztmcm/m/n/10 2 \OT1/ztmcm/m/n/10 | |
| $\EU1/TimesNewRoman(1)/m/it/10 , e $\OML/ztmcm/m/it/10 k; h \OMS/ztmcm/m/n/10 2 | |
| $ $2 | |
| [] | |
| [129] | |
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| [] | |
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| \OMS/ztmcm/m/n/10 ^^R | |
| [] | |
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| [] | |
| [130] | |
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| [131] [132] [133] [134] | |
| Capitolo 21. | |
| [135 | |
| ] [136] [137] | |
| Overfull \hbox (2.4921pt too wide) in paragraph at lines 3596--3598 | |
| $\OML/ztmcm/m/it/10 x$ \EU1/TimesNewRoman(1)/m/n/10 darebbe problemi se fosse m | |
| inore di $\OMS/ztmcm/m/n/10 ^^@\OT1/ztmcm/m/n/10 1$ \EU1/TimesNewRoman(1)/m/n/1 | |
| 0 perché renderebbe negativo l’argomento | |
| [] | |
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| [] | |
| [138] | |
| Overfull \hbox (2.24658pt too wide) in paragraph at lines 3603--3604 | |
| []\EU1/TimesNewRoman(1)/m/n/10 cioè se converge uniformemente su $\OT1/ztmcm/m/ | |
| n/10 [0\OML/ztmcm/m/it/10 ; \OT1/ztmcm/m/n/10 1]$ \EU1/TimesNewRoman(1)/m/n/10 | |
| convergerà anche puntualmente su $\OT1/ztmcm/m/n/10 [0\OML/ztmcm/m/it/10 ; \OT1 | |
| /ztmcm/m/n/10 1]$\EU1/TimesNewRoman(1)/m/n/10 ? | |
| [] | |
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| []\EU1/TimesNewRoman(1)/m/n/10 grazie” []a[] | |
| [] | |
| Overfull \hbox (14076.17456pt too wide) in paragraph at lines 3604--3611 | |
| \EU1/TimesNewRoman(1)/m/n/10 Io: “Dimmi di ke esercizio stai parlando .” []a[] | |
| [] | |
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| n/10 (0\OML/ztmcm/m/it/10 ; \OT1/ztmcm/m/n/10 1)$\EU1/TimesNewRoman(1)/m/n/10 ” | |
| []a[] | |
| [] | |
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| [] | |
| Overfull \hbox (14006.46425pt too wide) in paragraph at lines 3604--3611 | |
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| [] | |
| [139] [140] [141] [142] | |
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| [][] []\EU1/TimesNewRoman(1)/m/n/10 a[] | |
| [] | |
| [143] [144] [145] | |
| Capitolo 22. | |
| Overfull \hbox (7.181pt too wide) in paragraph at lines 3769--3770 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Si dice \EU1/TimesNewRoman(1)/m/n/10 de- | |
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| [146 | |
| ] | |
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| /m/it/10 è continua, de- | |
| [] | |
| [147] [148] | |
| Overfull \hbox (6.92216pt too wide) detected at line 3854 | |
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| [] | |
| Overfull \hbox (5.48344pt too wide) detected at line 3855 | |
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| [] | |
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| \OT1/ztmcm/m/n/10 = [] [] = [] [] = | |
| [] | |
| [149] [150] [151] [152] [153] | |
| Capitolo 23. | |
| [154 | |
| ] [155] | |
| Overfull \hbox (5.82668pt too wide) in paragraph at lines 4012--4013 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Se $\OML/ztmcm/m/it/10 f \OMS/ztmcm/m/n/10 2 \O | |
| ML/ztmcm/m/it/10 C[]\OT1/ztmcm/m/n/10 ( | |
| )$ | |
| [] | |
| Overfull \hbox (8.10773pt too wide) in paragraph at lines 4021--4022 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Se invece $\OML/ztmcm/m/it/10 f \OMS/ztmcm/m/n/ | |
| 10 2 | |
| [] | |
| [156] [157] [158] | |
| Overfull \hbox (2.2339pt too wide) in paragraph at lines 4087--4088 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Consideriamo $\OML/ztmcm/m/it/10 f \OT1/ztmcm/m | |
| /n/10 : | |
| [] | |
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| \EU1/TimesNewRoman(1)/m/n/10 di Ferrario, equivalente a quella della Felli con | |
| dimostrazione immediata dell’equivalen- | |
| [] | |
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| []$\OT1/ztmcm/m/n/10 | |
| \OMS/ztmcm/m/n/10 ^^R \U/msb/m/n/10 R[]$ | |
| [] | |
| [159] [160] | |
| Capitolo 24. | |
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| ] | |
| Overfull \hbox (9.89258pt too wide) in paragraph at lines 4162--4163 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Sia | |
| [] | |
| [162] [163] | |
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| \EU1/TimesNewRoman(1)/bx/n/14.4 Algebra Lineare, sistemiamo quel problema di es | |
| em- | |
| [] | |
| [164] [165] [166] | |
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| [] []\EU1/TimesNewRoman(1)/m/n/10 a[] | |
| [] | |
| [167] [168] | |
| Capitolo 25. | |
| [169 | |
| ] [170] | |
| Overfull \hbox (0.36993pt too wide) detected at line 4336 | |
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| [] | |
| Overfull \hbox (6.72116pt too wide) detected at line 4340 | |
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| [] | |
| Overfull \hbox (13.56497pt too wide) detected at line 4355 | |
| [] \OT1/ztmcm/m/n/10 4\OML/ztmcm/m/it/10 ^^K^^Z[] [][] [] ^^Z[] \OMS/ztmcm/m/n/ | |
| 10 ^^A \OML/ztmcm/m/it/10 ^^Z [] ^^R \OT1/ztmcm/m/n/10 + \OML/ztmcm/m/it/10 ^^Z | |
| [] [][] []: | |
| [] | |
| [171] [172] | |
| Capitolo 26. | |
| [173 | |
| ] | |
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| Overfull \hbox (14011.32916pt too wide) in paragraph at lines 4387--4390 | |
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| [] | |
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| [] | |
| [174] [175] | |
| Capitolo 27. | |
| [176 | |
| ] [177] [178] [179] [180] [181] [182] | |
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| i del- | |
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| [] | |
| [183] | |
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| [] | |
| [184] | |
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| []a[] | |
| [] | |
| [185] | |
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| ^^@ \OML/ztmcm/m/it/10 b[]\OT1/ztmcm/m/n/10 ) \OMS/ztmcm/m/n/10 ^^@ \OML/ztmcm/ | |
| m/it/10 f\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 af \OMS/ztmcm/m/n/10 ^^@ \OML/zt | |
| mcm/m/it/10 cb\OT1/ztmcm/m/n/10 ) + \OML/ztmcm/m/it/10 c\OT1/ztmcm/m/n/10 (\OML | |
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| ) \OML/ztmcm/m/it/10 > \OT1/ztmcm/m/n/10 0 =[]\OMS/ztmcm/m/n/10 ) \OML/ztmcm/ | |
| m/it/10 i\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 ae \OMS/ztmcm/m/n/10 ^^@ \OML/zt | |
| mcm/m/it/10 b[]\OT1/ztmcm/m/n/10 ) \OML/ztmcm/m/it/10 > f\OT1/ztmcm/m/n/10 (\OM | |
| L/ztmcm/m/it/10 af \OMS/ztmcm/m/n/10 ^^@ \OML/ztmcm/m/it/10 cb\OT1/ztmcm/m/n/10 | |
| ) \OMS/ztmcm/m/n/10 ^^@ \OML/ztmcm/m/it/10 c\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it | |
| /10 bf \OMS/ztmcm/m/n/10 ^^@ \OML/ztmcm/m/it/10 ce\OT1/ztmcm/m/n/10 ) =[]\OMS/ | |
| ztmcm/m/n/10 ) | |
| [] | |
| [186] [187] | |
| Capitolo 28. | |
| [188 | |
| ] | |
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| [190] [191] | |
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| [192] [193] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 I due termini si chiamano spes- | |
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| [194] [195] | |
| Capitolo 29. | |
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| ] | |
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| [200] [201] [202] [203] | |
| Capitolo 30. | |
| [204 | |
| ] | |
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| /m/it/10 è un rettangolo $\OML/ztmcm/m/it/10 n$\EU1/TimesNewRoman(1)/m/it/10 -d | |
| imensionale | |
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| [205] | |
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| [211] | |
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| \EU1/TimesNewRoman(1)/m/n/10 spettivamente | |
| [] | |
| [212] | |
| Capitolo 31. | |
| [213 | |
| ] [214] | |
| Overfull \hbox (15.72667pt too wide) detected at line 5372 | |
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| [215] | |
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| [216] [217] [218] [219] | |
| Capitolo 32. | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Siano $\OML/ztmcm/m/it/10 A \OMS/ztmcm/m/n/10 ^ | |
| ^R \U/msb/m/n/10 R[]$ \EU1/TimesNewRoman(1)/m/it/10 chiu- | |
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| [221] | |
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| [222] | |
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| []\OML/ztmcm/m/it/10 s[] \OMS/ztmcm/m/n/10 ^^@ []\OML/ztmcm/m/it/10 s[] \OT1/zt | |
| mcm/m/n/10 = [] [] + [] [] [][] \OML/ztmcm/m/it/10 R[] \OMS/ztmcm/m/n/10 ^^T | |
| [] | |
| [223] [224] | |
| File: Ax.jpg Graphic file (type QTm) | |
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| \EU1/TimesNewRoman(1)/m/n/10 gno sotto. []a[] | |
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| [225] | |
| File: D.jpg Graphic file (type QTm) | |
| <use "D.jpg" > [226] [227] | |
| Capitolo 33. | |
| [228 | |
| ] [229] [230] [231] [232] [233] | |
| Capitolo 34. | |
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| \U/msb/m/n/10 R[] \OT1/ztmcm/m/n/10 = \U/msb/m/n/10 R[] \OMS/ztmcm/m/n/10 ^^B \ | |
| U/msb/m/n/10 R$\EU1/TimesNewRoman(1)/m/n/10 . Invece $\OML/ztmcm/m/it/10 A[]$ \ | |
| EU1/TimesNewRoman(1)/m/n/10 è l’insieme degli $\OML/ztmcm/m/it/10 z$ \EU1/Times | |
| NewRoman(1)/m/n/10 per cui $\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 x; y; z\OT1/z | |
| tmcm/m/n/10 ) \OMS/ztmcm/m/n/10 2 \OML/ztmcm/m/it/10 A$\EU1/TimesNewRoman(1)/m/ | |
| n/10 , quindi $\OT1/ztmcm/m/n/10 [\OML/ztmcm/m/it/10 u[]\OT1/ztmcm/m/n/10 (\OML | |
| /ztmcm/m/it/10 x; y\OT1/ztmcm/m/n/10 )\OML/ztmcm/m/it/10 ; u[]\OT1/ztmcm/m/n/10 | |
| (\OML/ztmcm/m/it/10 x; y\OT1/ztmcm/m/n/10 )]$\EU1/TimesNewRoman(1)/m/n/10 . | |
| [] | |
| [235] | |
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| [237] | |
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| [238] [239] | |
| Capitolo 35. | |
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| \EU1/TimesNewRoman(1)/m/n/10 ci sono massimi locali. Quindi ha un grafico di qu | |
| esto tipo: []a[] | |
| [] | |
| [240 | |
| ] [241] | |
| File: Regione_.jpg Graphic file (type QTm) | |
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| /ztmcm/m/n/10 ^^@ [] \OML/ztmcm/m/it/10 dx \OT1/ztmcm/m/n/10 = | |
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| [242] | |
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| grazione, l’integrale: | |
| [] | |
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| dx \OT1/ztmcm/m/n/10 = [][][]\OML/ztmcm/m/it/10 dx \OT1/ztmcm/m/n/10 = | |
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| [246] [247] [248] | |
| Capitolo 36. | |
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| [249 | |
| ] | |
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| ren- | |
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| [250] [251] | |
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| L/ztmcm/m/it/10 : | |
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| [252] [253] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Consideriamo la $\OML/ztmcm/m/it/10 z$ \EU1/Tim | |
| esNewRoman(1)/m/it/10 e le polari di $\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 x; | |
| y\OT1/ztmcm/m/n/10 )$\EU1/TimesNewRoman(1)/m/it/10 , | |
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| [255] | |
| Capitolo 37. | |
| [256 | |
| ] [257] [258] [259] [260] | |
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| Capitolo 38. | |
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| [264] | |
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| \EU1/TimesNewRoman(1)/m/n/10 dove $\OML/ztmcm/m/it/10 h$ \EU1/TimesNewRoman(1)/ | |
| m/n/10 è una coordinata $\OML/ztmcm/m/it/10 z$\EU1/TimesNewRoman(1)/m/n/10 . Qu | |
| esto è il cerchio, lo strato. Noi vogliamo scrivere l’integrale | |
| [] | |
| [265] [266] [267] | |
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| [268] | |
| File: Regioneuv.jpg Graphic file (type QTm) | |
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| [269] [270] | |
| Capitolo 39. | |
| [271 | |
| ] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Sia $\OML/ztmcm/m/it/10 D \OMS/ztmcm/m/n/10 ^^R | |
| \U/msb/m/n/10 R[]$ \EU1/TimesNewRoman(1)/m/it/10 aperto mi- | |
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| [] | |
| [274] | |
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| ione. E chiudiamo qua. []a[] | |
| [] | |
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| Capitolo 40. | |
| [280 | |
| ] [281] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Siano $\OT1/ztmcm/m/n/10 | |
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| [282] | |
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| [] []\EU1/TimesNewRoman(1)/m/n/10 a[] | |
| [] | |
| [283] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Con $\OML/ztmcm/m/it/10 F; \OT1/ztmcm/m/n/10 | |
| $ \EU1/TimesNewRoman(1)/m/it/10 come sopra $\OML/ztmcm/m/it/10 F$ | |
| [] | |
| [284] | |
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| []\EU1/TimesNewRoman(1)/bx/n/10 (delle Contra- | |
| [] | |
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| 58. | |
| [285] | |
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| []$\OML/ztmcm/m/it/10 X \OT1/ztmcm/m/n/10 = (0\OML/ztmcm/m/it/10 ; \OT1/ztmcm/m | |
| /n/10 1)$ \EU1/TimesNewRoman(1)/m/it/10 coll’usuale distan- | |
| [] | |
| [286] [287] | |
| Capitolo 41. | |
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| <use "Guldino1.jpg" > | |
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| \EU1/TimesNewRoman(1)/m/it/10 per un motivo che sarà chiaro subito. []a[] | |
| [] | |
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| [] []\EU1/TimesNewRoman(1)/m/it/10 a[] | |
| [] | |
| [288 | |
| ] | |
| File: Guldino2.jpg Graphic file (type QTm) | |
| <use "Guldino2.jpg" > | |
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| \EU1/TimesNewRoman(1)/m/n/10 Immaginiamo di proiettare il solido su $\OML/ztmcm | |
| /m/it/10 xy$\EU1/TimesNewRoman(1)/m/n/10 . []a[] | |
| [] | |
| Overfull \hbox (14227.24948pt too wide) in paragraph at lines 6931--6934 | |
| [] []\EU1/TimesNewRoman(1)/m/n/10 a[] | |
| [] | |
| [289] [290] | |
| Overfull \hbox (4.91095pt too wide) in paragraph at lines 6955--6957 | |
| \EU1/TimesNewRoman(1)/m/n/10 che va bene su $\OT1/ztmcm/m/n/10 3\OML/ztmcm/m/it | |
| /10 x[] \OT1/ztmcm/m/n/10 + \OML/ztmcm/m/it/10 y[] \OT1/ztmcm/m/n/10 = 1$ \EU1/ | |
| TimesNewRoman(1)/m/n/10 perché quella roba viene $\OML/ztmcm/m/it/10 ^^Z[] \OT1 | |
| /ztmcm/m/n/10 = 1$\EU1/TimesNewRoman(1)/m/n/10 . Quindi si guarda l’equazione | |
| [] | |
| [291] [292] [293] | |
| Overfull \hbox (0.95163pt too wide) detected at line 7011 | |
| [] [] \OML/ztmcm/m/it/10 dx[] \OT1/ztmcm/m/n/10 = []\OML/ztmcm/m/it/10 x[] [] d | |
| x[] \OT1/ztmcm/m/n/10 = []\OML/ztmcm/m/it/10 x[] [] dx[] \OT1/ztmcm/m/n/10 = | |
| [] | |
| [294] | |
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| \EU1/TimesNewRoman(1)/m/n/10 Adesso viene la parte difficile. Andiamo per induz | |
| ione. Passo base: $\OML/ztmcm/m/it/10 n \OT1/ztmcm/m/n/10 = 3$\EU1/TimesNewRoma | |
| n(1)/m/n/10 . L’integralone | |
| [] | |
| [295] | |
| File: DoppiaPalla.jpg Graphic file (type QTm) | |
| <use "DoppiaPalla.jpg" > | |
| Overfull \hbox (14062.85034pt too wide) in paragraph at lines 7049--7052 | |
| \EU1/TimesNewRoman(1)/m/n/10 fuori da quella centrata in $\OT1/ztmcm/m/n/10 (0\ | |
| OML/ztmcm/m/it/10 ; \OT1/ztmcm/m/n/10 0)$ \EU1/TimesNewRoman(1)/m/n/10 e di rag | |
| gio $[]$. []a[] | |
| [] | |
| Overfull \hbox (14227.24948pt too wide) in paragraph at lines 7049--7052 | |
| [] []\EU1/TimesNewRoman(1)/m/n/10 a[] | |
| [] | |
| [296] [297] | |
| Capitolo 42. | |
| [298 | |
| ] | |
| Overfull \hbox (21.94824pt too wide) in paragraph at lines 7106--7107 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Siano | |
| [] | |
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| [] | |
| [] | |
| [299] [300] [301] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Siano $\OML/ztmcm/m/it/10 F \OMS/ztmcm/m/n/10 2 | |
| \OML/ztmcm/m/it/10 C[]\OT1/ztmcm/m/n/10 ((\OML/ztmcm/m/it/10 a; b\OT1/ztmcm/m/ | |
| n/10 ) \OMS/ztmcm/m/n/10 ^^B \U/msb/m/n/10 R[]\OML/ztmcm/m/it/10 ; \U/msb/m/n/1 | |
| 0 R[]\OT1/ztmcm/m/n/10 )$ \EU1/TimesNewRoman(1)/m/it/10 (u- | |
| [] | |
| [302] [303] | |
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| \EU1/TimesNewRoman(1)/m/n/10 soluzione. Noi ci vediamo Mercoledì. Lunedì invece | |
| avete esercitazione. []a[] | |
| [] | |
| [304] [305] | |
| Capitolo 43. | |
| [306 | |
| ] [307] [308] [309] [310] | |
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| \EU1/TimesNewRoman(1)/m/n/10 Quindi la funzione è continua nell’origine. []a[] | |
| [] | |
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| \EU1/TimesNewRoman(1)/m/n/10 rimane $[] \OML/ztmcm/m/it/10 ^^R$\EU1/TimesNewRom | |
| an(1)/m/n/10 . []a[] | |
| [] | |
| [311] [312] | |
| Capitolo 44. | |
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| \EU1/TimesNewRoman(1)/m/n/10 Quindi è continua nell’origine. Vediamo le derivat | |
| e direzionali. Fissiamo $[] \OT1/ztmcm/m/n/10 = []$\EU1/TimesNewRoman(1)/m/n/10 | |
| . | |
| [] | |
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| \EU1/TimesNewRoman(1)/m/n/10 Quindi la funzione è differenziabile. []a[] | |
| [] | |
| [313 | |
| ] | |
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| [] [] \OT1/ztmcm/m/n/10 = [] [] = | |
| [] | |
| [314] | |
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| \EU1/TimesNewRoman(1)/m/n/10 Quindi la continuità c’è. A questo punto derivate | |
| direzionali. Fissiamo $[] \OT1/ztmcm/m/n/10 = [] \OML/ztmcm/m/it/10 :$ | |
| [] | |
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| \EU1/TimesNewRoman(1)/m/n/10 tazzo di differenziabilità. []a[] | |
| [] | |
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| \EU1/TimesNewRoman(1)/m/n/10 Quindi la differenziabilità ce la sognamo. []a[] | |
| [] | |
| [315] | |
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| \OT1/ztmcm/m/n/10 = [] [] = | |
| [] | |
| [316] | |
| Capitolo 45. | |
| [317 | |
| ] | |
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| [318] [319] [320] [321] [322] [323] | |
| Capitolo 46. | |
| [324 | |
| ] | |
| Overfull \hbox (1.82454pt too wide) detected at line 7685 | |
| [] [] \OT1/ztmcm/m/n/10 = [] [] = [] [] = | |
| [] | |
| [325] | |
| Capitolo 47. | |
| [326 | |
| ] [327] | |
| Overfull \hbox (1.27225pt too wide) detected at line 7742 | |
| [] [] \OT1/ztmcm/m/n/10 = [] [] = | |
| [] | |
| [328] | |
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| \EU1/TimesNewRoman(1)/m/n/10 mentre per $\OML/ztmcm/m/it/10 y \OMS/ztmcm/m/n/10 | |
| 2 []$ \EU1/TimesNewRoman(1)/m/n/10 varierà in $[]$. Quindi l’integrale | |
| [] | |
| [329] [330] [331] [332] | |
| Capitolo 48. | |
| [333 | |
| ] | |
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| \EU1/TimesNewRoman(1)/m/n/10 scio qua. []a[] | |
| [] | |
| [334] [335] | |
| Capitolo 49. | |
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| \EU1/TimesNewRoman(1)/m/n/10 Capire l’intervallo massimale di unicità della sol | |
| uzione è un problema importante. Chie- | |
| [] | |
| [336 | |
| ] | |
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| \EU1/TimesNewRoman(1)/m/it/10 re $[] [] \OT1/ztmcm/m/n/10 = +\OMS/ztmcm/m/n/10 | |
| 1$\EU1/TimesNewRoman(1)/m/it/10 , ove $\OML/ztmcm/m/it/10 d\OT1/ztmcm/m/n/10 (( | |
| \OML/ztmcm/m/it/10 t; Y\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 t\OT1/ztmcm/m/n/10 | |
| ))\OML/ztmcm/m/it/10 ; @\OT1/ztmcm/m/n/10 | |
| ) = [] []$\EU1/TimesNewRoman(1)/m/it/10 . | |
| [] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 In mo- | |
| [] | |
| [337] [338] [339] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Siano $\OT1/ztmcm/m/n/10 | |
| \OMS/ztmcm/m/n/10 ^^R \U/msb/m/n/10 R[]$ | |
| [] | |
| [340] | |
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| [] [] \OT1/ztmcm/m/n/10 + [] + [] \OMS/ztmcm/m/n/10 ^^T | |
| [] | |
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| [] \OT1/ztmcm/m/n/10 + [] [] + [] [] + [] [] = | |
| [] | |
| [341] | |
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| \EU1/TimesNewRoman(1)/m/n/10 di domani avete esercitazione, noi ci vediamo Vene | |
| rdì? []a[] | |
| [] | |
| Overfull \hbox (5.236pt too wide) in paragraph at lines 8056--8057 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Se $\OML/ztmcm/m/it/10 h\OT1/ztmcm/m/n/10 (\OML | |
| /ztmcm/m/it/10 t\OT1/ztmcm/m/n/10 )\OML/ztmcm/m/it/10 ; []\OT1/ztmcm/m/n/10 (\O | |
| ML/ztmcm/m/it/10 t\OT1/ztmcm/m/n/10 )\OML/ztmcm/m/it/10 ; ^^L\OT1/ztmcm/m/n/10 | |
| (\OML/ztmcm/m/it/10 t\OT1/ztmcm/m/n/10 )$ \EU1/TimesNewRoman(1)/m/it/10 sono fu | |
| nzioni con- | |
| [] | |
| [342] | |
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| \EU1/TimesNewRoman(1)/m/n/10 nella disuguaglianza assunta vera per ipotesi, si | |
| ottiene la tesi. Quindi diamo un’occhiata | |
| [] | |
| [343] | |
| Capitolo 50. | |
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| [344 | |
| ] [345] [346] | |
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| \OML/ztmcm/m/it/10 f[]\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 x\OT1/ztmcm/m/n/10 | |
| ) = [][] [] \OML/ztmcm/m/it/10 n [] x \OT1/ztmcm/m/n/10 + [] [] [] \OML/ztmcm/m | |
| /it/10 : | |
| [] | |
| [347] [348] [349] | |
| Capitolo 51. | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Siano $\OT1/ztmcm/m/n/10 | |
| = (\OML/ztmcm/m/it/10 a; b\OT1/ztmcm/m/n/10 ) \OMS/ztmcm/m/n/10 ^^B \U/msb/m/n | |
| /10 R[]$\EU1/TimesNewRoman(1)/m/it/10 , | |
| [] | |
| [350 | |
| ] [351] | |
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| [] | |
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| [352] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Analogamente si ha che | |
| [] | |
| [353] [354] [355] | |
| Capitolo 52. | |
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| []\EU1/TimesNewRoman(1)/bx/n/10 (di esistenza globale) \EU1/TimesNewRoman(1)/m/ | |
| it/10 Sia $\OML/ztmcm/m/it/10 S \OT1/ztmcm/m/n/10 = (\OML/ztmcm/m/it/10 a; b\OT | |
| 1/ztmcm/m/n/10 ) \OMS/ztmcm/m/n/10 ^^B | |
| [] | |
| [356 | |
| ] [357] [358] [359] | |
| File: SoluzioniEqDiff_.jpg Graphic file (type QTm) | |
| <use "SoluzioniEqDiff_.jpg" > [360] [361] [362] | |
| Capitolo 53. | |
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| [] | |
| [] | |
| [363 | |
| ] [364] | |
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| [] | |
| [] | |
| [365] [366] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Si può dimostrare (non | |
| [] | |
| [367] [368] [369] | |
| Capitolo 54. | |
| [370 | |
| ] [371] | |
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| <use "Lav.jpg" > [372] [373] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Se $\OML/ztmcm/m/it/10 ^^U[]; [] ; ^^U[]$ | |
| [] | |
| Overfull \hbox (9.21307pt too wide) in paragraph at lines 8801--8802 | |
| \EU1/TimesNewRoman(1)/m/it/10 sono gli autovalori della matrice con molteplicit | |
| à algebriche $\OML/ztmcm/m/it/10 m[]; [] ; m[]$\EU1/TimesNewRoman(1)/m/it/10 , | |
| allora l’integrale | |
| [] | |
| [374] | |
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| [] | |
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| [375] | |
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| [] \OT1/ztmcm/m/n/10 = \OML/ztmcm/m/it/10 e[] [] \OT1/ztmcm/m/n/10 = [] | |
| [] | |
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| []\EU1/TimesNewRoman(1)/bx/n/12 Teorema: soluzione particolare più soluzioni de | |
| l sistema omo- | |
| [] | |
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| [] | |
| [] | |
| [376] [377] [378] | |
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| \OT1/ztmcm/m/n/10 = [] [] = | |
| [] | |
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| \OT1/ztmcm/m/n/10 = [] [] \OML/ztmcm/m/it/10 : | |
| [] | |
| [379] | |
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| [380] | |
| Capitolo 55. | |
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| [381 | |
| ] [382] [383] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 L’insieme del- | |
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| [384] | |
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| [] | |
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| \EU1/TimesNewRoman(1)/m/it/10 Siano $[] \OMS/ztmcm/m/n/10 2 \OML/ztmcm/m/it/10 | |
| C[]\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 I\OT1/ztmcm/m/n/10 )$ \EU1/TimesNewRom | |
| an(1)/m/it/10 una soluzione particolare di $\OT1/ztmcm/m/n/10 (\OMS/ztmcm/m/n/1 | |
| 0 ^^C^^C\OT1/ztmcm/m/n/10 )$ \EU1/TimesNewRoman(1)/m/it/10 e $\OML/ztmcm/m/it/1 | |
| 0 V[]$ \EU1/TimesNewRoman(1)/m/it/10 lo spazio delle soluzioni dell’equa- | |
| [] | |
| [385] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Sia $\OML/ztmcm/m/it/10 P\OT1/ztmcm/m/n/10 (\OM | |
| L/ztmcm/m/it/10 t\OT1/ztmcm/m/n/10 )$ | |
| [] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Siano $\OML/ztmcm/m/it/10 ^^U[]; ^^U[]; [] ; ^^ | |
| U[]$ | |
| [] | |
| [387] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Se ho $\OML/ztmcm/m/it/10 r$ \EU1/TimesNewRoman | |
| (1)/m/it/10 numeri com- | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Sia | |
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| [389] | |
| LaTeX Warning: Command \l invalid in math mode on input line 9168. | |
| Missing character: There is no ł in font zptmcm7m! | |
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| [] | |
| [] | |
| [390] [391] | |
| Capitolo 56. | |
| [392 | |
| ] [393] [394] [395] [396] [397] | |
| Capitolo 57. | |
| Overfull \hbox (0.48544pt too wide) in paragraph at lines 9340--9342 | |
| \EU1/TimesNewRoman(1)/m/n/10 Allora supponiamo di avere $\OML/ztmcm/m/it/10 z[] | |
| ; [] ; z[]$ \EU1/TimesNewRoman(1)/m/n/10 soluzioni linearmente indipendenti del | |
| l’equazione | |
| [] | |
| [398 | |
| ] [399] [400] | |
| Overfull \hbox (44.00395pt too wide) in paragraph at lines 9415--9417 | |
| \EU1/TimesNewRoman(1)/m/n/10 Sommando a $\OML/ztmcm/m/it/10 u$ \EU1/TimesNewRom | |
| an(1)/m/n/10 l’integrale generale dell’omogenea otteniamo l’integrale generale | |
| dell’inomogenea. | |
| [] | |
| [401] [402] | |
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| \EU1/TimesNewRoman(1)/m/n/10 la cui ampiezza aumenta man mano che passa il temp | |
| o. []a[] | |
| [] | |
| [403] [404] | |
| Capitolo 58. | |
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| []\EU1/TimesNewRoman(1)/bx/n/14.4 Curve in $\U/msb/m/n/14.4 R[]$\EU1/TimesNewRo | |
| man(1)/bx/n/14.4 : definizione, curve regolari, curve equi- | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Consideriamo la legge ora- | |
| [] | |
| [405 | |
| ] [406] | |
| Overfull \hbox (1.8078pt too wide) in paragraph at lines 9577--9578 | |
| [] \EU1/TimesNewRoman(1)/m/it/10 Se $\OML/ztmcm/m/it/10 ^^U[]\OT1/ztmcm/m/n/10 | |
| (\OML/ztmcm/m/it/10 t\OT1/ztmcm/m/n/10 ) \OML/ztmcm/m/it/10 > \OT1/ztmcm/m/n/10 | |
| 0$ | |
| [] | |
| File: SchemaComposizione.jpg Graphic file (type QTm) | |
| <use "SchemaComposizione.jpg" > [407] | |
| Overfull \hbox (2.7146pt too wide) in paragraph at lines 9601--9602 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Le classi di equivalenza di $[]$ si dicono \EU1 | |
| /TimesNewRoman(1)/m/n/10 cam- | |
| [] | |
| Overfull \hbox (8.84256pt too wide) in paragraph at lines 9617--9618 | |
| []$[][]\OT1/ztmcm/m/n/10 (\OML/ztmcm/m/it/10 t\OT1/ztmcm/m/n/10 ) = [] $ | |
| [] | |
| [408] | |
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| [] | |
| [] | |
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| []\EU1/TimesNewRoman(1)/m/it/10 Data $[] \OMS/ztmcm/m/n/10 2 \OML/ztmcm/m/it/10 | |
| C[]\OT1/ztmcm/m/n/10 ([\OML/ztmcm/m/it/10 a; b\OT1/ztmcm/m/n/10 ]\OML/ztmcm/m/ | |
| it/10 ; \U/msb/m/n/10 R[]\OT1/ztmcm/m/n/10 )$\EU1/TimesNewRoman(1)/m/it/10 , se | |
| [] | |
| [409] | |
| Overfull \hbox (5.60497pt too wide) in paragraph at lines 9665--9666 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Ogni curva $[] \OMS/ztmcm/m/n/10 2 \OML/ztmcm/m | |
| /it/10 C[]\OT1/ztmcm/m/n/10 ([\OML/ztmcm/m/it/10 a; b\OT1/ztmcm/m/n/10 ] \OMS/z | |
| tmcm/m/n/10 ! \U/msb/m/n/10 R[]\OT1/ztmcm/m/n/10 )$ | |
| [] | |
| Overfull \hbox (14189.78685pt too wide) in paragraph at lines 9668--9670 | |
| \EU1/TimesNewRoman(1)/m/n/10 Esiste l’integrale perché $[]$ è $\OML/ztmcm/m/it/ | |
| 10 C[]$\EU1/TimesNewRoman(1)/m/n/10 , dimostrata l’uguaglianza è provato il teo | |
| rema. []a[] | |
| [] | |
| [410] | |
| Capitolo 59. | |
| Overfull \hbox (3.68584pt too wide) detected at line 9690 | |
| [] [] \OT1/ztmcm/m/n/10 d\OML/ztmcm/m/it/10 t [] [] [] \OT1/ztmcm/m/n/10 d\OML/ | |
| ztmcm/m/it/10 t [] [] [] \OT1/ztmcm/m/n/10 d\OML/ztmcm/m/it/10 t \OT1/ztmcm/m/n | |
| /10 + [] [] d\OML/ztmcm/m/it/10 t \OT1/ztmcm/m/n/10 = | |
| [] | |
| [411 | |
| ] [412] | |
| Overfull \hbox (13.32672pt too wide) detected at line 9716 | |
| \OT1/ztmcm/m/n/10 ^^@ []([]) = [][](\OML/ztmcm/m/it/10 S[]\OT1/ztmcm/m/n/10 ([] | |
| )) [][] ([]) = [][](\OML/ztmcm/m/it/10 S[]\OT1/ztmcm/m/n/10 ([]))[] = [] \OMS/z | |
| tmcm/m/n/10 8[] 2 \OT1/ztmcm/m/n/10 [0\OML/ztmcm/m/it/10 ; L\OT1/ztmcm/m/n/10 ( | |
| [])]\OML/ztmcm/m/it/10 : | |
| [] | |
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| [] | |
| [] | |
| Overfull \hbox (9.05347pt too wide) in paragraph at lines 9726--9727 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Siano $\OT1/ztmcm/m/n/10 | |
| \OMS/ztmcm/m/n/10 ^^R \U/msb/m/n/10 R[]$ \EU1/TimesNewRoman(1)/m/it/10 aperto, | |
| $\OML/ztmcm/m/it/10 f \OMS/ztmcm/m/n/10 2 \OML/ztmcm/m/it/10 C[]\OT1/ztmcm/m/n | |
| /10 ( | |
| )$\EU1/TimesNewRoman(1)/m/it/10 , | |
| [] | |
| Overfull \hbox (7.71669pt too wide) in paragraph at lines 9731--9732 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Siano $\OT1/ztmcm/m/n/10 | |
| \OMS/ztmcm/m/n/10 ^^R \U/msb/m/n/10 R[]$ | |
| [] | |
| [413] | |
| Overfull \hbox (2.64774pt too wide) in paragraph at lines 9745--9746 | |
| []\EU1/TimesNewRoman(1)/m/it/10 Se $\OT1/ztmcm/m/n/10 ^^@$ | |
| [] | |
| File: Elica.jpg Graphic file (type QTm) | |
| <use "Elica.jpg" > [414] | |
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| [415] [416] [417] [418] | |
| Capitolo 60. | |
| [419 | |
| ] | |
| Overfull \hbox (2.78299pt too wide) in paragraph at lines 9850--9852 | |
| \EU1/TimesNewRoman(1)/m/n/10 smo. Quindi ad ogni partizione $\OML/ztmcm/m/it/10 | |
| P[]$ \EU1/TimesNewRoman(1)/m/n/10 di $[][]$ è associata in modo biiettivo dall | |
| ’omeomorfismo | |
| [] | |
| [420] [421] [422] [423] [424] [425] | |
| Overfull \hbox (3.37502pt too wide) in paragraph at lines 9975--9977 | |
| \EU1/TimesNewRoman(1)/m/n/10 Questa funzione però non è Lipschitziana in $\U/ms | |
| b/m/n/10 R$\EU1/TimesNewRoman(1)/m/n/10 , poiché in $\OMS/ztmcm/m/n/10 ^^@\OT1/ | |
| ztmcm/m/n/10 2$ \EU1/TimesNewRoman(1)/m/n/10 la derivata tende all’infinito. | |
| [] | |
| [426] [427] | |
| Capitolo 61. | |
| [428 | |
| ] | |
| showing defi | |
| showing deficonn | |
| [429] (./app_An_2.loe [430 | |
| ] [431] | |
| Overfull \hbox (2.5pt too wide) detected at line 469 | |
| \EU1/TimesNewRoman(1)/m/n/10 40.1.0.10 | |
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| [432] | |
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| \EU1/TimesNewRoman(1)/m/n/10 58.1.1.10 | |
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| \EU1/TimesNewRoman(1)/m/n/10 59.4.0.10 | |
| [] | |
| ) | |
| showing teor | |
| [433] (./app_An_2.loe | |
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| [][] [][]\EU1/TimesNewRoman(1)/m/n/10 Teorema (Integrale del limite uniforme e | |
| limite uniforme dell’integrale | |
| [] | |
| [434 | |
| ] | |
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| \EU1/TimesNewRoman(1)/m/n/10 52.1.0.10 | |
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| [][] [][]\EU1/TimesNewRoman(1)/m/n/10 Teorema (Caso particolare del Teorema Pr | |
| ecedente: Coefficienti Rea- | |
| [] | |
| ) | |
| showing coro | |
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| showing | |
| [436] (./app_An_2.loe | |
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| [][] [][]\EU1/TimesNewRoman(1)/m/n/10 Proposizione (Differenziabilità di funzi | |
| oni vettoriali e delle loro com- | |
| [] | |
| Overfull \hbox (7.9903pt too wide) in paragraph at lines 363--363 | |
| [][] [][]\EU1/TimesNewRoman(1)/m/n/10 Lemma (Condizione Necessaria e Sufficien | |
| te di Riemann-Integrabilità | |
| [] | |
| [437 | |
| ]) | |
| showing es | |
| [438] (./app_An_2.loe [439 | |
| ] [440]) | |
| showing ese | |
| [441] (./app_An_2.loe [442 | |
| ]) [443] (./app_An_2.toc | |
| Overfull \hbox (0.47398pt too wide) in paragraph at lines 14--14 | |
| [][] [][]\EU1/TimesNewRoman(1)/m/n/10 Definizione, relazione tra continuità di | |
| $\OML/ztmcm/m/it/10 f$ \EU1/TimesNewRoman(1)/m/n/10 e continuità delle com- | |
| [] | |
| [444 | |
| ] [445] | |
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| [][] [][]\EU1/TimesNewRoman(1)/m/n/10 Gradiente e differenziale, differenziabi | |
| lità delle proiezioni, espres- | |
| [] | |
| [446] [447] [448] [449] [450] [451] [452]) | |
| \tf@toc=\write4 | |
| \openout4 = `app_An_2.toc'. | |
| \tf@loe=\write5 | |
| \openout5 = `app_An_2.loe'. | |
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| ) | |
| Here is how much of TeX's memory you used: | |
| 25267 strings out of 493938 | |
| 479151 string characters out of 6148856 | |
| 566368 words of memory out of 5000000 | |
| 28072 multiletter control sequences out of 15000+600000 | |
| 38028 words of font info for 166 fonts, out of 8000000 for 9000 | |
| 1144 hyphenation exceptions out of 8191 | |
| 46i,29n,45p,1487b,542s stack positions out of 5000i,500n,10000p,200000b,80000s | |
| Output written on app_An_2.pdf (455 pages). |
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