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ab31cfe004 ... mako

Author SHA1 Message Date
Benjamin Mako Hill
7cb860a967 Merge branch 'master' into mako 2026-04-12 16:55:37 -07:00
Benjamin Mako Hill
28760d5622 new_tex_uwletter: also remove README and COPYING from generated directories 
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
 2026-04-12 16:55:37 -07:00
Benjamin Mako Hill
5748a2a9f3 Merge branch 'master' into mako 2026-04-12 16:54:07 -07:00
Benjamin Mako Hill
3ba1610503 new_tex_uwletter: remove itself from generated directories 
The install script was being copied into every new letter directory
it created. Delete it after unpacking so new letter directories only
contain the template itself.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
 2026-04-12 16:54:02 -07:00
Benjamin Mako Hill
b6994b75c9 Merge branch 'master' into mako 2026-04-12 16:48:18 -07:00
Benjamin Mako Hill
3d10917a40 title should be name not email 2026-04-12 16:47:44 -07:00
Benjamin Mako Hill
d4403d9fa1 Merge branch 'master' into mako 2026-04-12 16:47:07 -07:00
Benjamin Mako Hill
2d28230c53 Switch to lualatex and generate accessible PDF/UA-2 output 
Add \DocumentMetadata for PDF 2.0 / PDF/UA-2, load tagpdf with
activate-all, extend hypersetup with pdftitle/pdfauthor/pdflang/
pdfdisplaydoctitle, and add alt text to the letterhead and signature
images. Drop xetex-only xltxtra and switch the Makefile from xelatex
to lualatex. Verified compliant with verapdf's PDF/UA-2 profile.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
 2026-04-12 16:43:47 -07:00
Benjamin Mako Hill
c89a06cb19 Fix new_tex_uwletter to use master branch on master 
Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
 2026-03-29 10:56:30 -07:00
Benjamin Mako Hill
ce94879122 Add new_tex_uwletter script and update README 
Add new_tex_uwletter script (moved from ~/bin) with bug fixes: set -e,
quoted variables, WORK_DIR instead of TMPDIR, existence check for
destination, and mktemp inside the conditional. Update README to fix
stale URLs, ShareLaTeX -> Overleaf, MacOSX -> macOS, typo in
Dasgupta's email, and add script usage section.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
 2026-03-29 10:56:16 -07:00
Benjamin Mako Hill
b923a61a4a Add new_tex_uwletter script and update README 
Add new_tex_uwletter script (moved from ~/bin) with bug fixes: set -e,
quoted variables, WORK_DIR instead of TMPDIR, existence check for
destination, and mktemp inside the conditional. Update README to fix
stale URLs, ShareLaTeX -> Overleaf, MacOSX -> macOS, typo in
Dasgupta's email, and add script usage section.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
 2026-03-29 10:55:54 -07:00
Benjamin Mako Hill
fa38bf5a53 added escaped space in signature line 2026-03-25 13:34:25 +09:00
Benjamin Mako Hill
0d9bf817da princeton fellowship is over 2024-11-08 08:42:37 -08:00
Benjamin Mako Hill
e50857d9f0 updated with promotion and princeton fellowship 2023-11-28 22:14:31 -05:00
Benjamin Mako Hill
bfa1325b75 s/faculty affiliate/faculty associate/ 2021-11-07 12:47:18 -08:00
Benjamin Mako Hill
18600f1191 update my personal signature elements 2021-11-07 12:26:59 -08:00
Benjamin Mako Hill
93968e96b0 Merge branch 'master' into mako 2021-05-21 13:58:01 -07:00
Benjamin Mako Hill
92c0a4b911 removed unnecessary math mode 2021-02-10 17:31:14 -08:00
Benjamin Mako Hill
360b303ce0 added page numbers for longer letters 2021-02-10 17:30:50 -08:00
Benjamin Mako Hill
5c838b7461 first stab at makoifying 2021-02-10 17:30:10 -08:00
Benjamin Mako Hill
fa950e485e added several fonts 
- added symlinks for the old name for AGaramondPro
- add times new roman
 2018-10-29 22:08:43 -07:00
Benjamin Mako Hill
518dd4af71 added page numbers for longer letters 2018-04-04 10:26:40 -07:00
Benjamin Mako Hill
73fe956ea5 merge commits onto a clean tree 2018-02-18 19:47:54 -08:00
Benjamin Mako Hill
87e171c7a7 first stab at makoifying 2018-02-18 19:40:00 -08:00
81 changed files with 723 additions and 53 deletions
Expand all files Collapse all files

121
COPYING Normal file
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@@ -0,0 +1,121 @@
Creative Commons Legal Code
CC0 1.0 Universal
CREATIVE COMMONS CORPORATION IS NOT A LAW FIRM AND DOES NOT PROVIDE
LEGAL SERVICES. DISTRIBUTION OF THIS DOCUMENT DOES NOT CREATE AN
ATTORNEY-CLIENT RELATIONSHIP. CREATIVE COMMONS PROVIDES THIS
INFORMATION ON AN "AS-IS" BASIS. CREATIVE COMMONS MAKES NO WARRANTIES
REGARDING THE USE OF THIS DOCUMENT OR THE INFORMATION OR WORKS
PROVIDED HEREUNDER, AND DISCLAIMS LIABILITY FOR DAMAGES RESULTING FROM
THE USE OF THIS DOCUMENT OR THE INFORMATION OR WORKS PROVIDED
HEREUNDER.
Statement of Purpose
The laws of most jurisdictions throughout the world automatically confer
exclusive Copyright and Related Rights (defined below) upon the creator
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authorship and/or a database (each, a "Work").
Certain owners wish to permanently relinquish those rights to a Work for
the purpose of contributing to a commons of creative, cultural and
scientific works ("Commons") that the public can reliably and without fear
of later claims of infringement build upon, modify, incorporate in other
works, reuse and redistribute as freely as possible in any form whatsoever
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These owners may contribute to the Commons to promote the ideal of a free
culture and the further production of creative, cultural and scientific
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For these and/or other purposes and motivations, and without any
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1. Copyright and Related Rights. A Work made available under CC0 may be
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vii. other similar, equivalent or corresponding rights throughout the
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2. Waiver. To the greatest extent permitted by, but not in contravention
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revocation, rescission, cancellation, termination, or any other legal or
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as contemplated by Affirmer's express Statement of Purpose.
3. Public License Fallback. Should any part of the Waiver for any reason
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Waiver shall be preserved to the maximum extent permitted taking into
account Affirmer's express Statement of Purpose. In addition, to the
extent the Waiver is so judged Affirmer hereby grants to each affected
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of the License, and in such case Affirmer hereby affirms that he or she
will not (i) exercise any of his or her remaining Copyright and Related
Rights in the Work or (ii) assert any associated claims and causes of
action with respect to the Work, in either case contrary to Affirmer's
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4. Limitations and Disclaimers.
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c. Affirmer disclaims responsibility for clearing rights of other persons
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Further, Affirmer disclaims responsibility for obtaining any necessary
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d. Affirmer understands and acknowledges that Creative Commons is not a
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2
Makefile
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@@ -11,7 +11,7 @@ figures/signature.pdf:
gpg --yes --output $(DEC_SIGIMAGE) --decrypt $(ENC_SIGIMAGE)
%.pdf: %.tex
latexmk -f -xelatex $<
latexmk -f -lualatex $<
clean:
latexmk -C *.tex

111
README
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@@ -1,3 +1,10 @@
================================
=== UW LaTeX Letterhead ========
================================
Copyright (c) 2018-2026 Benjamin Mako Hill <mako@atdot.cc> / <makohill@uw.edu>
Copyright (c) 2017 Sayamindu Dasgupta <sdg1@uw.edu>
This is a LaTeX version of the University of Washington "matrix"
stationery or letterhead.
@@ -10,53 +17,84 @@ Services.
Requirements
=============
Because this document requires an OpenType and a TrueType fonts, you
will need use to XeTeX—a modern TeX compiler. It is supported by
https://sharelatex.com/ although it not the default. It should be
installable on GNU/Linux, Windows, and MacOSX. More details are
available here: https://tug.org/xetex/
Because this document uses OpenType and TrueType fonts, it requires
XeTeX rather than standard LaTeX. It is supported by Overleaf
(https://overleaf.com/) although it is not the default. More details
on XeTeX are available here: https://tug.org/xetex/
A number of the normal LaTeX font packages will not work with
XeLaTeX. For more information, see http://xetex.sourceforge.net/
On Debian or Ubuntu, install the following packages:
The two required fonts Matrix-II And OpenSans are both included in
this repository.
* latexmk
* texlive-xetex
* texlive-latex-recommended
* texlive-latex-extra
There is a makefile included which allows you to run `make pdf` to
build the PDF and `make clean` to clean up from a build. Running this
will required:
apt install latexmk texlive-xetex texlive-latex-recommended \
texlive-latex-extra
* GNU Make: https://www.gnu.org/software/make/
* latexmk: https://ctan.org/pkg/latexmk?lang=en
On other systems, installing a full TeX Live distribution should
provide everything needed.
The two required fonts Matrix-II and OpenSans are both included in
this repository, so no additional font packages are needed.
Encrypted signatures files
Encrypted signature files
===========================
If you'd like, you can encrypt the signature file. There are several
lines you in the Makefile you can uncomment to do this. We've included
an optional encrypted copy of the fake signature file. To use it, the
lines in the Makefile you can uncomment to do this. We've included an
optional encrypted copy of the fake signature file. To use it, the
passphrase is "weakpassword" (without quotes). You will want to
customize this. To use this, you will also need the GNU Privacy Guard
customize this. To use this, you will also need GNU Privacy Guard
(GPG) installed on your system.
Scripts
========
new_tex_uwletter
-----------------
Creates a new letter directory from the template. Takes a destination
directory as its argument:
new_tex_uwletter <directory>
Example:
new_tex_uwletter my-letter
This creates my-letter/ populated with the template files, with the
main source file renamed to my-letter.tex. Fonts are symlinked from
the source repository rather than copied, so the repository must
remain in place.
Symlink the script into your PATH with:
ln -s ~/tex/uw_tex_letterhead/new_tex_uwletter ~/bin/
Contributing changes
=======================
If you notice issues with this template, please fix them contribute
back a patch so others can use them!
If you notice issues with this template, please fix them and
contribute back a patch so others can benefit!
You can always find the latest version at the following URL:
The latest version can be found at:
https://gitea.communitydata.science/mako/uw_tex_letterhead
https://code.communitydata.cc/uw_tex_letterhead.git
You can clone the repository with:
Information on contributing back can be found here:
git clone https://gitea.communitydata.science/mako/uw_tex_letterhead.git
https://code.communitydata.cc/
Patches can be submitted by email to Benjamin Mako Hill:
Please email any changes, or questions, to Benjamin Mako Hill at
makohill@uw.edu.
Benjamin Mako Hill <makohill@uw.edu> [work]
Benjamin Mako Hill <mako@atdot.cc> [personal]
git format-patch origin/master
git send-email *.patch
Copyright and Usage
@@ -70,26 +108,17 @@ https://www.washington.edu/brand/templates/stationery/
It is hopefully obvious that there are many ethical and legal
restrictions on when one can and cannot (and should or shouldn't) use
official university letterhead (e.g., it should only be used for
official communication).
official communication). If you have any questions, contact UW Brand
and Creative Services at the link above.
If you have any questions, you should contact UW Brand and Creative
Services at the contact information available at the link above.
This TeX template itself was created, and is copyright, by:
(c) 2018 Benjamin Mako Hill <makohill@uw.edu>
(c) 2017 Sayamindu Dasgupta <sdg1@uw.ed>
We dedicated the work to the public domain by waiving all of our
This TeX template itself was created by Benjamin Mako Hill and
Sayamindu Dasgupta. We dedicated the work to the public domain by waiving all of our
rights to the work worldwide under copyright law, including all
related and neighboring rights, to the extent allowed by law. You can
copy, modify, distribute and perform the work, even for commercial
purposes, all without asking permission.
See details here:
https://creativecommons.org/publicdomain/zero/1.0/
See details here: https://creativecommons.org/publicdomain/zero/1.0/
As a result, if you completely remove the UW branding, there are no
restrictions in how you can or cannot use the work in this repository.
restrictions on how you can use the work in this repository.

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Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-3
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-4
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-5
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-8
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-iso8859-9
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-e
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-r
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-ru
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-u
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-koi8-uni
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-microsoft-cp1252
Times New Roman.ttf -monotype-times new roman-medium-r-normal--0-0-0-0-p-0-suneu-greek

41
new_tex_uwletter Executable file
View File

@@ -0,0 +1,41 @@
#!/bin/bash
# Helper script to export LaTeX templates for new UW letters
# Copyright (c) 2009-2016 Benjamin Mako Hill <mako@atdot.cc>
# Released under the GPLv3 or later.
set -e
SOURCEDIR="$HOME/tex/uw_tex_letterhead"
CURDIR=$(pwd)
if [ -n "$1" ]
then
if [ -e "$1" ]; then
echo "error: '$1' already exists"
exit 1
fi
WORK_DIR=$(mktemp -d)
cd "$SOURCEDIR"
git archive --format=tar mako | tar x -C "$WORK_DIR"
cd "$CURDIR"
mv "$WORK_DIR" "$1"
cd "$1"
mv "washington_letterhead_letter-matrix-deptartment.tex" "$(basename "$1").tex"
rm -f "new_tex_uwletter" "README" "COPYING"
# create a symlink farm for the fonts
rm -rf ./fonts/*
# first create the directories
for fontdir in "${SOURCEDIR}/fonts/"*; do
mkdir "./fonts/$(basename "${fontdir}")"
# then the files
for fontfile in "${fontdir}/"*; do
ln -s "${fontfile}" "./fonts/$(basename "${fontdir}")/$(basename "${fontfile}")"
done
done
else
echo "specify a directory where the template should go"
fi

261
washington_letterhead_letter-matrix-deptartment.tex
View File

@@ -1,17 +1,26 @@
\DocumentMetadata{
pdfversion=2.0,
pdfstandard=ua-2,
lang=en-US,
}
\documentclass[11pt,letterpaper]{article}
% MODIFY THE DETAILS IN THIS SECTION TO MATCH WHAT YOU WANT ON /YOUR/ LETTERHEAD
\def\department{Department of Awesomeness}
\def\department{Department of Communication}
\def\uwaddress{Communications (CMU) 306~~Box 353740~~4109 NE Stevens Way~~Seattle, WA~~98195-3740}
\def\phone{mobile 206-409-7191}
\def\email{makohill@uw.edu}
\def\web{https://mako.cc/academic/}
\def\letterauthor{Benjamin Mako Hill}
\def\lettertitle{Letter from \letterauthor}
\usepackage[top=1.25in,left=1.25in,bottom=1.20in,right=1.25in]{geometry}
\usepackage{xltxtra}
\usepackage{fontspec}
\usepackage{tagpdf}
\tagpdfsetup{activate-all}
\newopentypefeature{Contextuals}{NoAlternate}{-calt}
\defaultfontfeatures{Kerning=Uppercase,Ligatures=TeX}
\setsansfont{OpenSans}[
Path = ./fonts/OpenSans/,
@@ -22,7 +31,25 @@ ItalicFont = *-Italic,
BoldItalicFont = *-BoldItalic
]
\setmainfont{OpenSans}
\setmainfont{GaramondPremrPro}[
Path = ./fonts/Garamond/,
Extension = .otf,
BoldFont = *-Bd,
ItalicFont = *-It,
BoldItalicFont = *-BdIt
]
% \setmainfont{Times New Roman}[
% Path = ./fonts/Times New Roman/,
% Extension = .ttf,
% BoldFont = * Bold,
% ItalicFont = * Italic,
% BoldItalicFont = * Bold Italic
% ]
\usepackage{amsmath}
\usepackage{amsthm}
%\usepackage{mathrsfs}
\usepackage{polyglossia}
\setdefaultlanguage{english}
@@ -31,6 +58,11 @@ BoldItalicFont = *-BoldItalic
\usepackage[colorlinks=false,
pdfborder={0 0 0},
]{hyperref}
\hypersetup{unicode=true,
pdftitle={\lettertitle},
pdfauthor={\letterauthor},
pdflang={en-US},
pdfdisplaydoctitle=true}
\usepackage{tikz}
\usepackage{lastpage}
@@ -43,7 +75,7 @@ BoldItalicFont = *-BoldItalic
\ifnum\thepage=1
\begin{tikzpicture}[remember picture,overlay,every node/.style={inner sep=0,outer sep=0}]
\node at (current page.north west) [anchor=north west]
{\includegraphics{figures/matrix_header.pdf}};
{\includegraphics[alt={University of Washington letterhead}]{figures/matrix_header.pdf}};
% add the department name
\node at (current page.north west) [anchor=north west, xshift=1.19in, yshift=-0.56in]
{{\fontsize{14pt}{16pt} \fontspec{MatrixIIOT-Book.otf}[
@@ -77,12 +109,15 @@ BoldItalicFont = *-BoldItalic
\setlength{\parskip}{0.5\baselineskip}
\setlength{\headheight}{14pt}
\setlength{\footskip}{35pt}
% \raggedright
\linespread{1.05}
\begin{document}
% these two sections turn off the aggressively long alternate q
\addfontfeatures{Contextuals=NoAlternate}
\hfill \today
\bigskip
@@ -119,6 +154,206 @@ Enim facilisis gravida neque convallis a cras semper auctor. Lorem ipsum dolor s
Nunc consequat interdum varius sit. Nibh tortor id aliquet lectus. Lacus laoreet non curabitur gravida arcu ac tortor dignissim. Tortor condimentum lacinia quis vel eros donec ac odio tempor. Varius sit amet mattis vulputate. Ut tristique et egestas quis. Enim blandit volutpat maecenas volutpat blandit aliquam. Ullamcorper morbi tincidunt ornare massa eget egestas purus. Maecenas ultricies mi eget mauris pharetra et ultrices neque ornare. Libero nunc consequat interdum varius sit. Turpis tincidunt id aliquet risus feugiat in ante metus. Ut enim blandit volutpat maecenas volutpat blandit aliquam. Nisl vel pretium lectus quam id leo in vitae turpis. Porttitor eget dolor morbi non arcu risus quis varius. Mi in nulla posuere sollicitudin. Eleifend donec pretium vulputate sapien nec. Aliquet nibh praesent tristique magna sit amet. Sagittis purus sit amet volutpat consequat mauris nunc congue nisi.
Consider a change of variable $(x,y)\mapsto
(u,v)=\big(u(x,y),v(x,y)\big)$ in the plane $\R^2$, identified
with~$\Cx$. This change of variable really only deserves the name if
$f$ is locally bijective (i.e., one-to-one); this is the case if the
jacobian of the map is nonzero (then so is the jacobian of the
inverse map):
\begin{equation*}
\left| \frac{{D}(u,v)}{{D}(x,y)}\right| =
\begin{vmatrix}
\ds\frac{\displaystyle\partial u}{\displaystyle\partial x} &
\ds\frac{\displaystyle\partial u}{\displaystyle\partial y} \\[4mm]
\ds\frac{\displaystyle\partial v}{\displaystyle\partial x} &
\ds\frac{\displaystyle\partial v}{\displaystyle\partial y}
\end{vmatrix}\neq 0
\qquad\text{and}\qquad
\left| \frac{{D}(x,y)}{{D}(u,v)}\right|
=\begin{vmatrix}\ds\dep{x}{u} &\ds \dep{x}{v}\\[4mm]
\ds\dep{y}{u} &\ds \dep{y}{v}
\end{vmatrix}\neq 0.
\end{equation*}
\begin{theorem}
In a complex change of variable
\begin{equation*}
z= x+\ii y\longmapsto w=f(z)=u+\ii v,
\end{equation*}
and \emph{if $f$ is holomorphic}, then the jacobian of the map is equal to
\begin{equation*}
J_f(z)=\left| \frac{{D}(u,v)}{{D}(x,y)}\right|=
\abs{f'(z)}^2.
\end{equation*}
\end{theorem}
\begin{demo}
Indeed, we have $f'(z)=\dep{u}{x}+\ii\dep{v}{x}$ and hence, by the
Cauchy-Riemann relations,
\begin{align*}
\abs{f'(z)}^2 & =
\left(\dep{u}{x}\right)^2+\left(\dep{v}{x}\right)^2
=
\dep{u}{x}\dep{v}{y}-\dep{v}{x}\dep{u}{y}=J_f(z).
\end{align*}
\end{demo}
\begin{definition}
\index{Conformal map}%
\index{Transformation!conformal ---}%
A \emph{conformal map} or \emph{conformal transformation} of an
open subset $\Omega\subset\R^2$ into another open subset
$\Omega'\subset\R^2$ is any map $f:\Omega\mapsto \Omega'$, locally
bijective, that preserves angles and orientation.
\end{definition}
\begin{theorem}
Any conformal map is given by a holomorphic function $f$ such
that the derivative of $f$ does not vanish.
\end{theorem}
This justifies the next definition:
%% ----------------------------------------------------------------------
\begin{definition}
\index{Conformal map}%
\index{Transformation!conformal ---}%
A \emph{conformal transformation} or \emph{conformal map} of
an open subset
$\Omega\subset\Cx$ into another open subset
$\Omega'\subset\Cx$ is any holomorphic function
$f:\Omega\mapsto \Omega'$ such that
$f'(z)\neq 0$ for all $z\in\Omega$.
\end{definition}
%% ----------------------------------------------------------------------
%% ----------------------------------------------------------------------
\begin{demo}[that the definitions are equivalent]
We will denote in general $w=f(z)$. Consider, in the complex plane, two
line segments $\gamma_1$ and $\gamma_2$ contained inside the set $\Omega$
where $f$ is defined, and intersecting at a point $z_0$ in $\Omega$.
Denote by $\gamma'_1$ and $\gamma_2'$ their images by~$f$.
We want to show that if the angle between $\gamma_1$ and $\gamma_2$ is
equal to $\theta$, then the same holds for their images, which means that
the angle between the tangent lines to $\gamma'_1$ and $\gamma'_2$ at
$w_0=f(z_0)$ is also equal to $\theta$.
Consider a point $z\in\gamma_1$ close to~$z_0$. Its image $w=f(z)$
satisfies
\begin{equation*}
\lim_{z\to z_0} \frac{w-w_0}{z-z_0}=f'(z_0),
\end{equation*}
and hence
$$\displaystyle \lim_{z\to z_0} \Arg
(w-w_0)-\Arg(z-z_0) = \Arg f'(z_0), $$%
which shows that the angle between the curve $\gamma'_1$ and the real
axis is equal to the angle between the original segment $\gamma_1$ and
the real axis, plus the angle $\alpha=\Arg f'(z_0)$ (which is well
defined because $f'(z)\neq 0$).
Similarly, the angle between the image curve $\gamma'_2$ and the real
axis is equal to that between the segment $\gamma_2$ and the real axis,
plus the same~$\alpha$.
Therefore, the angle between the two image curves is the same as that
between the two line segments, namely, $\theta$.
Another way to see this is as follows: the tangent vectors of the curves
are transformed according to the rule $\vect{V}'=\dd f_{z_0}\vect{V}$. But the
differential of $f$ (when $f$ is seen as a map from $\R^2$ to~$\R^2$) is
of the form
\begin{equation}
\displaystyle \dd f_{z_0}=\begin{pmatrix}
\displaystyle \dep{P}{x} & \displaystyle \dep{P}{y} \\[4mm]
\displaystyle \dep{Q}{x} & \displaystyle \dep{Q}{y}\end{pmatrix}
=
\abs{f'(z_0)}\begin{pmatrix}\cos\alpha& -\sin\alpha
\\ \sin\alpha &\cos\alpha \end{pmatrix},
\label{eq:FSimil}
\end{equation}
where $\alpha$ is the argument of $f'(z_0)$. This is the matrix of a
rotation composed with a homothety, that is, a similitude.
\medskip
%% ······································································
% {\begin{picture}(300,100)
% \put(0,0){\epsfig{file=\Figures/TC.\Ext,height=3.2cm}}
% \put(20,65){$\gamma_2$} \put(80,55){$\theta$}
% \put(100,80){$\gamma_1$} \put(195,85){$\gamma'_1$}
% \put(245,35){$\theta$} \put(270,60){$\gamma'_2$}
% \end{picture}}
%% ······································································
Conversely, if $f$ is a map which is $\R^2$-differentiable and preserves
angles, then at any point $\dd f$ is an endomorphism of~$\R^2$ which
preserves angles. Since $f$ also preserves orientation, its determinant
is positive, so $\dd f$ is a similitude, and its matrix is exactly
as in equation~\eqref{eq:FSimil}. The Cauchy-Riemann equations are
immediate consequences.
\end{demo}
%% ----------------------------------------------------------------------
%% ----------------------------------------------------------------------
\begin{remarque}
\index{Antiholomorphic function}%
\index{Function!antiholomorphic ---}%
An \emph{antiholomorphic} map also preserves angles, but it
reverses the orientation.
\end{remarque}
%% ----------------------------------------------------------------------
\newpage
\subsection*{Calcul différentiel}
Pour obtenir la différentielle totale de cette expression, considérée comme fonction de $x$, $y$, ..., donnons à $x$, $y$, ... des accroissements $d\!x$, $d\!y$, .... Soient $\Delta u$, $\Delta v$, ..., $\Delta f$ les accroissements correspondants de $u$, $v$, ...,$f$. On aura
\begin{equation*}
\Delta f= \dfrac{\partial\! f}{\partial u} \Delta u + \dfrac{\partial\! f}{\partial v} \Delta v + \hdots + R\Delta u + R_1 \Delta v + \hdots,
\end{equation*}
$R$, $R_1$, ... tendant vers zéro avec $\Delta u$, $\Delta v$, ....
Mais on a, d'autre part,
\begin{align*}
\Delta u & = \dfrac{\partial u}{\partial x} d\! x + + \dfrac{\partial u}{\partial y} \Delta y + \hdots + S\Delta x + S_1 \Delta y + \hdots \\
& = du + Sd\! x + S_1 d\! y + \hdots \\
\Delta v & = \dfrac{\partial v}{\partial x} d\! x + + \dfrac{\partial v}{\partial y} \Delta y + \hdots + T\Delta x + T_1 \Delta y + \hdots \\
& = dv + Td\! x + T_1 d\! y + \hdots \\
\hdots
\end{align*}
$S$, $S_1$, ..., $T$, $T_1$,... tendant vers zéro avec $d\! x$, $d\! y$, ....
Substituant ces valeurs dans l'expression de $\Delta f$, il vient
\begin{equation*}
\begin{array}{rcl}
\vbox to 25pt {} \Delta f & = &\dfrac{\partial\! f}{\partial u} d u + \dfrac{\partial\! f}{\partial v} d v + \hdots + \rho d\! x + \rho_1 d\! y + \hdots \\
\vbox to 25pt {}& = & \phantom{+} \left( \dfrac{\partial\! f}{\partial u} \dfrac{\partial u}{\partial x} + \dfrac{\partial\! f}{\partial v} \dfrac{\partial v}{\partial x} + \hdots \right) d\! x \\
\vbox to 25pt {}& & + \left( \dfrac{\partial\! f}{\partial u} \dfrac{\partial u}{\partial y} + \dfrac{\partial\! f}{\partial v} \dfrac{\partial v}{\partial y} + \hdots \right) d\! y \\
\vbox to 25pt {}&& + \hdots + \rho d\! x + \rho_1 d\! y + \hdots
\end{array}
\end{equation*}
$\rho$, $\rho_1$, ... tendant vers zéro avec $d\! x$, $d\! y$, ....
On aura donc
\begin{align*}
\dfrac{\partial\! f}{\partial x}& = \dfrac{\partial\! f}{\partial u} \dfrac{\partial u}{\partial x} + \dfrac{\partial\! f}{\partial v} \dfrac{\partial v}{\partial x} + \hdots, \\
\dfrac{\partial\! f}{\partial y}& = \dfrac{\partial\! f}{\partial u} \dfrac{\partial u}{\partial y} + \dfrac{\partial\! f}{\partial v} \dfrac{\partial v}{\partial y} + \hdots, \\
\hdots
\end{align*}
et, d'autre part,
\begin{equation*}
df = \dfrac{\partial\! f}{\partial u} {\mathrm d} u + \dfrac{\partial\! f}{\partial v} {\mathrm d} v + \hdots ;
\end{equation*}
d'où les deux propositions suivantes :
{\em La dérivée, par rapport à une variable indépendante $x$, d'une fonction composée $f(u,v,\hdots)$ s'obtient en ajoutant ensemble les dérivées partielles $\dfrac{\partial\! f}{\partial u}$, $\dfrac{\partial\! f}{\partial v}$, ..., respectivement multipliées par les dérivées de $u$, $v$, ... par rapport à $x$.
La différentielle totale $df$ s'exprimer au moyen de $u$, $v$, ..., $du$, $dv$, ..., de la même manière que si $u$, $v$, ... étaient des variables indépendantes.
}
\hbox to \textwidth { \hfill
{\sc Camille Jordan}, {\em Cours d'analyse de l'\'Ecole polytechnique}
}
Varius sit amet mattis vulputate enim nulla aliquet. Augue ut lectus arcu bibendum at. Auctor eu augue ut lectus arcu bibendum at varius vel. Cras ornare arcu dui vivamus arcu felis. Diam maecenas sed enim ut sem viverra aliquet eget sit. Purus in mollis nunc sed id semper risus in. Arcu risus quis varius quam quisque id diam vel quam. Justo nec ultrices dui sapien eget. Tortor consequat id porta nibh venenatis. Porttitor massa id neque aliquam. Tortor id aliquet lectus proin nibh nisl. Volutpat blandit aliquam etiam erat velit scelerisque in dictum non.
Pharetra magna ac placerat vestibulum. Turpis massa sed elementum tempus egestas sed. Mollis aliquam ut porttitor leo a diam sollicitudin tempor. Mattis vulputate enim nulla aliquet porttitor. Tempus egestas sed sed risus pretium. Non pulvinar neque laoreet suspendisse interdum consectetur libero id faucibus. Pellentesque elit ullamcorper dignissim cras. Cras ornare arcu dui vivamus. Viverra maecenas accumsan lacus vel facilisis volutpat est. Tristique senectus et netus et. Adipiscing vitae proin sagittis nisl rhoncus. Vulputate mi sit amet mauris.
@@ -127,10 +362,16 @@ Sed ullamcorper morbi tincidunt ornare massa eget egestas purus. Feugiat pretium
Sincerely,
\includegraphics[width=1.7in]{figures/signature.pdf}\\
John Hancock\\
Assistant Professor of Communication\\
Adjunct Assistant Professor of Human-Centered Design and Engineering
\includegraphics[width=1.7in,alt={Signature of \letterauthor}]{figures/signature.pdf}\\
Benjamin Mako Hill\\
Associate Professor, Communication\\
Adjunct Associate Professor, Paul G.\ Allen School of Computer Science \& Engineering\\
Adjunct Associate Professor, Department of Human-Centered Design \& Engineering\\
Adjunct Associate Professor, Information School
Faculty Associate\\
Berkman Klein Center for Internet \& Society\\
Harvard University
\end{document}