% (find-LATEX "2023-1-C2-edos-lineares.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2023-1-C2-edos-lineares.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2023-1-C2-edos-lineares.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page      "~/LATEX/2023-1-C2-edos-lineares.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2023-1-C2-edos-lineares.pdf"))
% (defun e () (interactive) (find-LATEX "2023-1-C2-edos-lineares.tex"))
% (defun o () (interactive) (find-LATEX "2022-2-C2-edos-lineares.tex"))
% (defun u () (interactive) (find-latex-upload-links "2023-1-C2-edos-lineares"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2023-1-C2-edos-lineares.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
%          (code-eec-LATEX "2023-1-C2-edos-lineares")
% (find-pdf-page   "~/LATEX/2023-1-C2-edos-lineares.pdf")
% (find-sh0 "cp -v  ~/LATEX/2023-1-C2-edos-lineares.pdf /tmp/")
% (find-sh0 "cp -v  ~/LATEX/2023-1-C2-edos-lineares.pdf /tmp/pen/")
%     (find-xournalpp "/tmp/2023-1-C2-edos-lineares.pdf")
%   file:///home/edrx/LATEX/2023-1-C2-edos-lineares.pdf
%               file:///tmp/2023-1-C2-edos-lineares.pdf
%           file:///tmp/pen/2023-1-C2-edos-lineares.pdf
%  http://anggtwu.net/LATEX/2023-1-C2-edos-lineares.pdf
% (find-LATEX "2019.mk")
% (find-Deps1-links "Caepro5 Piecewise1")
% (find-Deps1-cps   "Caepro5 Piecewise1")
% (find-Deps1-anggs "Caepro5 Piecewise1")
% (find-MM-aula-links "2023-1-C2-edos-lineares" "C2" "c2m231edols" "c2el")

% «.defs»		(to "defs")
% «.defs-caepro»	(to "defs-caepro")
% «.defs-pict2e»	(to "defs-pict2e")
% «.title»		(to "title")
% «.links»		(to "links")
% «.nao-usei»		(to "nao-usei")
%
% «.djvuize»		(to "djvuize")



% <videos>
% Video (not yet):
% (find-ssr-links     "c2m231edols" "2023-1-C2-edos-lineares")
% (code-eevvideo      "c2m231edols" "2023-1-C2-edos-lineares")
% (code-eevlinksvideo "c2m231edols" "2023-1-C2-edos-lineares")
% (find-c2m231edolsvideo "0:00")

\documentclass[oneside,12pt]{article}
\usepackage[colorlinks,citecolor=DarkRed,urlcolor=DarkRed]{hyperref} % (find-es "tex" "hyperref")
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{pict2e}
\usepackage[x11names,svgnames]{xcolor} % (find-es "tex" "xcolor")
\usepackage{colorweb}                  % (find-es "tex" "colorweb")
%\usepackage{tikz}
%
% (find-dn6 "preamble6.lua" "preamble0")
%\usepackage{proof}   % For derivation trees ("%:" lines)
%\input diagxy        % For 2D diagrams ("%D" lines)
%\xyoption{curve}     % For the ".curve=" feature in 2D diagrams
%
\usepackage{edrx21}               % (find-LATEX "edrx21.sty")
\input edrxaccents.tex            % (find-LATEX "edrxaccents.tex")
\input edrx21chars.tex            % (find-LATEX "edrx21chars.tex")
\input edrxheadfoot.tex           % (find-LATEX "edrxheadfoot.tex")
\input edrxgac2.tex               % (find-LATEX "edrxgac2.tex")
%\usepackage{emaxima}              % (find-LATEX "emaxima.sty")
%
% (find-es "tex" "geometry")
\usepackage[a6paper, landscape,
            top=1.5cm, bottom=.25cm, left=1cm, right=1cm, includefoot
           ]{geometry}
%
\begin{document}

% «defs»  (to ".defs")
% (find-LATEX "edrx21defs.tex" "colors")
% (find-LATEX "edrx21.sty")

\def\drafturl{http://anggtwu.net/LATEX/2023-1-C2.pdf}
\def\drafturl{http://anggtwu.net/2023.1-C2.html}
\def\draftfooter{\tiny \href{\drafturl}{\jobname{}} \ColorBrown{\shorttoday{} \hours}}

% (find-LATEX "2023-1-C2-carro.tex" "defs-caepro")
% (find-LATEX "2023-1-C2-carro.tex" "defs-pict2e")

\catcode`\^^J=10
\directlua{dofile "dednat6load.lua"}  % (find-LATEX "dednat6load.lua")

% «defs-caepro»  (to ".defs-caepro")
%L dofile "Caepro5.lua"              -- (find-angg "LUA/Caepro5.lua" "LaTeX")
\def\Caurl   #1{\expr{Caurl("#1")}}
\def\Cahref#1#2{\href{\Caurl{#1}}{#2}}
\def\Ca      #1{\Cahref{#1}{#1}}

% «defs-pict2e»  (to ".defs-pict2e")
%L V = nil                           -- (find-angg "LUA/Pict2e1.lua" "MiniV")
%L dofile "Piecewise1.lua"           -- (find-LATEX "Piecewise1.lua")
%L Pict2e.__index.suffix = "%"
\def\pictgridstyle{\color{GrayPale}\linethickness{0.3pt}}
\def\pictaxesstyle{\linethickness{0.5pt}}
\def\pictnaxesstyle{\color{GrayPale}\linethickness{0.5pt}}
\celllower=2.5pt

\pu



%  _____ _ _   _                               
% |_   _(_) |_| | ___   _ __   __ _  __ _  ___ 
%   | | | | __| |/ _ \ | '_ \ / _` |/ _` |/ _ \
%   | | | | |_| |  __/ | |_) | (_| | (_| |  __/
%   |_| |_|\__|_|\___| | .__/ \__,_|\__, |\___|
%                      |_|          |___/      
%
% «title»  (to ".title")
% (c2m231edolsp 1 "title")
% (c2m231edolsa   "title")

\thispagestyle{empty}

\begin{center}

\vspace*{1.2cm}

{\bf \Large Cálculo 2 - 2023.1}

\bsk

Aulas 23 e 24: EDOs lineares

com coeficientes constantes

\bsk

Eduardo Ochs - RCN/PURO/UFF

\url{http://anggtwu.net/2023.1-C2.html}

\end{center}

\newpage

% «links»  (to ".links")
% (c2m231edolsp 99 "links")
% (c2m231edolsa    "links")

{\bf Links}

\scalebox{0.8}{\def\colwidth{12cm}\firstcol{

Ainda não \LaTeX ei o material dessas aulas!

Os quadros delas estão aqui:

\par \Ca{2gQ46} Aula 23 (20/junho/2023)
\par \Ca{2gQ50} Aula 24 (23/junho/2023)

\bsk

Capítulos de livros (``Pt''=``Português'', ``Eng''=``Inglês''):

\ssk

\par \Ca{BoyceDip3p5} Capítulo 3: Equações lineares de 2ª ordem
\par \Ca{BoyceDip3p11} Seção 3.2: o operador diferencial $L$
\par \Ca{BoyceDip3p13} Teorema 3.2.2: o princípio da superposição

\ssk

\par \Ca{BoyceDipEng3p4} Chapter 3: Second-order linear ODEs
\par \Ca{BoyceDipEng3p11} Section 3.2: the differential operator $L$
\par \Ca{BoyceDipEng3p13} Theorem 3.2.2: principle of superposition

\ssk

\par \Ca{StewPtCap17p5} Equações diferenciais de 2ª ordem
\par \Ca{StewPtApendiceHp5} Apêndice H: Números complexos

}\anothercol{
}}




\newpage

% «nao-usei»  (to ".nao-usei")
% (c2m231edolsp 3 "nao-usei")
% (c2m231edolsa   "nao-usei")

\def\Mscale{0.5}
\def\dqeq{\;\text{``$=$''}\;}
\def\M#1{\scalebox{\Mscale}{$\pmat{#1}$}}

$\M{0&1\\0&0} \M{0&0\\1&0} = \M{1&0\\0&0}$

\ssk

$\M{0&0\\1&0} \M{0&1\\0&0} = \M{0&0\\0&1}$

\msk

$\M{a&b} \M{c\\d} = \M{ac+bd}$

$\M{c\\d} \M{a&b} = \M{ac&bc\\ad&bd}$

\msk

$S = \M{0&1 \\ &0&1 \\ &&0&1 \\ &&&0&1 \\ &&&&0}
 \quad
 1 = \M{1 \\ &1 \\ &&1 \\ &&&1 \\ &&&&1}
 \quad
 S-1 = \M{-1&1 \\ &-1&1 \\ &&-1&1 \\ &&&-1&1 \\ &&&&-1}$

\msk

$v = \M{v_1\\v_2\\v_3\\v_4\\v_5\\}
 \quad
 f = \M{f(1)\\f(2)\\f(3)\\f(4)\\f(5)\\}
 \quad
 Sf = \M{f(2)\\f(3)\\f(4)\\f(5)\\0}
 \quad
 (S-1)f = \M{f(2)-f(1)\\f(3)-f(2)\\f(4)-f(3)\\f(5)-f(4)\\0-f(5)\\}
$

\bsk

Obs: não usei isso aqui --

não deu tempo de \LaTeX ar tudo...


\GenericWarning{Success:}{Success!!!}  % Used by `M-x cv'

\end{document}


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