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Warning: this is an htmlized version!
The original is here, and the conversion rules are here. |
% (find-LATEX "2023-2-C2-edolccs.tex")
% (defun c () (interactive) (find-LATEXsh "lualatex -record 2023-2-C2-edolccs.tex" :end))
% (defun C () (interactive) (find-LATEXsh "lualatex 2023-2-C2-edolccs.tex" "Success!!!"))
% (defun D () (interactive) (find-pdf-page "~/LATEX/2023-2-C2-edolccs.pdf"))
% (defun d () (interactive) (find-pdftools-page "~/LATEX/2023-2-C2-edolccs.pdf"))
% (defun e () (interactive) (find-LATEX "2023-2-C2-edolccs.tex"))
% (defun o () (interactive) (find-LATEX "2023-1-C2-edos-lineares.tex"))
% (defun u () (interactive) (find-latex-upload-links "2023-2-C2-edolccs"))
% (defun v () (interactive) (find-2a '(e) '(d)))
% (defun d0 () (interactive) (find-ebuffer "2023-2-C2-edolccs.pdf"))
% (defun cv () (interactive) (C) (ee-kill-this-buffer) (v) (g))
% (code-eec-LATEX "2023-2-C2-edolccs")
% (find-pdf-page "~/LATEX/2023-2-C2-edolccs.pdf")
% (find-sh0 "cp -v ~/LATEX/2023-2-C2-edolccs.pdf /tmp/")
% (find-sh0 "cp -v ~/LATEX/2023-2-C2-edolccs.pdf /tmp/pen/")
% (find-xournalpp "/tmp/2023-2-C2-edolccs.pdf")
% file:///home/edrx/LATEX/2023-2-C2-edolccs.pdf
% file:///tmp/2023-2-C2-edolccs.pdf
% file:///tmp/pen/2023-2-C2-edolccs.pdf
% http://anggtwu.net/LATEX/2023-2-C2-edolccs.pdf
% (find-LATEX "2019.mk")
% (find-Deps1-links "Caepro5 Piecewise2 Escadas1")
% (find-Deps1-cps "Caepro5 Piecewise2 Escadas1 Maxima2")
% (find-Deps1-anggs "Caepro5 Piecewise2 Escadas1")
% (find-MM-aula-links "2023-2-C2-edolccs" "C2" "c2m232edolccs" "c2el")
% «.defs» (to "defs")
% «.defs-T-and-B» (to "defs-T-and-B")
% «.defs-caepro» (to "defs-caepro")
% «.defs-pict2e» (to "defs-pict2e")
% «.title» (to "title")
% «.links» (to "links")
% «.solucoes-nao-basicas» (to "solucoes-nao-basicas")
%
% «.djvuize» (to "djvuize")
% <videos>
% Video (not yet):
% (find-ssr-links "c2m232edolccs" "2023-2-C2-edolccs")
% (code-eevvideo "c2m232edolccs" "2023-2-C2-edolccs")
% (code-eevlinksvideo "c2m232edolccs" "2023-2-C2-edolccs")
% (find-c2m232edolccsvideo "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/2023-2-C2.pdf}
\def\drafturl{http://anggtwu.net/2023.2-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-T-and-B» (to ".defs-T-and-B")
\long\def\ColorDarkOrange#1{{\color{orange!90!black}#1}}
\def\T(Total: #1 pts){{\bf(Total: #1)}}
\def\T(Total: #1 pts){{\bf(Total: #1 pts)}}
\def\T(Total: #1 pts){\ColorRed{\bf(Total: #1 pts)}}
\def\B (#1 pts){\ColorDarkOrange{\bf(#1 pts)}}
% «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 dofile "Piecewise2.lua" -- (find-LATEX "Piecewise2.lua")
%L dofile "Escadas1.lua" -- (find-LATEX "Escadas1.lua")
%L dofile "Maxima2.lua" -- (find-angg "LUA/Maxima2.lua")
%L V = MiniV
\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")
% (c2m232edolccsp 1 "title")
% (c2m232edolccsa "title")
\thispagestyle{empty}
\begin{center}
\vspace*{1.2cm}
{\bf \Large Cálculo 2 - 2023.2}
\bsk
Aula 30: EDOs lineares
com coeficientes constantes
\bsk
Eduardo Ochs - RCN/PURO/UFF
\url{http://anggtwu.net/2023.2-C2.html}
\end{center}
\newpage
% «links» (to ".links")
% (c2m232edolccsp 2 "links")
% (c2m232edolccsa "links")
{\bf Links}
\scalebox{0.5}{\def\colwidth{16cm}\firstcol{
% (find-books "__analysis/__analysis.el" "stewart-pt" "1020" "17.1 Equações Lineares de Segunda Ordem")
% (find-books "__analysis/__analysis.el" "stewart-pt" "1034" "subamortecimento")
% (find-books "__analysis/__analysis.el" "stewart-pt" "51" "H Números Complexos")
\par \Ca{StewPtCap17p6} (p.1020) Equações diferenciais de 2ª ordem
\par \Ca{StewPtCap17p20} (p.1034) Caso 3: subamortecimento
\par \Ca{StewPtApendiceHp5} (p.A51) Apêndice H: Números complexos
\ssk
% (find-books "__analysis/__analysis.el" "leithold" "156" "3.3. Teoremas sobre derivação")
\par \Ca{Leit3p22} (p.158) $D_x[c·f(x)] = c·D_xf(x)$
\par \Ca{Leit3p22} (p.158) $D_x[f(x)+g(x)] = D_xf(x)+D_xg(x)$
\ssk
% (find-books "__analysis/__analysis.el" "boyce-diprima-pt" "105" "3. Equações lineares de segunda")
% (find-books "__analysis/__analysis.el" "boyce-diprima-pt" "111" "operador diferencial")
% (find-books "__analysis/__analysis.el" "boyce-diprima-pt" "113" "princípio da superposição")
% (find-books "__analysis/__analysis.el" "boyce-diprima-pt" "121" "3.3. Raízes complexas")
% (find-books "__analysis/__analysis.el" "boyce-diprima-pt" "123" "Figura 3.3.1")
\par \Ca{BoyceDip3p5} (p.105) Capítulo 3: Equações lineares de 2ª ordem
\par \Ca{BoyceDip3p11} (p.111) Seção 3.2: o operador diferencial $L$
\par \Ca{BoyceDip3p13} (p.113) Teorema 3.2.2: o princípio da superposição
\par \Ca{BoyceDip3p21} (p.121) 3.3. Raízes complexas da equação característica
\par \Ca{BoyceDip3p23} (p.123) Figura 3.3.1
\ssk
% (find-books "__analysis/__analysis.el" "zill-cullen-pt" "173" "4.3" "coeficientes constantes")
% (find-books "__analysis/__analysis.el" "zill-cullen-pt" "196" "Exemplo 1: ...pode ser fatorado...")
% (find-books "__analysis/__analysis.el" "zill-cullen" "150" "FACTORING OPERATORS")
\par \Ca{ZillCullenCap4p33} (p.173) 4.3. Equações lineares homogêneas com coeficientes constantes
\par \Ca{ZillCullenCap4p60} (p.196) Exemplo 1: ...pode ser fatorado... $(D+3)(D+2)$
\par \Ca{ZillCullenEngCap4p40} (p.150) Factoring operators ... $(D+3)(D+2)$
\msk
% (find-books "__analysis/__analysis.el" "boyce-diprima" "103" "3 Second-Order Linear")
% (find-books "__analysis/__analysis.el" "boyce-diprima" "110" "differential operator")
% (find-books "__analysis/__analysis.el" "boyce-diprima" "112" "Theorem 3.2.2" "Superposition")
% (find-books "__analysis/__analysis.el" "boyce-diprima" "120" "3.3 Complex Roots")
\par \Ca{BoyceDipEng3p4} (p.103) Chapter 3: Second-order linear ODEs
\par \Ca{BoyceDipEng3p11} (p.110) Section 3.2: the differential operator $L$
\par \Ca{BoyceDipEng3p13} (p.112) Theorem 3.2.2: principle of superposition
\par \Ca{BoyceDipEng3p21} (p.120) 3.3 Complex Roots of the Characteristic Equation
\par \Ca{BoyceDipEng3p24} (p.123) Figure 3.3.1
\ssk
Quadros:
% (find-angg ".emacs" "c2q232" "30,nov01: EDOLCCs")
\par \Ca{2hQ61} Aula 30 de 2023.2 (01/nov/2023)
\standout{Aviso:} falta digitar muita coisa! Veja os quadros!
% (c2m231dicasp2p 4 "raizes-chutar-testar")
% (c2m231dicasp2a "raizes-chutar-testar")
% 2gT128 Raízes por chutar-e-testar
\bsk
\bsk
Quadros antigos:
% (find-angg ".emacs" "c2q231" "jun20: EDOs lineares")
\par \Ca{2gQ46} Aula 23 de 2023.1 (20/junho/2023)
\par \Ca{2gQ50} Aula 24 de 2023.1 (23/junho/2023)
\bsk
}\anothercol{
}}
\newpage
% (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...
\newpage
% (c2m232p1p 4 "questao-5-grids")
% (c2m232p1a "questao-5-grids")
%L fry = FromYs.from {ys={0,-1,1,-2,2,-3,3,-3,2,-2,1,-1,0}, Y0=0} :setall()
%L fry = FromYs.from {ys={0,-1,-3,3,1,0,1,2,1,0,-1,-2,-1,0}, Y0=0} :setall()
%L fry = FromYs.from {ys={2,1,0,1,2,-2,1,-2,0,-2,0,1,2,1,0,-1,-2,-1,0}, Y0=-3} :setall()
%L Pict {
%L fry:ypict() :prethickness("1pt"):sa("fig f"),
%L fry:Ypict() :prethickness("1pt"):sa("fig F"),
%L fry:grid(-4,4):sa("grid F"),
%L } :output()
\pu
\unitlength=10pt
$\begin{array}{rcl}
g(x) &=& \ga{fig F} \\ \\[-5pt]
g'(x) &=& \ga{fig f} \\
\end{array}
$
\newpage
%M (%i1) f : exp( 3*x);
%M (%o1) e^{3\,x}
%M (%i2) f : exp(-3*x);
%M (%o2) e^ {- 3\,x }
%M (%i3) f : exp( 2*x);
%M (%o3) e^{2\,x}
%M (%i4) fp : diff(f,x);
%M (%o4) 2\,e^{2\,x}
%M (%i5) fpp : diff(f,x,2);
%M (%o5) 4\,e^{2\,x}
%M (%i6) Lf : fpp + fp - 6*f;
%M (%o6) 0
%M (%i7)
%L maximahead:sa("L1", "")
\pu
%M (%i1) D (f) := diff(f,x);
%M (%o1) D\left(f\right):=\mathrm{diff}\left(f , x\right)
%M (%i2) DD(f) := diff(f,x,2);
%M (%o2) \mathrm{DD}\left(f\right):=\mathrm{diff}\left(f , x , 2\right)
%M (%i3) L (f) := D(D(f)) + D(f) - 6*f;
%M (%o3) L\left(f\right):=D\left(D\left(f\right)\right)+D\left(f\right)+\left(-6\right)\,f
%M (%i4) D(x^2);
%M (%o4) 2\,x
%M (%i5) D(D(x^2));
%M (%o5) 2
%M (%i6) L(x^2);
%M (%o6) -\left(6\,x^2\right)+2\,x+2
%M (%i7) L(exp( 3*x));
%M (%o7) 6\,e^{3\,x}
%M (%i8) L(exp(-3*x));
%M (%o8) 0
%M (%i9) L(exp( 2*x));
%M (%o9) 0
%M (%i10)
%L maximahead:sa("L2", "")
\pu
\scalebox{0.4}{\def\colwidth{9cm}\firstcol{
\ga{L1}
}\anothercol{
\def\hboxthreewidth {10cm}
\ga{L2}
}}
\newpage
% «solucoes-nao-basicas» (to ".solucoes-nao-basicas")
% (c2m232edolccsp 6 "solucoes-nao-basicas")
% (c2m232edolccsa "solucoes-nao-basicas")
{\bf Soluções não-básicas}
% (find-c2q232page 64 "30,nov01: EDOLCCs")
\def\und #1#2{\underbrace{#1}_{#2}}
\def\uuund#1#2#3#4{\und{\und{\und{#1}{#2}}{#3}}{#4}}
\scalebox{0.8}{\def\colwidth{12cm}\firstcol{
$$\begin{array}{rcl}
M(αv + βw) &=& M(αv) + M(βw) \\
&=& α(Mv) + β(Mw) \\
\end{array}
$$
$$\und{(D-2)(D+3)}{M}
(\und{42}{α} \und{e^{2x}}{v} + \und{99}{β} \und{e^{-3x}}{w})
$$
\sa{(D-2)e^{2x}}{
\uuund{(D-2)e^{2x}}
{De^{2x} -2e^{2x}}
{2e^{2x} -2e^{2x}}
{0}
}
\sa{(D+3)e^{-3x}}{
\uuund{(D+3)e^{-3x}}
{De^{-3x}+3e^{-3x}}
{-3e^{-3x}+3e^{-3x}}
{0}
}
$$\begin{array}{l}
(D-2)(D+3)(42e^{2x} + 99e^{-3x}) \\
= \; 42(D-2)(D+3)e^{2x} + 99(D-2)(D+3)e^{-3x} \\
= \; \und{42\und{(D+3)\ga{(D-2)e^{2x}}}{0}}{0}
\,+\, \und{99\und{(D-2)\ga{(D+3)e^{-3x}}}{0}}{0} \\
\end{array}
$$
}\anothercol{
}}
\GenericWarning{Success:}{Success!!!} % Used by `M-x cv'
\end{document}
% ____ _ _
% | _ \(_)_ ___ _(_)_______
% | | | | \ \ / / | | | |_ / _ \
% | |_| | |\ V /| |_| | |/ / __/
% |____// | \_/ \__,_|_/___\___|
% |__/
%
% «djvuize» (to ".djvuize")
% (find-LATEXgrep "grep --color -nH --null -e djvuize 2020-1*.tex")
* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-fline "~/2023.2-C2/")
# (find-fline "~/LATEX/2023-2-C2/")
# (find-fline "~/bin/djvuize")
cd /tmp/
for i in *.jpg; do echo f $(basename $i .jpg); done
f () { rm -v $1.pdf; textcleaner -f 50 -o 5 $1.jpg $1.png; djvuize $1.pdf; xpdf $1.pdf }
f () { rm -v $1.pdf; textcleaner -f 50 -o 10 $1.jpg $1.png; djvuize $1.pdf; xpdf $1.pdf }
f () { rm -v $1.pdf; textcleaner -f 50 -o 20 $1.jpg $1.png; djvuize $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0 -f 15" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0 -f 30" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 1.0 -f 45" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.5" $1.pdf; xpdf $1.pdf }
f () { rm -fv $1.png $1.pdf; djvuize WHITEBOARDOPTS="-m 0.25" $1.pdf; xpdf $1.pdf }
f () { cp -fv $1.png $1.pdf ~/2023.2-C2/
cp -fv $1.pdf ~/LATEX/2023-2-C2/
cat <<%%%
% (find-latexscan-links "C2" "$1")
%%%
}
f 20201213_area_em_funcao_de_theta
f 20201213_area_em_funcao_de_x
f 20201213_area_fatias_pizza
% __ __ _
% | \/ | __ _| | _____
% | |\/| |/ _` | |/ / _ \
% | | | | (_| | < __/
% |_| |_|\__,_|_|\_\___|
%
% <make>
* (eepitch-shell)
* (eepitch-kill)
* (eepitch-shell)
# (find-LATEXfile "2019planar-has-1.mk")
make -f 2019.mk STEM=2023-2-C2-edolccs veryclean
make -f 2019.mk STEM=2023-2-C2-edolccs pdf
% Local Variables:
% coding: utf-8-unix
% ee-tla: "c2el"
% ee-tla: "c2m232edolccs"
% End: