\( \newcommand{\N}{\mathbb N} \newcommand{\Z}{\mathbb Z} \newcommand{\Q}{\mathbb Q} \newcommand{\R}{\mathbb R} \newcommand{\ts}{\textstyle} \newcommand{\ds}{\displaystyle} \newcommand{\va}{\mathbf{a}} \newcommand{\vb}{\mathbf{b}} \newcommand{\vc}{\mathbf{c}} \newcommand{\vC}{\mathbf{C}} \newcommand{\vE}{\mathbf{E}} \newcommand{\vd}{\mathbf{d}} \newcommand{\ve}{\mathbf{e}} \newcommand{\vg}{\mathbf{g}} \newcommand{\vh}{\mathbf{h}} \newcommand{\vi}{\mathbf{i}} \newcommand{\vj}{\mathbf{j}} \newcommand{\vl}{\mathbf{l}} \newcommand{\vk}{\mathbf{k}} \newcommand{\vn}{\mathbf{n}} \newcommand{\vm}{\mathbf{m}} \newcommand{\vp}{\mathbf{p}} \newcommand{\vq}{\mathbf{q}} \newcommand{\vr}{\mathbf{r}} \newcommand{\vs}{\mathbf{s}} \newcommand{\vt}{\mathbf{t}} \newcommand{\vu}{\mathbf{u}} \newcommand{\vv}{\mathbf{v}} \newcommand{\vphi}{\pmb{\phi}} \newcommand{\vw}{\mathbf{w}} \newcommand{\vx}{\mathbf{x}} \newcommand{\vy}{\mathbf{y}} \newcommand{\vz}{\mathbf{z}} \newcommand{\vZero}{\mathbf{0}} \newcommand{\vF}{\mathbf{F}} \newcommand{\vR}{\mathbf{R}} \newcommand{\vT}{\mathbf{T}} \newcommand{\vN}{\mathbf{N}} \newcommand{\vL}{\mathbf{L}} \newcommand{\vB}{\mathbf{B}} \newcommand{\vD}{\mathbf{D}} \newcommand{\vH}{\mathbf{H}} \newcommand{\vK}{\mathbf{K}} \newcommand{\vG}{\mathbf{G}} \newcommand{\vA}{\mathbf{A}} \newcommand{\vS}{\mathbf{S}} \newcommand{\vV}{\mathbf{V}} \newcommand{\proj}{\text{proj}\, } \newcommand{\comp}{\text{comp}\, } \newcommand{\rot}{\text{rot}\, } \renewcommand{\div }{\text{div}\, } \newcommand{\grad }{\text{grad}\, } \newcommand{\Om}{\Omega} \newcommand{\om}{\omega} \newcommand{\vOm}{\pmb{\Omega}} \newcommand{\svOm}{\pmb{\scriptsize\Omega}} \renewcommand{\a}{\alpha} \renewcommand{\b}{\beta} \newcommand{\g}{\gamma} \newcommand{\e}{\epsilon} \newcommand{\veps}{\varepsilon} \renewcommand{\d}{\delta} \newcommand{\f}{\phi} \renewcommand{\j}{\theta} \newcommand{\ka}{\kappa} \newcommand{\la}{\lambda} \newcommand{\be}{\beta} \newcommand{\al}{\alpha} \newcommand{\dvect}[2]{\left[\begin{array}{r} #1\\ #2\end{array} \right]} \newcommand{\tvect}[3]{\left[\begin{array}{r} #1\\ #2 \\ #3\end{array} \right]} \newcommand{\ctvec}[3]{\left[\begin{array}{c} #1\\ #2 \\ #3\end{array} \right]} \newcommand{\plan}[1]{\mathcal{#1}} \newcommand{\diff}[2]{\frac{d#1}{d#2}} \newcommand{\pdiff}[2]{ \frac{\partial #1}{\partial #2}} \newcommand{\difftwo}[2]{ \frac{d^2#1}{d{#2}^2}} \newcommand{\De}{\Delta} \newcommand{\Atop}[2]{\genfrac{}{}{0pt}{}{#1}{#2}} \newcommand{\atp}[2]{ \genfrac{}{}{0in}{}{#1}{#2} } \newcommand{\smsum}{\mathop{{\ts \sum}}} \newcommand{\half}{ \frac{1}{2} } \newcommand{\Set}[2]{\big\{ \ #1\ \big|\ #2\ \big\}} \newcommand{\set}[1]{ \left\{#1\right\} } \DeclareMathOperator{\sgn}{sgn} \newcommand{\dee}[1]{d#1} \newcommand{\eqf}[1]{{\buildrel \rm #1 \over =}} \newcommand{\ave}{\mathrm{ave}} \newcommand{\llt}{\left ( } \newcommand{\rgt}{\right ) } \newcommand{\vnabla}{ { \mathchoice{\pmb{\nabla}} {\pmb{\nabla}} {\pmb{\scriptstyle\nabla}} {\pmb{\scriptscriptstyle\nabla}} } } \DeclareMathOperator{\sech}{sech} \DeclareMathOperator{\csch}{csch} \DeclareMathOperator{\arcsec}{arcsec} \DeclareMathOperator{\arccot}{arcCot} \DeclareMathOperator{\arccsc}{arcCsc} \DeclareMathOperator{\arccosh}{arcCosh} \DeclareMathOperator{\arcsinh}{arcsinh} \DeclareMathOperator{\arctanh}{arctanh} \DeclareMathOperator{\arcsech}{arcsech} \DeclareMathOperator{\arccsch}{arcCsch} \DeclareMathOperator{\arccoth}{arcCoth} \def\eqover#1{\ {\buildrel #1 \over =}\ } \newcommand{\impliesover}[1]{ {\buildrel #1 \over\implies} } \newcommand{\cA}{\mathcal{A}} \newcommand{\cB}{\mathcal{B}} \newcommand{\cC}{\mathcal{C}} \newcommand{\cD}{\mathcal{D}} \newcommand{\cE}{\mathcal{E}} \newcommand{\cR}{\mathcal{R}} \newcommand{\cS}{\mathcal{S}} \newcommand{\cT}{\mathcal{T}} \newcommand{\cV}{\mathcal{V}} \newcommand{\cH}{\mathcal{H}} \newcommand{\YEaxis}[2]{\draw[help lines] (-#1,0)--(#1,0) node[right]{$x$};\draw[help lines] (0,-#2)--(0,#2) node[above]{$y$};} \newcommand{\YEaaxis}[4]{\draw[help lines] (-#1,0)--(#2,0) node[right]{$x$};\draw[help lines] (0,-#3)--(0,#4) node[above]{$y$};} \newcommand{\YEtaxis}[4]{\draw[help lines] (-#1,0)--(#2,0) node[right]{$t$};\draw[help lines] (0,-#3)--(0,#4) node[above]{$y$};} \newcommand{\YEtaaxis}[4]{\draw[help lines, <->] (-#1,0)--(#2,0) node[right]{$t$}; \draw[help lines, <->] (0,-#3)--(0,#4) node[above]{$y$};} \newcommand{\YExcoord}[2]{\draw (#1,.2)--(#1,-.2) node[below]{$#2$};} \newcommand{\YEycoord}[2]{\draw (.2,#1)--(-.2,#1) node[left]{$#2$};} \newcommand{\YEnxcoord}[2]{\draw (#1,-.2)--(#1,.2) node[above]{$#2$};} \newcommand{\YEnycoord}[2]{\draw (-.2,#1)--(.2,#1) node[right]{$#2$};} \newcommand{\YEstickfig}[3]{ \draw (#1,#2) arc(-90:270:2mm); \draw (#1,#2)--(#1,#2-.5) (#1-.25,#2-.75)--(#1,#2-.5)--(#1+.25,#2-.75) (#1-.2,#2-.2)--(#1+.2,#2-.2);} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} \)