\documentclass{article} \usepackage{amssymb} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Created=Monday, June 25, 2001 17:45:57} %TCIDATA{LastRevised=Monday, March 24, 2003 14:18:00} %TCIDATA{} %TCIDATA{} %TCIDATA{CSTFile=On line bluem.cst} %TCIDATA{PageSetup=72,72,72,72,0} %TCIDATA{AllPages= %H=36 %F=36,\PARA{038
\QTR{small}{Matematick\U{e1} anal\U{fd}za II online - D\U{f4}kazy\dotfill \thepage }} %} \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}} \input{tcilatex} \begin{document} \author{A. U. Thor} \title{Lab Report} \date{The Date } \maketitle \begin{abstract} A Laboratory report created with Scientific Notebook \end{abstract} \section{Plochy a plo\v{s}n\'{e} integr\'{a}ly} \subsection{D\^{o}kaz vety} \textbf{D\^{o}kaz: \ }Pod\v{l}a predpokladu je aspo\v{n} jedno z $% J_{1},J_{2},J_{3}$ r\^{o}zne od nuly, nech je to $J_{3}\left( \mathbf{a}% \right) \neq 0.$ Teda $\frac{\partial \left( F_{2},F_{1}\right) }{\partial \left( u,v\right) }\left( \mathbf{a}\right) \neq 0.$ Preto funkcia $\mathbf{f% }\left( u,v\right) =\left( F_{1}\left( u,v\right) ,F_{2}\left( u,v\right) \right) $ sp\'{l}\v{n}a predpoklady vety o inverznej funkcii, teda je $% \mathbf{f}$ je lok\'{a}lne invertovate\v{l}n\'{a}. Nech $\mathbf{g}$ je lok% \'{a}lna inverzia: $\left( u,v\right) =\left( g_{1}\left( x,y\right) ,g_{2}\left( x,y\right) \right) .$ Potom \ \[ z=F_{3}\left( u,v\right) =\left( F_{3}\circ \mathbf{g}\right) \left( x,y\right) , \]% \v{c}o dokazuje v\'{y}sledok s $\Phi =F_{3}\circ \mathbf{g.}$ Bolo mo\v{z}n% \'{e} pou\v{z}i\v{t} aj vetu o implicitnej funkcii. $\blacksquare $ \begin{center} \begin{tabular}{|c|} \hline {\small \hyperref{Sp\"{a}\v{t}}{}{}{Ma72.tex#3}} \\ \hline \end{tabular} \end{center} \rule{6.5in}{0.04in} \textsl{Matematick\'{a} anal\'{y}za II} \end{document}