\documentclass{article} \usepackage{amssymb} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Created=Monday, June 25, 2001 17:45:57} %TCIDATA{LastRevised=Monday, March 24, 2003 14:10:34} %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{Krivkov\'{e} integr\'{a}ly} \subsection{D\^{o}kaz vety} \textbf{D\^{o}kaz: }Preto\v{z}e $\mathbf{p}(\tau )=\mathbf{c}\left( \Phi \left( \tau \right) \right) ,$ kde $\Phi :\left\langle \alpha ,\beta \right\rangle \longrightarrow \left\langle a,b\right\rangle ,$ je $C^{1}$ bijekcia. Potom \[ \int_{P}\left( \mathbf{F\cdot T}\right) ds=\int_{\alpha }^{\beta }\mathbf{F}% \left( \mathbf{p}\left( \tau \right) \right) \cdot \mathbf{p}\,^{\prime }\left( \tau \right) d\tau =\int_{\alpha }^{\beta }\mathbf{F}\left( \mathbf{c% }\left( \Phi \left( \tau \right) \right) \right) \cdot \mathbf{c}\,^{\prime }\left( \Phi \left( \tau \right) \right) \Phi \,^{\prime }\left( \tau \right) d\tau = \]% Nech $t=\Phi \left( \tau \right) ,$\ potom dostaneme \[ =\int_{\Phi \left( \alpha \right) }^{\Phi \left( \beta \right) }\mathbf{F}% \left( \mathbf{c}\left( t\right) \right) \cdot \mathbf{c}\,^{\prime }\left( t\right) dt. \]% Ak $\Phi $\ zachov\'{a}va orient\'{a}ciu , potom $\Phi \left( \alpha \right) =a$\ a $\Phi \left( \beta \right) =b$\ a my m\'{a}me dok\'{a}zan\'{u} prv% \'{u} formulu, ak $\Phi $ men\'{\i} orient\'{a}ciu na opa\v{c}n\'{u}, potom $% \Phi \left( \alpha \right) =b$\ a $\Phi \left( \beta \right) =a$\ a my m\'{a}% me dok\'{a}zan\'{u} druh\'{u} formulu.$\blacksquare $ \begin{center} \begin{tabular}{|c|} \hline {\small \hyperref{Sp\"{a}\v{t}}{}{}{Ma62.tex#2}} \\ \hline \end{tabular} \end{center} \rule{6.5in}{0.04in} \textsl{Matematick\'{a} anal\'{y}za II} \end{document}