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\QTR{small}{Matematick\U{e1} anal\U{fd}za II online - Krivkov\U{e9} integr\U{e1}ly - Ot\U{e1}zky\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} \begin{center} \begin{tabular}{|c|c|c|c|} \hline \textbf{% %TCIMACRO{\hyperref{Obsah}{}{}{maiindex.tex}}% %BeginExpansion \msihyperref{Obsah}{}{}{maiindex.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Obsah kapitoly}{}{}{Ma6.tex}}% %BeginExpansion \msihyperref{Obsah kapitoly}{}{}{Ma6.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Cvi\v{c}enia}{}{}{C6.tex}}% %BeginExpansion \msihyperref{Cvi\v{c}enia}{}{}{C6.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Index}{}{}{Glos.tex}}% %BeginExpansion \msihyperref{Index}{}{}{Glos.tex}% %EndExpansion } \\ \hline \end{tabular} \end{center} \section{Ot\'{a}zky} Preverte si znalosti z\'{\i}skan\'{e} v tejto kapitole. Zodpovedajte v\v{s}% etky ot\'{a}zky. Ak neviete nejak\'{u} ot\'{a}zku zodpoveda\v{t} znovu pre% \v{s}tudujte pr\'{\i}slu\v{s}n\'{u} \v{c}as\v{t} a op\"{a}\v{t} odpovedajte. Po d\^{o}kladnom preveren\'{\i} Va\v{s}ich vedomost\'{\i} sa venujte po\v{c}% \'{\i}taniu pr\'{\i}kladov. \begin{enumerate} \item Definujte cestu (krivku) v $\mathbf{R}^{n}.$ \item Definujte jednoduch\'{u} cestu (krivku). \item Definujte uzavret\'{u} cestu (krivku). \item Definujte $C^{1}$ cestu (krivku). \item Definujte hladk\'{u} cestu (krivku). \item \v{C}o je parametriz\'{a}cia krivky? \item Nap\'{\i}\v{s}te formulu pre v\'{y}po\v{c}et d\'{l}\v{z}ky krivky? \item Definujte krivkov\'{y} integr\'{a}l zo sk\'{a}l\'{a}rneho po\v{l}a. \item Definujte krivkov\'{y} integr\'{a}l z vektorov\'{e}ho po\v{l}a. \item Plat\'{\i} tvrdenie: krivkov\'{y} integr\'{a}l zo sk\'{a}l\'{a}rneho po% \v{l}a je z\'{a}visl\'{y} od parametriz\'{a}cie krivky aj od orient\'{a}cie krivky? Ak tvrdenie neplat\'{\i} uve\v{d}te spr\'{a}vne tvrdenie. \item Plat\'{\i} tvrdenie: krivkov\'{y} integr\'{a}l zo sk\'{a}l\'{a}rneho po% \v{l}a nie je z\'{a}visl\'{y} od parametriz\'{a}cie krivky ale je z\'{a}visl% \'{y} od orient\'{a}cie krivky? Ak tvrdenie neplat\'{\i} uve\v{d}te spr\'{a}% vne tvrdenie. \item Plat\'{\i} tvrdenie: krivkov\'{y} integr\'{a}l z vektorov\'{e}ho po% \v{l}a nie je z\'{a}visl\'{y} od parametriz\'{a}cie krivky ale z\'{a}vis% \'{\i} od orient\'{a}cie krivky? Ak tvrdenie neplat\'{\i} uve\v{d}te spr\'{a}% vne tvrdenie. \item \v{C}o znamen\'{a}, \v{z}e krivkov\'{y} integr\'{a}l z vektorov\'{e}ho po\v{l}a nez\'{a}visi od cesty. \item Definujte potenci\'{a}l vektorov\'{e}ho po\v{l}a. \item Formulujte posta\v{c}uj\'{u}cu podmienku nez\'{a}vislosti orientovan% \'{e}ho krivkov\'{e}ho integr\'{a}lu od cesty. Je t\'{a}to podmienka aj nutnou podmienkou? \end{enumerate} \begin{center} \begin{tabular}{|c|c|c|c|} \hline \textbf{% %TCIMACRO{\hyperref{Obsah}{}{}{maiindex.tex}}% %BeginExpansion \msihyperref{Obsah}{}{}{maiindex.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Obsah kapitoly}{}{}{Ma6.tex}}% %BeginExpansion \msihyperref{Obsah kapitoly}{}{}{Ma6.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Cvi\v{c}enia}{}{}{C6.tex}}% %BeginExpansion \msihyperref{Cvi\v{c}enia}{}{}{C6.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Index}{}{}{Glos.tex}}% %BeginExpansion \msihyperref{Index}{}{}{Glos.tex}% %EndExpansion } \\ \hline \end{tabular} \end{center} \rule{6.5in}{0.04in} \textsl{Matematick\'{a} anal\'{y}za II} \section{Krivkov\'{e} integr\'{a}ly} \end{document}