%% This document created by Scientific Notebook (R) Version 3.5 %% Starting shell: article \documentclass{article} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Version=5.00.0.2570} %TCIDATA{} %TCIDATA{Created=Wednesday, February 10, 1999 13:29:48} %TCIDATA{LastRevised=Sunday, February 13, 2005 18:35:36} %TCIDATA{} %TCIDATA{} %TCIDATA{CSTFile=On line bluem.cst} %TCIDATA{PageSetup=72,72,72,72,0} %TCIDATA{Counters=arabic,1} %TCIDATA{AllPages= %H=36 %F=36,\PARA{038
\QTR{small}{Matematick\U{e1} anal\U{fd}za III online - Komplexn\U{e9} \U{10d}\U{ed}sla a funkcie komplexnej premennej - 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{Komplexn\'{e} \v{c}\'{\i}sla a funkcie komplexnej premennej} \begin{center} \begin{tabular}{|c|c|c|c|} \hline \textbf{% %TCIMACRO{\hyperref{Obsah}{}{}{mcindex.tex}}% %BeginExpansion \msihyperref{Obsah}{}{}{mcindex.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Obsah kapitoly}{}{}{K1.tex}}% %BeginExpansion \msihyperref{Obsah kapitoly}{}{}{K1.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Cvi\v{c}enia}{}{}{Cv1.tex}}% %BeginExpansion \msihyperref{Cvi\v{c}enia}{}{}{Cv1.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Index}{}{}{ind.tex}}% %BeginExpansion \msihyperref{Index}{}{}{ind.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 Ak\'{e} \v{c}\'{\i}sla naz\'{y}vame komplexn\'{e} \v{c}\'{\i}sla? \item Ak\'{y} je geometrick\'{y} v\'{y}znam komplexn\'{e}ho \v{c}\'{\i}sla? \item Definujte modul a argument komplexn\'{e}ho \v{c}\'{\i}sla. \item Nap\'{\i}\v{s}te Eulerovu formulu. \item Nap\'{\i}\v{s}te komplexn\'{e} \v{c}\'{\i}slo $z$\ v algebrickom, trigonometrickom a exponenci\'{a}lnom tvare. \item Ako definujeme algebrick\'{e} oper\'{a}cie pre komplexn\'{e} \v{c}% \'{\i}sla v algebrickom tvare? \item Ako definujeme oper\'{a}cie n\'{a}sobenia a delenia pre komplexn\'{e} \v{c}\'{\i}sla v trigonometrickom a exponenci\'{a}lnom tvare? \item Ak\'{y}m sp\^{o}sobom definujeme prirodzen\'{u} mocninu komplexn\'{e}% ho \v{c}\'{\i}sla v trigonometrickom a exponenci\'{a}lnom tvare? \item Nap\'{\i}\v{s}te Moivreovu formulu. \item Nap\'{\i}\v{s}te fomulu pre v\'{y}po\v{c}et n-tej odmocniny z komplexn% \'{e}ho \v{c}\'{\i}sla. \item Definujte oblas\v{t} v komplexnej rovine. \item Definujte jednoducho s\'{u}visl\'{u} oblas\v{t}. \item Definujte limitu postupnosti komplexn\'{y}ch \v{c}\'{\i}sel. \item Ako zist\'{\i}te konvergenciu radu komplexn\'{y}ch \v{c}\'{\i}sel. \item Vysvetlite pojem absol\'{u}tnej konvergencie radu komplexn\'{y}ch \v{c}% \'{\i}sel. \item Definujte funkciu komplexnej premennej. \item \v{C}o znamen\'{a} z\'{a}pis $\lim_{z\longrightarrow z_{0}}f\left( z\right) =A,$ ke\v{d} $z_{0},\,A$\ s\'{u} kone\v{c}n\'{e} komplexn\'{e} \v{c}% \'{\i}sla. \item \v{C}o znamenaj\'{u} z\'{a}pisy $\lim_{z\longrightarrow z_{0}}f\left( z\right) =\infty ,\lim_{z\longrightarrow \infty }f\left( z\right) =A,$ ke% \v{d} $z_{0},\,A$\ s\'{u} kone\v{c}n\'{e} komplexn\'{e} \v{c}\'{\i}sla. \item Ak $f\left( z\right) =u\left( x,y\right) +iv\left( x,y\right) ,\,z_{0}=x_{0}+iy_{0}.$ \v{C}omu je ekvivalentn\'{y} z\'{a}pis \ $% \lim_{z\longrightarrow z_{0}}f\left( z\right) =A+iB.$ \item Definujte spojitos\v{t} funkcie komplexnej premennej v bode. \item \v{C}o naz\'{y}vame oblas\v{t}ou konvergencie pre rad $% \sum_{k=1}^{n}u_{k}(z)?$ \item Kedy hovor\'{\i}me, \v{z}e rad rovnomerne konverguje? \item Definujte mocninov\'{y} rad komplexnej premennej. \item Definujte oblas\v{t} konvergencie pre mocninov\'{y} rad. \item Ak\'{y}m sp\^{o}sobom n\'{a}jdeme oblas\v{t} konvergencie radu so z% \'{a}porn\'{y}mi mocninami $\left( z-a\right) ?$ \item Definujte jednotliv\'{e} element\'{a}rne funkcie. \end{enumerate} \begin{center} \begin{tabular}{|c|c|c|c|} \hline \textbf{% %TCIMACRO{\hyperref{Obsah}{}{}{mcindex.tex}}% %BeginExpansion \msihyperref{Obsah}{}{}{mcindex.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Obsah kapitoly}{}{}{K1.tex}}% %BeginExpansion \msihyperref{Obsah kapitoly}{}{}{K1.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Cvi\v{c}enia}{}{}{Cv1.tex}}% %BeginExpansion \msihyperref{Cvi\v{c}enia}{}{}{Cv1.tex}% %EndExpansion } & \textbf{% %TCIMACRO{\hyperref{Index}{}{}{ind.tex}}% %BeginExpansion \msihyperref{Index}{}{}{ind.tex}% %EndExpansion } \\ \hline \end{tabular} \end{center} \rule{6.5in}{0.04in} \textsl{Matematick\'{a} anal\'{y}za III} \section{Komplexn\'{e} \v{c}\'{\i}sla a funkcie komplexnej premennej} \end{document}