\documentclass{article} \usepackage{amssymb} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Created=Monday, June 25, 2001 17:45:57} %TCIDATA{LastRevised=Friday, January 24, 2003 22:59:53} %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 III 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{Cauchyho integr\'{a}lna veta} \subsection{D\^{o}kaz vety} \textbf{D\^{o}kaz: }Dok\'{a}\v{z}eme t\'{u}to vetu pre pr\'{\i}pad $n=2.$ Pou% \v{z}it\'{\i}m pomocn\'{y}ch kriviek $ab,\,cd,ef$ vytvor\'{\i}me jednoduch% \'{e}, uzavret\'{e}, po \v{c}astiach hladk\'{e} krivky $\gamma ,\,\Delta $ tak, \v{z}e $\gamma $ prech\'{a}dza bodmi $a,m,f,e,r,d,c,p,b$ a $\Delta $ zas bodmi $a,b,q,c,d,s,e,f,n$ a poradie t\'{y}chto bodov n\'{a}m d\'{a}va orient\'{a}ciu kriviek $\gamma $ a $\Delta $. \hyperref{Veta}{}{}{K32.tex#1} implikuje \[ \int_{\gamma }f\left( z\right) dz=0\text{ \ a \ }\int_{\Delta }f\left( z\right) dz=0, \]% odkia\v{l} \[ \int_{\gamma }f\left( z\right) dz=+\int_{\Delta }f\left( z\right) dz=0, \]% odkia\v{l} \[ 0=\int_{amf}f+\int_{fe}f+\int_{erd}f+\int_{dc}f+\int_{cpb}f+\int_{ba}f+% \int_{ab}f+\int_{bqc}f+\int_{cd}f+\int_{dse}f+\int_{ef}f+\int_{fha}f= \]% \[ =\int_{amf}f-\int_{ef}f-\int_{dre}f-\int_{cd}f-\int_{bcp}f-\int_{ab}f+% \int_{ab}f-\int_{cqb}f+\int_{cd}f-\int_{esd}f+\int_{ef}f+\int_{fha}f= \] \[ =\int_{amf}f+\int_{fha}f-\int_{dre}f-\int_{esd}f-\int_{bcp}f-\int_{cqb}f=% \int_{C_{0}}f-\int_{C_{1}}f-\int_{C_{2}}f \]% t.j.% \[ \int_{C_{0}}f\left( z\right) dz=\int_{C_{1}}f\left( z\right) dz+\int_{C_{2}}f\left( z\right) dz.\,\,\blacksquare \] \begin{center} \begin{tabular}{|c|} \hline {\small \hyperref{Sp\"{a}\v{t}}{}{}{K32.tex#2}} \\ \hline \end{tabular} \end{center} \rule{6.5in}{0.04in} \textsl{Matematick\'{a} anal\'{y}za III} \end{document}