realanal.tex

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    pdfkeywords={real analysis, Riemann integral, derivative, limit, sequence},
    pdfsubject={Real Analysis},
    pdftitle={Basic Analysis: Introduction to Real Analysis},
    pdfauthor={Jiri Lebl}
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\author{Ji\v{r}\'i Lebl}

\title{Basic Analysis: Introduction to Real Analysis}

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% List of Symbols/Notation
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\begin{document}

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{\Huge\bfseries \sffamily Basic Analysis I }
\noindent\rule[-1ex]{\textwidth}{5pt}\\[2.5ex]
\hfill\emph{\Large \sffamily Introduction to Real Analysis, Volume I}
\end{minipage}}

\vspace{\stretch{1}}
\noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth}
\flushright
{\bfseries 
by Ji{\v r}\'i Lebl\\[3ex]} 
\today
\\
(version 6.1)
% --- 6th edition, 1st update)
\end{minipage}}

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\noindent
Typeset in \LaTeX.


\bigskip

\noindent
Copyright \copyright 2009--2024 Ji{\v r}\'i Lebl

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%\noindent
%ISBN-13: 979-8851944635

%PRINT
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%\medskip
%\noindent
%Cover image: Mt. Olomana, Oahu, Hawaii, \copyright 2019 Ji{\v r}\'i Lebl, all rights reserved.  Cover
%image cannot be reused in derivative works.

\bigskip

\noindent
\includegraphics[width=1.38in]{figures/license}
\quad
\includegraphics[width=1.38in]{figures/license2}

\bigskip

\noindent
This work
%PRINT
% not for lulu
%(except the cover art)
is dual licensed under
the Creative Commons
Attribution-Non\-commercial-Share Alike 4.0 International License and
the Creative Commons
Attribution-Share Alike 4.0 International License.
To view a
copy of these licenses, visit
\url{https://creativecommons.org/licenses/by-nc-sa/4.0/}
or
\url{https://creativecommons.org/licenses/by-sa/4.0/}
or send a letter to
Creative Commons
PO Box 1866, Mountain View, CA 94042, USA\@.

\bigskip

\noindent
You can use, print, duplicate, and share this book as much as you want.  You can
base your own notes on it and reuse parts if you keep the license the
same.  You can assume the license is either CC-BY-NC-SA or CC-BY-SA\@,
whichever is compatible with what you wish to do.
Your derivative work must use at least one of the licenses.
Derivative works must be prominently marked as such.

\bigskip

\noindent
During the writing of this book, 
the author was in part supported by NSF grants DMS-0900885 and
DMS-1362337.

\bigskip

\noindent
The date is the main identifier of version.  The major version / edition
number is raised only if there have been substantial changes.
From 6th edition onwards, both volumes share the same version number.
Edition
number started at 4, that is, version 4.0, as it was not kept track of
before.  %The edition given with the ISBN number is the major version.

\bigskip

\noindent
See \url{https://www.jirka.org/ra/} for more information
(including contact information, possible updates, and errata).

\bigskip

\noindent
The \LaTeX\ source for the book is available
for possible modification and customization
at github: \url{https://github.com/jirilebl/ra}


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\addcontentsline{toc}{chapter}{Further Reading}
\markboth{FURTHER READING}{FURTHER READING}
\begin{bibchapter}[Further Reading]
\begin{biblist}[\normalsize]

\bib{BS}{book}{
   author={Bartle, Robert G.},
   author={Sherbert, Donald R.},
   title={Introduction to Real Analysis},
   edition={3},
   publisher={John Wiley \& Sons Inc.},
   place={New York},
   date={2000},
}

\bib{DW}{book}{
   author={D'Angelo, John P.},
   author={West, Douglas B.},
   title={Mathematical Thinking: Problem-Solving and Proofs},
   edition={2},
   publisher={Prentice Hall},
   date={1999},
}

\bib{GIAM}{misc}{
   author={Fields, Joseph E.},
   title={A Gentle Introduction to the Art of Mathematics},
   note={Available at \url{http://giam.southernct.edu/GIAM/}},
}

\bib{Hammack}{misc}{
   author={Hammack, Richard},
   title={Book of Proof},
   note={Available at \url{http://www.people.vcu.edu/~rhammack/BookOfProof/}},
}

\bib{Rosenlicht}{book}{
   author={Rosenlicht, Maxwell},
   title={Introduction to Analysis},
   note={Reprint of the 1968 edition},
   publisher={Dover Publications Inc.},
   place={New York},
   date={1986},
   pages={viii+254},
   isbn={0-486-65038-3},
}

\bib{Rudin:baby}{book}{
   author={Rudin, Walter},
   title={Principles of Mathematical Analysis},
   edition={3},
   note={International Series in Pure and Applied Mathematics},
   publisher={McGraw-Hill Book Co.},
   place={New York},
   date={1976},
   pages={x+342},
}

\bib{Trench}{book}{
   author={Trench, William F.},
   title={Introduction to Real Analysis},
   year={2003},
   publisher={Pearson Education},
   note={\url{http://ramanujan.math.trinity.edu/wtrench/texts/TRENCH_REAL_ANALYSIS.PDF}},
}

\end{biblist}
\end{bibchapter}

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