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diffyqs.tex
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\author{Ji\v{r}\'i Lebl}
\title{Notes on Diffy Qs: Differential Equations for Engineers}
% Set up our index
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%mbx <!--BEFORE book-->
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%mbxdocinfo <title>www.jirka.org/diffyqs/</title>
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%mbx <title>Notes on Diffy Qs</title>
%mbx <subtitle>Differential Equations for Engineers</subtitle>
%mbx
%mbx <frontmatter>
%mbx <titlepage>
%mbx
%mbx <author>
%mbx <personname>Jiří Lebl</personname>
%mbx <department>Department of Mathematics</department>
%mbx <institution>Oklahoma State University</institution>
%mbx <email>[email protected]</email>
%mbx </author>
%mbx
%mbx <date><today /></date>
%mbx
%mbx </titlepage>
%mbx
%mbx <colophon>
%mbx
%mbx <copyright>
%mbx <year>2008<ndash />2024</year>
%mbx <holder>Jiří Lebl</holder>
%mbx <minilicense>Creative Commons Attribution-Non-commercial-Share Alike 4.0 International License and the Creative Commons Attribution-Share Alike 4.0 International License</minilicense>
%mbx <shortlicense>
%mbx This work is dual licensed under the Creative Commons Attribution-Non-commercial-Share Alike 4.0 International License and
%mbx the Creative Commons Attribution-Share Alike 4.0 International License. To view a copy of these licenses, visit
%mbx <url href="https://creativecommons.org/licenses/by-nc-sa/4.0/" /> or
%mbx <url href="https://creativecommons.org/licenses/by-sa/4.0/" />
%mbx or send a letter to Creative Commons PO Box 1866, Mountain View, CA 94042, USA.
%mbx </shortlicense>
%mbx </copyright>
%mbx <p>
%mbx Version 6.7
%mbx </p>
%mbx <p>
%mbx You can use, print, duplicate, and share this book as much as you want. You can
%mbx base your own notes on it and reuse parts if you keep the license the
%mbx same. You can assume the license is either CC-BY-NC-SA or CC-BY-SA,
%mbx whichever is compatible with what you wish to do.
%mbx Your derivative work must use at least one of the licenses.
%mbx Derivative works must be prominently marked as such.
%mbx </p>
%mbx <p>
%mbx During the writing of this book,
%mbx the author was in part supported by NSF grant DMS-0900885 and
%mbx DMS-1362337.
%mbx </p>
%mbx <p>
%mbx The date is the main identifier of version. The major version / edition
%mbx number is raised only if there have been substantial changes.
%mbx Edition number started at 5, that is, version 5.0, as it was not kept track of
%mbx before.
%mbx </p>
%mbx <p>
%mbx See <url href="https://www.jirka.org/diffyqs/" />
%mbx for more information
%mbx (including contact information).
%mbx The LaTeX source for the book is available for possible modification and customization
%mbx at github: <url href="https://github.com/jirilebl/diffyqs" />
%mbx </p>
%mbx
%mbx </colophon>
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\begin{small}
\noindent
Typeset in \LaTeX.
\bigskip
\noindent
Copyright \copyright 2008--2024 Ji\v{r}\'i Lebl
%PRINT
% not for lulu
%\medskip
%\noindent
%Amazon KDP edition\\
%ISBN-13: 978-1-70623-023-6
%PRINT
% not for lulu
%\medskip
%\noindent
%Cover image: Arch in St.\ Louis, \copyright 2008 Ji{\v r}\'i Lebl, all rights reserved. Cover
%image cannot be reused in derivative works.
\bigskip
%\begin{floatingfigure}{1.4in}
%\vspace{-0.05in}
\noindent
\includegraphics[width=1.38in]{figures/license}
\quad
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\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\@.
%Creative Commons, 171 Second Street, Suite 300, San Francisco, California,
%94105, 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.
%If you plan to use it commercially (sell it for more than just
%duplicating cost), then you need to contact me and we will work something out.
%If you are printing a course pack for your students, then it is fine if the
%duplication service is charging a fee for printing and selling the printed
%copy. I consider that duplicating cost.
\bigskip
\noindent
During the writing of this book,
the author was in part supported by NSF grant 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.
%, if only
%very minor changes or fixes are done only the minor version is raised.
Edition
number started at 5, that is, version 5.0, as it was not kept track of
before.
%The Createspace edition ISBN number identifies the major version, and is not
%changed for minor updates fixing errata.
%The edition given with the ISBN number is the major version.
\bigskip
\noindent
See \url{https://www.jirka.org/diffyqs/} for more information
(including contact information).
\bigskip
\noindent
The \LaTeX\ source for the book is available
for possible modification and customization
at github: \url{https://github.com/jirilebl/diffyqs}
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\newpage
%mbxENDIGNORE
%mbx <!--HERE IS WHERE WE ADD MBX PREAMBLE AFTER book-->
%mbx <!--HERE IS WHERE WE ADD MBX PREAMBLE 2-->
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Introduction chapter
\input{ch-intro.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% First order ODEs chapter
\input{ch-first-order-ode.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Higher order linear ODEs chapter
\input{ch-higher-order-ode.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Systems of ODEs chapter
\input{ch-systems.tex}
%mbxSTARTIGNORE
%This makes contents fit if needed
%FIXMEevillayouthack
\addextraspacetotoc
%mbxENDIGNORE
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Fourier series and PDEs chapter
\input{ch-fourier-and-pde.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Eigenvalue problems chapter
\input{ch-eigenvalue-probs.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% The Laplace transform chapter
\input{ch-laplace.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Power series methods chapter
\input{ch-power-ser.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Nonlinear systems chapter
\input{ch-nonlin-systems.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\appendix
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% mbx wants appendices to be in backmatter it seems
%mbx <backmatter>
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Linear algebra appendix
\input{ap-linear-algebra.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Nonlinear systems chapter
\input{ap-laplace-list.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%must be in separate "paragraph" (empty lines before and after)
% This closes the chapters/appedices above and starts actual backmatter
%mbxCLOSECHAPTER
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%mbxSTARTIGNORE
%This makes contents fit if needed
%FIXMEevillayouthack
%\addextraspacetotoc
\renewcommand{\bibname}{Further Reading}
\begin{thebibliography}{MM}
\addfakecontentsline{Further Reading}
\label{furtherreading:chapter}
\bibitem[BM]{BM}
Paul W.\ Berg and James L.\ McGregor,
\emph{\href{https://books.google.com/books?id=EfJQAAAAMAAJ}{Elementary
Partial Differential Equations}},
Holden-Day,
San Francisco, CA\@,
1966.
\bibitem[BD]{BD}
William E.\ Boyce and
Richard C.\ DiPrima,
\emph{\href{https://books.google.com/books?id=nYWcQgAACAAJ}{Elementary
Differential Equations and Boundary Value Problems}},
11th edition,
John Wiley \& Sons Inc.,
New York, NY\@, 2017.
\bibitem[EP]{EP}
C.H.\ Edwards and D.E.\ Penney,
\emph{\href{https://books.google.com/books?id=wuWvoAEACAAJ}{Differential
Equations and Boundary Value Problems: Computing and Modeling}},
5th edition,
Pearson,
2014.
\bibitem[F]{F}
Stanley J.\ Farlow,
\emph{\href{https://books.google.com/books?id=_ozWAAAAMAAJ}{An Introduction
to Differential Equations and Their Applications}},
McGraw-Hill, Inc.,
Princeton, NJ\@,
1994. (Published also by Dover Publications, 2006.)
\bibitem[I]{I}
E.L.\ Ince,
\emph{\href{https://books.google.com/books?id=uYz-pqUD75gC}{Ordinary
Differential Equations}},
Dover Publications, Inc.,
New York, NY\@,
1956.
\bibitem[T]{T}
William F.\ Trench,
\emph{Elementary Differential Equations with Boundary Value
Problems}. Books and Monographs. Book 9. 2013.
\url{https://digitalcommons.trinity.edu/mono/9}
\end{thebibliography}
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%mbx <references xml:id="furtherreading_chapter">
%mbx <title>Further Reading</title>
%mbx
%mbx <biblio type="raw" xml:id="biblio-BM" tag="BM">Paul W. Berg and
%mbx James L. McGregor,
%mbx <title><url href="https://books.google.com/books?id=EfJQAAAAMAAJ"
%mbx visual="books.google.com/books?id=EfJQAAAAMAAJ"
%mbx >Elementary Partial Differential Equations</url></title>,
%mbx Holden-Day, San Francisco, CA, 1966.</biblio>
%mbx
%mbx <biblio type="raw" xml:id="biblio-BD" tag="BD">William E. Boyce and
%mbx Richard C. DiPrima,
%mbx <title><url href="https://books.google.com/books?id=SyaVDwAAQBAJ"
%mbx visual="books.google.com/books?id=SyaVDwAAQBAJ"
%mbx >Elementary Differential Equations and Boundary Value
%mbx Problems</url></title>,
%mbx 11th edition, John Wiley & Sons Inc., New York, NY, 2017.</biblio>
%mbx
%mbx <biblio type="raw" xml:id="biblio-EP" tag="EP">C.H. Edwards
%mbx and D.E. Penney,
%mbx <title><url href="https://books.google.com/books?id=wuWvoAEACAAJ"
%mbx visual="books.google.com/books?id=wuWvoAEACAAJ"
%mbx >Differential Equations and Boundary Value Problems: Computing and
%mbx Modeling</url></title>,
%mbx 5th edition, Pearson, 2014.</biblio>
%mbx
%mbx <biblio type="raw" xml:id="biblio-F" tag="F">Stanley J. Farlow,
%mbx <title><url href="https://books.google.com/books?id=_ozWAAAAMAAJ"
%mbx visual="books.google.com/books?id=_ozWAAAAMAAJ"
%mbx >An Introduction to Differential Equations and Their
%mbx Applications</url></title>,
%mbx McGraw-Hill, Inc., Princeton, NJ, 1994. (Published also by Dover
%mbx Publications, 2006.)</biblio>
%mbx
%mbx <biblio type="raw" xml:id="biblio-I" tag="I">E.L. Ince,
%mbx <title><url href="https://books.google.com/books?id=uYz-pqUD75gC"
%mbx visual="books.google.com/books?id=uYz-pqUD75gC"
%mbx >Ordinary Differential Equations</url></title>,
%mbx Dover Publications, Inc., New York, NY, 1956.</biblio>
%mbx
%mbx <biblio type="raw" xml:id="biblio-T" tag="T">William F. Trench,
%mbx <title>Elementary Differential Equations with Boundary Value
%mbx Problems</title>, Books and Monographs, Book 9, 2013,
%mbx <url href="https://digitalcommons.trinity.edu/mono/9" />.</biblio>
%mbx
%mbx </references>
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%mbxSTARTIGNORE
\printanswers
%mbxENDIGNORE
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%mbxSTARTIGNORE
\diffyindex
%mbxENDIGNORE
%mbx <index>
%mbx <title>Index</title>
%mbx <index-list />
%mbx </index>
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%mbx </backmatter>
\end{document}