\relax 
\bibstyle{amsalpha}
\@writefile{toc}{\contentsline {chapter}{\numberline {1}Preface}{5}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {1.1}Computers}{5}}
\@writefile{toc}{\contentsline {chapter}{\numberline {2}Definite and Indefinite Integrals}{7}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {2.1}The Definite Integral}{7}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.1}The definition of area under curve}{7}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.2}Relation between velocity and area}{7}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.3}Definition of Integral}{8}}
\newlabel{defn:int}{{2.1.2}{8}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.1.4}The Fundamental Theorem of Calculus}{8}}
\newlabel{thm:fexists}{{2.1.5}{9}}
\@writefile{toc}{\contentsline {section}{\numberline {2.2}Indefinite Integrals and Change}{9}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.1}Indefinite Integrals}{9}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.2}Examples}{10}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.2.3}Physical Intuition}{11}}
\@writefile{toc}{\contentsline {section}{\numberline {2.3}Substitution and Symmetry}{12}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.1}The Substitution Rule}{12}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.2}The Substitution Rule for Definite Integrals}{14}}
\@writefile{toc}{\contentsline {subsection}{\numberline {2.3.3}Symmetry}{14}}
\@writefile{toc}{\contentsline {chapter}{\numberline {3}Applications to Areas, Volume, and Averages}{17}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {3.1}Using Integration to Determine Areas Between Curves}{17}}
\newlabel{eqn:boundedform}{{3.1.1}{17}}
\@writefile{toc}{\contentsline {subsection}{\numberline {3.1.1}Examples}{18}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.1.1}{\ignorespaces What is the enclosed area?}}{18}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.1.2}{\ignorespaces What is the enclosed area?}}{19}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.1.3}{\ignorespaces Find the area}}{19}}
\@writefile{toc}{\contentsline {section}{\numberline {3.2}Computing Volumes of Surfaces of Revolution}{20}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.2.1}{\ignorespaces How Big is Pharaoh's Place?}}{21}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.2.2}{\ignorespaces Find the volume of the flower pot}}{21}}
\newlabel{ex:spherevol}{{3.2.3}{21}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.2.3}{\ignorespaces Cross section of a half of sphere with radius 1}}{22}}
\@writefile{toc}{\contentsline {section}{\numberline {3.3}Average Values}{22}}
\newlabel{def:avg}{{3.3.1}{23}}
\newlabel{ex:avg1}{{3.3.2}{23}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.3.1}{\ignorespaces What is the average value of $\qopname  \relax o{sin}(x)$?}}{23}}
\newlabel{fig:avg1}{{3.3.1}{23}}
\newlabel{ex:avg2}{{3.3.3}{24}}
\@writefile{lof}{\contentsline {figure}{\numberline {3.3.2}{\ignorespaces What is the average value?}}{24}}
\newlabel{fig:avg2}{{3.3.2}{24}}
\@writefile{toc}{\contentsline {chapter}{\numberline {4}Polar Coordinates and Complex Numbers}{25}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {4.1}Polar Coordinates}{25}}
\newlabel{eqn:polar1}{{4.1.1}{25}}
\newlabel{eqn:polar2}{{4.1.3}{25}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.1.1}{\ignorespaces Graph of $r=\qopname  \relax o{sin}(\theta )$.}}{26}}
\newlabel{eqn:polar3}{{4.1.5}{26}}
\@writefile{toc}{\contentsline {section}{\numberline {4.2}Areas in Polar Coordinates}{27}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.2.1}{\ignorespaces Graph of $y=\qopname  \relax o{cos}(2x)$ and $r=\qopname  \relax o{cos}(2\theta )$}}{27}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.2.1}Examples}{28}}
\newlabel{eqn:costwosintwo}{{4.2.1}{28}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.2.2}{\ignorespaces Graph of $r=3\qopname  \relax o{cos}(\theta )$ and $r=1+\qopname  \relax o{cos}(\theta )$}}{29}}
\@writefile{toc}{\contentsline {section}{\numberline {4.3}Complex Numbers}{29}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.3.1}Polar Form}{30}}
\@writefile{toc}{\contentsline {section}{\numberline {4.4}Complex Exponentials and Trig Identities}{32}}
\newlabel{eqn:angleadd}{{4.4}{32}}
\newlabel{thm:ediff}{{4.4.2}{33}}
\@writefile{toc}{\contentsline {subsection}{\numberline {4.4.1}Trigonometry and Complex Exponentials}{34}}
\newlabel{eqn:sincose}{{4.4.1}{34}}
\@writefile{lof}{\contentsline {figure}{\numberline {4.4.1}{\ignorespaces What is $\qopname  \relax o{sin}(x)^3$?}}{35}}
\newlabel{fig:sin3}{{4.4.1}{35}}
\@writefile{toc}{\contentsline {chapter}{\numberline {5}Integration Techniques}{37}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {5.1}Integration By Parts}{37}}
\newlabel{eqn:intpartbs}{{5.1.1}{37}}
\newlabel{ex:parts2}{{5.1.5}{40}}
\@writefile{toc}{\contentsline {section}{\numberline {5.2}Trigonometric Integrals}{40}}
\newlabel{sec:trigint}{{5.2}{40}}
\newlabel{eqn:costwosintwob}{{5.2.1}{40}}
\newlabel{eqn:sincose2}{{5.2.3}{41}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.2.1}Some Remarks on Using Complex-Valued Functions}{43}}
\newlabel{eqn:ri}{{5.2.2}{43}}
\@writefile{toc}{\contentsline {section}{\numberline {5.3}Trigonometric Substitutions}{44}}
\newlabel{eqn:invsubhw1}{{5.3.1}{44}}
\newlabel{eqn:invsub}{{5.3.2}{45}}
\@writefile{toc}{\contentsline {section}{\numberline {5.4}Factoring Polynomials}{48}}
\newlabel{eqn:polyfacinttex}{{5.4.1}{48}}
\newlabel{eqn:ratfun1}{{5.4.2}{49}}
\@writefile{toc}{\contentsline {section}{\numberline {5.5}Integration of Rational Functions Using Partial Fractions}{49}}
\@writefile{toc}{\contentsline {section}{\numberline {5.6}Approximating Integrals}{53}}
\@writefile{lof}{\contentsline {figure}{\numberline {5.6.1}{\ignorespaces Graph of $e^{-\sqrt  {x}}$}}{55}}
\@writefile{toc}{\contentsline {section}{\numberline {5.7}Improper Integrals}{56}}
\@writefile{lof}{\contentsline {figure}{\numberline {5.7.1}{\ignorespaces Graph of $e^{-x}$}}{56}}
\@writefile{lof}{\contentsline {figure}{\numberline {5.7.2}{\ignorespaces Graph of $\frac  {1}{\sqrt  {1-x^2}}$}}{57}}
\newlabel{example_ex_improper_blowup}{{5.7.2}{57}}
\newlabel{ex:multipleimproper}{{5.7.3}{57}}
\@writefile{lof}{\contentsline {figure}{\numberline {5.7.3}{\ignorespaces Graph of $\qopname  \relax o{tan}^{-1}(x)$}}{58}}
\newlabel{fig:example_atan}{{5.7.3}{58}}
\@writefile{lof}{\contentsline {figure}{\numberline {5.7.4}{\ignorespaces Graph of $\frac  {1}{x-2}$}}{59}}
\newlabel{fig:example_invx2}{{5.7.4}{59}}
\@writefile{toc}{\contentsline {subsection}{\numberline {5.7.1}Convergence, Divergence, and Comparison}{59}}
\newlabel{thm:comparison}{{5.7.8}{60}}
\@writefile{lof}{\contentsline {figure}{\numberline {5.7.5}{\ignorespaces Graph of $\frac  {\qopname  \relax o{cos}(x)^2}{1+x^2}$ and $\frac  {1}{1+x^2}$}}{60}}
\newlabel{fig:example_compare1}{{5.7.5}{60}}
\@writefile{toc}{\contentsline {chapter}{\numberline {6}Sequences and Series}{63}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {6.1}Sequences}{63}}
\newlabel{prop:limserfun}{{6.1.4}{64}}
\@writefile{toc}{\contentsline {section}{\numberline {6.2}Series}{64}}
\newlabel{sec:series}{{6.2}{64}}
\newlabel{ex:geoser}{{6.2.2}{65}}
\@writefile{toc}{\contentsline {section}{\numberline {6.3}The Integral and Comparison Tests}{66}}
\newlabel{eqn:zeta2}{{6.3.1}{66}}
\@writefile{lof}{\contentsline {figure}{\numberline {6.3.1}{\ignorespaces Riemann Zeta Function: $f(x)=\DOTSB \sum@ \slimits@ _{n=1}^{\infty } \frac  {1}{n^x}$}}{67}}
\newlabel{fig:zetareal}{{6.3.1}{67}}
\@writefile{lof}{\contentsline {figure}{\numberline {6.3.2}{\ignorespaces Absolute Value of Riemann Zeta Function}}{68}}
\newlabel{fig:zetaabs}{{6.3.2}{68}}
\newlabel{eqn:harmonic}{{6.3.2}{69}}
\newlabel{thm:inttest}{{6.3.2}{69}}
\newlabel{eqn:inttest}{{6.3.3}{69}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.3.1}Estimating the Sum of a Series}{70}}
\@writefile{toc}{\contentsline {section}{\numberline {6.4}Tests for Convergence}{71}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.1}The Comparison Test}{71}}
\newlabel{thm:compare}{{6.4.1}{71}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.2}Absolute and Conditional Convergence}{72}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.3}The Ratio Test}{72}}
\newlabel{thm:ratiotest}{{6.4.6}{72}}
\newlabel{ex:27n}{{6.4.8}{73}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.4.4}The Root Test}{73}}
\@writefile{toc}{\contentsline {section}{\numberline {6.5}Power Series}{75}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.5.1}Shift the Origin}{76}}
\@writefile{toc}{\contentsline {subsection}{\numberline {6.5.2}Convergence of Power Series}{76}}