%  This is a LaTex file.

%  Homework for the course "Calculus I", 
%  Fall semester, 2021, Wei-Cheng Wang.

% \documentclass[12pt]{article}
% \usepackage{amsmath}
% \usepackage{amsfonts}
% \usepackage{amssymb}
\documentclass[12pt]{article}
\usepackage{amsmath,amsfonts,amssymb,amstext}
\DeclareSymbolFontAlphabet{\Bbb}{AMSb}


%          The page format, somewhat wider and taller page than in art12.sty.

\topmargin  0.1in \headsep 0in \textheight 8.9in \footskip 0.6in
\oddsidemargin 0in  \evensidemargin 0in  \textwidth 6.5in

\def\V{\mathcal V}
\def\L{\mathcal L}
\def\S{\mathcal S}
\def\T{\mathcal T}
\def\U{\mathcal U}
\def\A{\boldmath A}
\def\M{\boldmath M}
\def\l{\mbox{\boldmath $l$}}
\def\r{\mbox{\boldmath $r$}}
\def\v{\mbox{\boldmath $v$}}

%          The page format, somewhat wider and taller page than in art12.sty.

\topmargin -0.1in \headsep 0in \textheight 8.9in \footskip 0.6in
\oddsidemargin 0in  \evensidemargin 0in  \textwidth 6.5in

\begin{document}

%          The title and header.

\noindent
{\scriptsize Calculus I, Fall 2021 
(http://www.math.nthu.edu.tw/\~\,wangwc/)} \hfill 

\begin{center}
\large
Homework Assignment for Week 16   
\normalsize
\end{center}

\vspace{.3in}

%           The questions!

\begin{enumerate}

\item Section 8.2: % Integration by Parts
% 13e some new problems, some changed number.
Problems 5, 11, 15, 23, 25, 27, 29, 33, 35, 43, 45, 51, 63, 71, 75, 76.

\item Section 8.3: % Trigonometric Integrals
Problems 11, 17, 27, 28, 33, 34, 35, 37, 45, 57, 63, 65, 67.

% \item Section 8.3: % Trigonometric Integrals
% Read Examples 4-6.

\item Section 8.3: % Trigonometric Integrals
Derive formula 75 76 of `A brief table of integrals' near the end
of the textbook (take $a=1$ for simplicity).
Then derive similar formula for 
$ \displaystyle{ \int (\tan^m x)( \sec^n x) \ dx } $.

\item Section 8.4: % Trigonometric Substitutions
Problems 3, 5, 13, 23, 35, 37, 45, 47, 48, 54, 57.

%% \item Section 8.5: % Integration of Rational Functions by Partial Fractions
%% % Problems 1, 3, 11, 13, 33, 39, 41, 49.
%% % Homework for next week (these are harder, but you can try first):
%% % Problems 15, 17, 19, 21, 23, 27, 29, 32, 35, 37, 43, 45.
%% Problems 1, 3, 21, 23, 27, 29, 32, %long division 
%% 35, 37, 39, 41, 43, 45, 47, 49.
%% 
%% %% \item Chap 8: % Half-Angle substitution
%% %% Problems 41, 43, 45, 47, 49 (p 512). (p534 in 13e)
%% 
%% \item Chap 8: % Assorted Integrals
%% (Important)
%% As time permits, do as many as you can in odd number
%% problems in 69-113, p 509. % 114-116 = half angle substitution
%% They contain all the integration techniques
%% and you have to figure out which one(s) to use for each problem.

\end{enumerate}

\end{document}