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author | Karl Berry <karl@freefriends.org> | 2019-01-16 22:21:34 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2019-01-16 22:21:34 +0000 |
commit | 4c9243ad0db2bdfec525be1892bc99408683597c (patch) | |
tree | b11838764bf08603b98b25162661754d2b68dd57 /Master/texmf-dist/doc | |
parent | f8c4f57df57c19c548d40d4a5a907b7577d72bac (diff) |
exframe (16jan19)
git-svn-id: svn://tug.org/texlive/trunk@49727 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc')
-rw-r--r-- | Master/texmf-dist/doc/latex/exframe/README.txt | 38 | ||||
-rw-r--r-- | Master/texmf-dist/doc/latex/exframe/exframe.pdf | bin | 0 -> 346156 bytes | |||
-rw-r--r-- | Master/texmf-dist/doc/latex/exframe/exfsmp1.tex | 211 |
3 files changed, 249 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/exframe/README.txt b/Master/texmf-dist/doc/latex/exframe/README.txt new file mode 100644 index 00000000000..3db12e1f300 --- /dev/null +++ b/Master/texmf-dist/doc/latex/exframe/README.txt @@ -0,0 +1,38 @@ +exframe v3.0 +Copyright 2011-2019 Niklas Beisert + +exframe is a LaTeX2e package which provides a general purpose +framework to describe and typeset exercises and exam questions +along with their solutions. The package features mechanisms to +hide or postpone solutions, to assign and handle points, to +collect problems on exercise sheets, to store and use metadata +and to implement a consistent numbering. It also provides a +very flexible interface for configuring and customising the +formatting, layout and representation of the exercise content. + +The package consists of the files + + README.txt readme file + exframe.ins installation file + exframe.dtx source file + exframe.sty package file + exfsmp1.tex sample latex file + exframe.pdf manual + +The distribution consists of the files +README.txt, exframe.ins and exframe.dtx. + +Run "(pdf)latex exframe.dtx" to compile the manual exframe.pdf. + +Run "latex exframe.ins" to create the package exframe.sty +and the sample exfsmp1.tex. +Copy the file exframe.sty to an appropriate directory of your LaTeX +distribution, e.g. texmf-root/tex/latex/exframe. + +This work may be distributed and/or modified under the +conditions of the LaTeX Project Public License, either version 1.3 +of this license or (at your option) any later version. +The latest version of this license is in + http://www.latex-project.org/lppl.txt +and version 1.3 or later is part of all distributions of LaTeX +version 2005/12/01 or later. diff --git a/Master/texmf-dist/doc/latex/exframe/exframe.pdf b/Master/texmf-dist/doc/latex/exframe/exframe.pdf Binary files differnew file mode 100644 index 00000000000..9da7188b572 --- /dev/null +++ b/Master/texmf-dist/doc/latex/exframe/exframe.pdf diff --git a/Master/texmf-dist/doc/latex/exframe/exfsmp1.tex b/Master/texmf-dist/doc/latex/exframe/exfsmp1.tex new file mode 100644 index 00000000000..7326930d603 --- /dev/null +++ b/Master/texmf-dist/doc/latex/exframe/exfsmp1.tex @@ -0,0 +1,211 @@ +%% +%% This is file `exfsmp1.tex', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% exframe.dtx (with options: `sample1') +%% +%% Copyright (C) 2011-2019 Niklas Beisert +%% +%% This work may be distributed and/or modified under the +%% conditions of the LaTeX Project Public License, either version 1.3 +%% of this license or (at your option) any later version. +%% The latest version of this license is in +%% http://www.latex-project.org/lppl.txt +%% and version 1.3 or later is part of all distributions of LaTeX +%% version 2005/12/01 or later. +%% +\NeedsTeXFormat{LaTeX2e}[1996/12/01] +\ProvidesFile{exfsmp1.tex}[2019/01/16 v3.0 sample 1 for exframe] +\documentclass[12pt]{article} + +\usepackage{geometry} +\geometry{layout=a4paper} +\geometry{paper=a4paper} +\geometry{margin=2.5cm} +\parindent0pt +\parskip0.5ex + +\usepackage{amsmath} +\usepackage{hyperref} +\usepackage[extstyle]{exframe} + +\exercisesetup{solutions=true} +%%\exercisesetup{solutions=false} + +\exercisestyle{plainheader} +\exerciseconfig{composeheaderbelowright}{\getsheetdata{points}}% + +\exerciseconfig{countersheet}{\Roman{sheet}} +\exerciseconfig{countersubproblem}{\roman{subproblem})} +\exerciseconfig{countersubproblemmax}{vii)} + +\exerciseconfig{termsheet}{\"Ubungsblatt} +\exerciseconfig{termsheets}{\"Ubungsbl\"atter} + +\exercisestyle{pointsat=margin} +\reversemarginpar +\exerciseconfig{composepointsmargin}[1]{#1p.} + +\exerciseconfig{styletitle}{\sffamily\bfseries} + +\exerciseconfig{skipproblembelow}{1.5cm} + +\exercisestyle{fracpoints} +\exercisestyle{solutionbelow=problem} +\exercisestyle{solutionsep} + +\exerciseconfig{composemetasheet}[2]{\getexercisedata{course}, + \exerciseifempty{#2}{\getexerciseconfig{termsheet} #1}{#2}} + +\exercisesetup{pdfdata=sheet} +\exercisedata{title=% + {\getexercisedata{course}, \getexercisedata{material}}} +\exercisedata{author=% + {\getexercisedata{instructor}, \getexercisedata{institution}}} + +\exercisedata{institution={Katharinen-Volksschule}} +\exercisedata{course={Mathematik}} +\exercisedata{instructor={J.\ G.\ B\"uttner}} +\exercisedata{period={ca.\ 1786}} +\exercisedata{material={\"Ubungsaufgaben}} + +\begin{document} + +\begin{sheet}[number=5] + +\begin{problem}[title={Sums}] + +This problem deals with sums and series. + +\begin{subproblem}[points=2,difficulty=simple,label={\problemtag-simplesum}] +Compute the sum +\showpoints +\begin{equation} +1+2+3. +\end{equation} + +\begin{solution} +The result is +\begin{equation} +1+2+3=6. +\end{equation} +\end{solution} + +\end{subproblem} + +\begin{subproblem}[points=97,difficulty=lengthy] +Compute the sum +\begin{equation} +1+2+3+\ldots+98+99+100. +\end{equation} +Keep calm and calculate! +%%That ought to keep him occupied for a while +\end{subproblem} + +\begin{solution}[author={C.\ F.\ Gau\ss}] +We use the result $1+2+3=6$ from part \ref{\problemtag-simplesum} +to jumpstart the calculation. The remaining sums yield +\awardpoints[1 for each remaining sum]{97} +\begin{equation} +6+4+5+\ldots+99+100=5050. +\end{equation} +Alternatively the summands can be grouped into pairs as follows: +\begin{align} +1+100&=101,\\ +2+99&=101,\\ +3+98&=101,\\ +\ldots &\nonumber\\ +50+51&=101. +\end{align} +These amount to 50 times the same number 101. +Therefore the sum equals +\begin{equation} +1+2+\ldots+99+100=50\cdot 101=5050. +\end{equation} +\textit{Ligget se!} \awardpoints*{97} +\end{solution} + +You may give the final part a try: + +\begin{subproblem}[optional={optional}, difficulty={requires inspiration}] +Compute the series +\begin{equation} +1+2+3+\ldots +\end{equation} + +\begin{solution} +The series is divergent, so the result is $\infty$ \awardpoints*{1}. +\par +However, after subtracting the divergent part, +the result clearly is +\begin{equation} +\zeta(-1)=-\frac{1}{12}\,, +\end{equation} +where the zeta-function $\zeta(s)$ is defined by +\begin{equation} +\zeta(s):=\sum_{k=1}^\infty \frac{1}{k^s}\,. +\end{equation} +This definition holds only for $s>1$ where the sum is convergent, +but one can continue the complex analytic function to $s<0$ +\awardpoints*{1.5}. +\par +Another way of understanding the result +is to use the indefinite summation formula +for arbitrary exponent $s$ in the summand +(which also follows from the Euler--MacLaurin formula) +\begin{equation} +\sum_n n^s += \frac{n^{s+1}}{s+1} + -\sum_{j=0}^s \frac{\zeta(j-s)\,s!}{(s-j)!\,j!}\,n^j += \ldots - \zeta(-s)\,n^0. +\end{equation} +Curiously, the constant term with $j=0$ is just the desired result +but with the wrong sign +(in fact, the constant term of an indefinite sum is ambiguous; +for the claim we merely set $j=0$ +in the expression which holds for others values of $j$) +\awardpoints*{0.5}. +In order to understand the sign, +we propose that the above formula describes the regularised result +for the sum with limits $+\infty$ and $n$ +\begin{equation} +\sum_{k=+\infty}^n k^s +\simeq \frac{n^{s+1}}{s+1} + -\sum_{j=0}^s \frac{\zeta(j-s)\,s!}{(s-j)!\,j!}\,n^j. +\end{equation} +Then we flip the summation limits of the desired sum +to bring it into the above form +\awardpoints*{0.5} +\begin{equation} +\sum_{k=1}^\infty k^s += -\sum_{k=\infty}^0 k^s +\simeq \zeta(-s). +\end{equation} +\end{solution} + +\end{subproblem} + +\end{problem} + +\begin{problem}[points=1, difficulty=insane] +Show that the equation +\begin{equation} +a^3+b^3=c^3 +\end{equation} +has no positive integer solutions. +\end{problem} + +\begin{solution} +\normalmarginpar +This is beyond the scope of this example. +\marginpar{\footnotesize\raggedright does not fit here.\par} +\end{solution} + +\end{sheet} + +\end{document} +\endinput +%% +%% End of file `exfsmp1.tex'. |