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author | Karl Berry <karl@freefriends.org> | 2014-05-05 22:02:58 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2014-05-05 22:02:58 +0000 |
commit | c2e26b130cd3c16ddba1e50bd65f8ff334ba8acc (patch) | |
tree | b1e3190b569092239516018cca8b73c918accb9f /Master/texmf-dist/doc/latex/exam-n/exam-n-example.tex | |
parent | e6a0a4076d4c6d8eb715a0350a499642c68164df (diff) |
exam-n (5may14)
git-svn-id: svn://tug.org/texlive/trunk@33862 c570f23f-e606-0410-a88d-b1316a301751
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diff --git a/Master/texmf-dist/doc/latex/exam-n/exam-n-example.tex b/Master/texmf-dist/doc/latex/exam-n/exam-n-example.tex new file mode 100644 index 00000000000..396c01ae8f0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/exam-n/exam-n-example.tex @@ -0,0 +1,133 @@ +%% +%% This is file `exam-n-example.tex', +%% generated with the docstrip utility. +%% +%% The original source files were: +%% +%% exam-n.dtx (with options: `example') +%% exam-n: format exam questions +%% Release version 1.1, 2014 May 03. +%% +%%%% File: exam-n.dtx +%%%% Copyright 2005--2014, Norman Gray +%% +%% 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. +%% +%% This work has the LPPL maintenance status `maintained'. +%% +%% The Current Maintainer of this work is Norman Gray <http://nxg.me.uk> +%% +%% This work consists of the files exam-n.dtx and exam-n.ins, +%% the derived file exam-n.cls, +%% and the associated *.clo files. + +%%%% Source: Mercurial revision 6f818b549982, 2014-05-03 13:42 +0100, tag 1.1 + 0 +%% + + +%%%START example (Makefile strips out this block) +\documentclass{exam-n} % standard final version +%%\documentclass[draft,showsolutions]{exam-n} % draft style, showing solutions +%%\documentclass[compose]{exam-n} % compose (author's) style + +\examdate{Wednesday, 18 May 2005} +\examtime{9.30am -- 12 noon\\(or) 9.30am -- 1.45am} + +\exambanner{Examination for the Degrees of \BSc(Science) and + \MSci\ on the Honours Standard} +\schoolcoursecode{P304D and P304H} +\universitycoursecode{PHYS3031 and PHYS4025} +\coursetitle{Quantum Mechanics} +\degreedescriptions{Physics 3\\Chemical Physics 3\\Physics with + Astrophysics 3\\Theoretical Physics 3M\\Joint Physics 3} +\paperident{GR/P304} + +\rubric{Candidates for examination in \emph{Quantum Mechanics} should + answer question 1 (16 marks) and \emph{either 2A or 2B} (24 marks each)} + +\numquestions{3} + +\begin{document} +\maketitle + +\section{I} + +\begin{question}{20} +\part At various points in the development of the mathematical theory of +General Relativity, we pick a coordinate system in which +differentiation is simple, and do a calculation using non-covariant +differentiation, indicated by a comma. We then immediately deduce the +covariant result, replacing this comma with a semicolon. + +Separately, the strong equivalence principle is sometimes +referred to as the `comma goes to semicolon' rule. + +Explain the logic of each of these replacements of a comma with a +semicolon, putting particular stress on the distinction between +them.\partmarks{10} + +\part The radial and angular coordinates, $r$ and $\phi$ respectively, +of a test particle moving in the Schwartzschild metric exterior to a +star of mass $M\ll r$, are related by the equation +\[ + r = \frac{h^2}M \left( + 1 + e\cos\phi + \frac{3M^2}{h^2}e\phi\sin\phi + \right)^{-1}, +\] +where $h$ and $e$ are constants. Show that this equation takes the +form of a precessing ellipse, of semi-latus rectum $l=h^2/M$, in which +the pericentre line advances each orbit by an amount +$\Delta=6\pi M^2/h^2$, stating clearly any assumptions that +you make.\partmarks{6} + +The solar-mass star HD83443 has a 0.35 Jupiter-mass planet that +follows a circular orbit of period 2.986 days and radius 0.038\units\au. +Calculate the rate of precession, in arcseconds per year, of the +pericentre line of the planet's orbit.\partmarks{4} + +[Schwartzschild radius of the Sun${}= 3.0\times10^3\units{m}$, +$1\units\au=1.5\times10^{11}\units m$]. + +\begin{solution} + In the first type of calculation, we do a calculation in the LIF, in +which~$\Gamma^i_{jk}=0$, so that single partial differentiation is the +same as covariant differentiation. If this process produces a +geometrical object such as a scalar or a tensor, then we know that the +result is frame-invariant. If the result involves only single partial +differentiation -- that is, no second derivatives -- then since +partial differentiation is the same as covariant differentiation in +these coordinates, we cannot distinguish partial and covariant +derivatives, and can replace the commas by semicolons. Since these +are now manifestly covariant derivatives, so that the result is a +tensor, and thus frame-invariant, the same expression would be true in +any frame. + +The second situation is the statement that the expressions of physical +laws in SR, such as the conservation equation +$T^{\mu\nu}_{,\nu}=0$, must take the same \emph{form} when written +as a covariant equation in GR, crucially without any curvature +coupling. The slogan `comma goes to semicolon' is just a mnemonic for +this. + +The distinction is that the first is a mathematical trick, of sorts, +whereas the second is a version of the equivalence principle, and thus +a statement with deep physical content. + +They don't have to explain things at this length or with this +coherence (?) to get quite a few marks. They just have to show they +have a clue. +\end{solution} +\end{question} + +\end{document} +%%%END example + +\endinput +%% +%% End of file `exam-n-example.tex'. |