1. Typeset a = b c = d e = f g = b h = d k = f. m 1 m 2 r 2. e E

Transcription

1 PHYS 87 Exercises (May, 08):. Typeset a = b c = d e = f g = b h = d k = f. Typeset a = b + c 3. Typeset two of 4. Typeset F = G N m m r 5. Typeset n ± (E, T ) = = e E k B T ± e ω/k BT ± Note: This uses the greek letter \omega and the symbol \hbar. 6. Typeset F µν = [D µ, D ν ] = µ A ν ν A µ = [µ A ν] Note: This uses the greek letters \mu and \nu, and the symbol \partial. 7. Typeset these (the first is inline, the next two are separate displayed equations): Taylor expansion e x = n=0 (This uses the greek letter zeta). 0 n! xn. df dx = f() f(0) dx e ζ(s) = e /ns n=

2 Solutions Exercise : \begin{align*} a&=b & c&=d & e&=f \\ g&=b & h&=d & k&=f \end{align*} Note: the star in align* is used in order to omit equation numbering. Exercise : \item Typeset \[ a^=b^+c^ \bigskip Exercise 3: Use package wasysym for \female, \male, \taurus, amssymb for $\boxminus$, and tipa for \textschwa Exercise 4: \[ F = G_N\frac{m_m_}{r^} \bigskip Exercise 5: \[ n_{\pm}(e,t)=\frac{e^{\frac{e}{k_bt}}\pm} =\frac{e^{{\hbar\omega}/{k_bt}}\pm} \bigskip Exercise 6: \[ F_{\mu\nu} = [D_\mu, D_\nu] =\partial_\mu A_\nu-\partial_\nu A_\mu =\partial_{[\mu} A_{\nu]} Exercise 7: Taylor expansion $e^x=\sum_{n=0}^\infty \frac{n!}x^n$. \[\int_{0}^ \frac{df}{dx}dx= f()-f(0) \[e^{\zeta(s)}=\prod_{n=}^\infty e^{/n^s}

3 Exercises (May 9, 08):. Typeset PHYS 87 F = G N m m r. Typeset n ± (E, T ) = = e E k B T ± e ω/k BT ± Note: This uses the greek letter \omega and the symbol \hbar. 3. Typeset F µν = [D µ, D ν ] = µ A ν ν A µ = [µ A ν] Note: This uses the greek letters \mu and \nu, and the symbol \partial. 4. Typeset these (the first is inline, the next two are separate displayed equations): Taylor expansion e x = n=0 0 n! xn. df dx = f() f(0) dx e ζ(s) = (This uses the greek letter zeta). n= e /ns 5. Typeset these two expressions as separate displayed equations: ( [3 a ( a )] ( z + d + 7 x A n + 3 b + ) )] c n 6. Typeset this, using the multline* environment: ( Make the first entry of Exercise 5 look like this: [3 az ( ) ] ad ) 0 =

4 Solutions Exercise : \[ F = G_N\frac{m_m_}{r^} \bigskip Exercise : \[ n_{\pm}(e,t)=\frac{e^{\frac{e}{k_bt}}\pm} =\frac{e^{{\hbar\omega}/{k_bt}}\pm} \bigskip Exercise 3: \[ F_{\mu\nu} = [D_\mu, D_\nu] =\partial_\mu A_\nu-\partial_\nu A_\mu =\partial_{[\mu} A_{\nu]} Exercise 4: Taylor expansion $e^x=\sum_{n=0}^\infty \frac{n!}x^n$. \[\int_{0}^ \frac{df}{dx}dx= f()-f(0) \[e^{\zeta(s)}=\prod_{n=}^\infty e^{/n^s} Exercise 5: \[ \left[3\frac{a}{z}+\left(\frac{a}{d}+7\right)\right] and \[ \left.x^\left(\sum_na_n+3\left(b+\fracc\right)\right)\right]_0 Exercise 6: \begin{multline*} \left(+\frac+\frac{^}+\frac{^3}+\frac{^4} +\frac{^5}+\frac{^6}+\frac{^7} +\frac{^8}+\frac{^9}\right.\\ \left.+\frac{^{0}}+\frac{^{}}\right)=\frac{4095}{04} \end{multline*} Exercise 7: \[ \Bigg[3\frac{a}{z}+ \bigg(\frac{a}{d}+7\bigg)\bigg]

5 Exercises (May 6, 08):. Typeset: The Pauli matrices are: ( ) ( ) 0 0 i σ =, σ 0 = i 0 ( and σ 3 = 0 ) Note: The blank in the nd entry of the st row of σ 3 is a deliberate typo. Typset this: a b c + d α γ Typeset this: Jersey First Name Last Name 0 Cristiano Ronaldo Didier Drogba 4. Modify the previous table to typeset this: 5. Typeset this: Jersey First Name Last Name 0 Cristiano Ronaldo 0 Edson Arantes do Nascimento (Pele) Didier Drogba Shape Area Perimeter Disk of radius R πr πr Rectangle of sides L and L L L (L + L ) Square of side L = L Right triangle, base b and height h bh b + h + b + h 6. Optional exercise: Typeset this (note the alignment at equal sign) a x + y = 30 b 00 = sin(θ) + cos ϕ c q p = q p

6 Solutions Exercise : The Pauli matrices are: \[\sigma^=\begin{pmatrix}0&\\&0\end{pmatrix},\quad \sigma^=\begin{pmatrix}0&-i\\i&0\end{pmatrix}\quad\text{and}\quad \sigma^3=\begin{pmatrix}&\\0&-\end{pmatrix} Exercise : \[ \begin{array}{ r l } a\times b& c+d\\ \alpha &\gamma\\ 3&. \end{array} Exercise 3: \begin{center} \begin{tabular}{c l l} Jersey & First Name & Last Name \\ 0 & Cristiano & Ronaldo \\ & Didier & Drogba \end{tabular} \end{center} Exercise 4: \begin{center} \begin{tabular}{c l l} Jersey & First Name & Last Name \\ 0 & Cristiano & Ronaldo \\ 0 & Edson & Arantes do Nascimento (Pele)\\ & Didier & Drogba \end{tabular} \end{center} Exercise 5: \begin{center} \begin{tabular}{ p{in} c c } Shape&Area&Perimeter\\ Disk of radius $R$ &$\pi R^$ & $\pi R$\\ Rectangle of sides $L_$ and $L_$ & $L_L_$&$(L_+L_)$\\ \cline{-} Square of side $L_=L_$ & & \\ Right triangle, base $b$ and height $h$ & $\fracbh$&$b+h+\sqrt{b^+h^}$ \end{tabular} \end{center} Exercise 6: \begin{center} \begin{tabular}{ l r@{~$=$~}l } a&$x^+y$&30\\ b&00&$\sin(\theta)+\cos\varphi$\\ c&$q\cup p$&$q \cap p$\\ \end{tabular} \end{center}

7 Exercises (May 3, 08):. Experiments: (a) Paste a lot of text into your document, enough for a couple of pages of typeset material, at least 6 good paragraphs. (Hint: Find one good paragraph, copy it into the buffer, and paste it many times into your document). Then insert your Dream Team Table between paragraphs and 3. Include a caption with a \label{dreamteam} (you provide the text). Insert \ref{dreamteam} somewhere in the text before and again after where you inserted the table. Typeset once with each of positioning b, t and h. (b) Copy the table and caption and paste into the space between paragraphs 4 and 5. Typeset. Check console (warning on repeated labels). Change label of second table: \label{dreamteam}. Insert a few \ref{dreamteam} somewhere in the text before and again after where you inserted the table.. Resize and crop the triton image to get this: 3. Experiment with images just as you did with tables above, and with both tables and figures in the same document. Download additional figures from the web.

8 Solutions Exercise : Make sure you leave a blank line between paragraphs! Exercise : \begin{center} \includegraphics[width=3cm,trim= 7cm 6cm 8cm cm,clip]{gl-5-triton.png}+ \end{center}

9 Exercises (June 6, 08):. Typset the following (note the spacing between text and math expressions and the spacing in the exponent!): We like this:. Typeset this definition: ( ) better than this: ( ) 0 f(x) dx lim t t 0 f(x) dx 3. Typeset this equation: n x /n = ( n x) n = x /n 4. Typeset: a + b = a a + a b + b b

10 Solutions Exercise : \[ \text{we like this:} \quad \left( \frac{}{} \right)^{\!\!\!} \qquad \text{better than this:}\quad \left( \frac{}{} \right)^{} Exercise : \[ \int_0^\infty \!\!\! f(x) \, dx\equiv \lim_{t \to \infty} \int_0^t \!\!\! f(x) \,dx Exercise 3: \[ \sqrt[n] {x^{{/n}}} = (\sqrt[n]{x})^{\frac{}{n}} = x^{/n^} Exercise 4: \[ \vec a +\vec b ^ = \vec a \cdot \vec a+\vec a \cdot \vec b+\vec b \cdot \vec b