PHYS 87. Don t expect to go through all of these today. Will continue next week. 1. Typeset a = b c = d e = f g = b h = d k = f. m 1 m 2 r 2.

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1 Exercises (May 7, 07): PHYS 87 Don t expect to go through all of these today. Will continue next week.. Typeset a = b c = d e = f g = b h = d k = f. Typeset a = b + c 3. Typeset two of these:,,, 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 this (the first is inline, the next two are separate displayed equations): Taylor expansion e x = 0 n=0 (This uses the greek letter zeta). n! xn. df dx = f() f(0) dx e ζ(s) = n= e /ns

2 Solutions Exercise : \begin{align*} a&=b & c&=d & e&=f \\ g&=b & h&=d & k&=f \end{align*} Exercise : \item Typeset \[ a^=b^+c^ Exercise 3: \female, \male, \taurus, $\boxminus$ Make sure packages wasysym and amssymb are loaded! Exercise 4: \[ F = G_N\frac{m_m_}{r^} Exercise 5: \[ n_{\pm}(e,t)=\frac{e^{\frac{e}{k_bt}}\pm} =\frac{e^{{\hbar\omega}/{k_bt}}\pm} 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 PHYS 87 Exercises (May 4, 07): Don t expect to go through all of these today. Will continue next week.. Typeset 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 this (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 0

4 Solutions Exercise : \[ F = G_N\frac{m_m_}{r^} Exercise : \[ n_{\pm}(e,t)=\frac{e^{\frac{e}{k_bt}}\pm} =\frac{e^{{\hbar\omega}/{k_bt}}\pm} 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] \[ \left.x^\left(\sum_na_n+3\left(b+\fracc\right)\right)\right]_0

5 Exercises (May 3, 07):. Typeset this, using the multline* environment: ( We previously had \[ \left[3\frac{a}{z}+ \left(\frac{a}{d}+7\right)\right] ) = giving Make it look like this: [3 a ( a )] z + d + 7 [3 az + ( ad + 7 ) ] 3. 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 4. Typeset this: 5. Typeset this: Jersey First Name Last Name 0 Cristiano Ronaldo Didier Drogba 0 Edson Arantes do Nascimento (Pele) 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 Solutions Exercise : \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 : \[ \Bigg[3\frac{a}{z}+ \bigg(\frac{a}{d}+7\bigg)\bigg] Exercise 3: 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 4: \begin{center} \begin{tabular}{c l l} Jersey & First Name & Last Name \\ 0 & Cristiano & Ronaldo \\ & Didier & Drogba\\ 0 & Edson & Arantes do Nascimento (Pele) \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}

7 Exercises (June 7, 07):. Typeset this: Jersey First Name Last Name 0 Cristiano Ronaldo Didier Drogba 0 Edson Arantes do Nascimento (Pele). Experiment with table environment: (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. (b) Typeset once with each of positioning b, t and h. (c) 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. 3. Find a triton on google images; then resize and crop it to get this:

8 Solutions Exercise : \begin{center} \begin{tabular}{c l l} Jersey & First Name & Last Name \\ 0 & Cristiano & Ronaldo \\ & Didier & Drogba\\ 0 & Edson & Arantes do Nascimento (Pele) \end{tabular} \end{center} Exercise : \includegraphics[width=4cm,trim= 7cm 6cm 8cm cm,clip]{gl-5-triton.png}