Problem Write-up

Problem write up

The ring of peer feedback

First round

Second person gives feedback to first in each pair

Lucas $\to$ Emma Ben $\to$ Ebtihal Solomon $\to$ Jaime Wes $\to$ Hugh Jen $\to$ Joel Tylor $\to$ [Paul]

Lucas $\to$ [Paul] Emma $\to$ Ben Ebtihal $\to$ Solomon Jaime $\to$ Wes Hugh $\to$ Jen Joel $\to$ Tylor

You will choose one problem to do a more formal write up. The problem should be:

a less-than-trivial problem from the ones at the end of chapters.
Not a problem that was assigned for another purpose.
You must pick your own problem: No two people will work the same problem. You *may* consult other people about your problem. (Give credit, as appropriate.)

Assignment

You'll write up a solution with equations, diagrams as appropriate, and text which explains the approach you took to the problem, and references the physical principles you're using. See notes on Jupyter notebooks under CoCalc. And see below for more tips on LaTeX and using CoCalc.

Like (some) writing assignments from other classes, you'll hand in a first draft of this, and after feedback, a final draft. The rubric used to grade this comprises these categories:

Exposition of the problem - Copy out the statement of the problem. Use a different font to visually distinguish your work from the specification of the problem. Label the problem with chapter and problem number.
Diagrams and plots - Use a diagram to sketch out the physical system if appropriate, and label the names of quantities (angles, coordinates, etc). You may hand draw this! Include plots of functions as appropriate, for example to indicate maxima or minima, or equipotentials, or a potential energy surface, or otherwise enlighten the problem in some way.
Grammar and spelling - Use a more formal voice than when speaking, e.g. "a maxima" not "a max", "substitute in" rather than "plug in". Punctuation in physics papers is a unique issue. You should punctuate equations as if they were any other part of your writing: periods or commas frequently go at the end of a displayed equation.
Correctness of your solution - Gotta make sure you do the problem right! See if you can include some sort of "sanity check" on your results as you go along. For example, an estimation of the answer by some other means.
Clarity of narration - Think of your audience as other students in this class, with some general familiarity with the material.
Many of you probably saw Annalisa Crannell's guide to Writing about Mathematics in Calculus I. Re-read and re-apply her checklist to this writing assignment!
Name the principles and techniques you're using to solve the problem at each section of your problem. You may refer to equations in the textbook. But also, give some context to say where such an equation comes from.
Math typesetting / notation - Use real subscripts (not t0 when you mean $t_0$). Figure out how to get greek letters. Distinguish visually between vector and scalar quantities: scalars are usually displayed as non-bold italic quantities. Using LaTeX will get you this by default in the midst of your markdown. Vector quantities are generally non-italic, and either have a little arrow over them, e.g. $\myv{b}$, or else appear as bold face, e.g. $\bf{b}$. SageMath commands will generally appear as a monospaced font like this "plot( sin(x),......)" without you having to do anything special. When displaying definite integrals, use the ' notation to distinguish between the integration variable and the integration limits, e.g. $$\int_{v_0}^{v(t)} \frac{dv'}{F(v')}.$$ It may be useful to number equations to refer back to them, or put in a hand lettered "star" or other convenient symbol beside one that you wish to refer back to.
Motivation / context - Set the stage for your problem. What is the point of this problem? What larger principle does is illuminate?

Tips on LaTeX

"LaTeX" is a widely used mathematical text processing language. The idea is to have a human-readable way of marking up mathematical expressions, and then some software takes care of the subtle typesetting conventions for laying out math.

You'll be using CoCalc "Jupyter" notebooks for your problem writeups. Jupyter "cells" can contain either code (typically using Sagemath) or "Markdown" text. You can use Markdown for communicating the overall organization of your document: You can specify different heading levels, Format text as code to make it look different, and embed LaTeX commands in your markdown.

Here are some ways to include LaTeX commands in your markdown...

Embed in-line math commands between single dollar signs, e.g. \$\int_a^b f(x)\,dx\$ produces $\int_a^b f(x)\,dx$.
Embed an equation on its own line with double dollar signs. e.g.
\$\$\int_a^b f(x)\,dx\$\$
produces $$\begin{equation*}\int_a^b f(x)\,dx.\end{equation*}$$
Equation numbering is supposed to work like this in $\LaTeX$... You can "tag" an equation with a number or descriptive text. Also include a "label" if you want to refer back to the equation later on. E.g.
```
$$\int_a^b f(x)\,dx.\label{ti}\tag{typical integral}$$
As can be seen from eq ($\ref{ti}$)...
```
$$\int_a^b f(x)\,dx.\label{ti}\tag{typical integral}$$
Workaround: But this has not been working in CoCalc. Here's an alternate way to label some of your equations. Put this LaTeX code inside a Markdown cell:
```
$$ \eta = \frac{W}{Q_2} \hspace{5em}\text{[Eq 1]}$$
$$ dU=\delta Q- \delta W \hspace{5em}\text{[Eq 2]}$$
```
You'll get this output: $$\nonumber \eta = \frac{W}{Q_2} \hspace{5em}\text{[Eq 1]}$$ $$\nonumber dU=\delta Q- \delta W \hspace{5em}\text{[Eq 2]}$$ Explanation: \hspace lets you insert some horizontal space. One 'em' is a typography unit meaning the width of the letter 'm' in the current font.

It might be even clearer to label these particular equations with descriptive names like '[Carnot efficiency]' and '[First law]' instead of numbers.
To embed an image: You can mix HTML in your markdown without needing dollar signs. This is how you display an image with HTML:
<br><img src="mypicture.jpg"><br>
assuming you have previously uploaded the jpg image "mypicture.jpg" into the same folder as your Jupyter notebook. (<br> is a "line break".)