Updated Rubric for Worked Problems and Projects#
19 Oct 2023
Choosing and Explaining an Appropriate Problem (30%)#
30 points total - An appropriate problem is often one one on the border of analytical and numerical methods (or one that can be simplified or extended to be either). If you can solve it completely analytically, then consider how it can be extended for a computing activity. If you have questions or thoughts, please ask Danny, Alia, or Ian.
15 pts - Identify a physical system that you are interested in investigating, Describe the physical system in terms of the relevant physics principles and the model that is being used, Explain and justify assumptions or approximations that are made in the model. (e.g., Think the small angle approximation being removed for a pendulum, the numerical results will differ from the analytical ones, but you can still use the small angle approximation to get close)
15 pts - Create a plan / describe a method that you will be using to solve the problem analytically and numerically (usually one from a recent class period); describe how the method works and why it is necessary compared to solving analytically, or why it is no longer trivially solved analytically (e.g, some expressions get very messy analytically, n-body problems, analytically possible but approximations can be made that make the problem easier).
Writing a Jupyter Notebook Analysis (50%)#
50 points total - It is important that all the analysis appears in a single narrative document. You are explaining an analysis in a way that other people are meant to understand. It is important to be clear and transparent. It is less important to be correct. Why? Because getting an analysis correct the first time is unlikely, but a clear and transparent analysis let’s us find where those issues lie, diagnose them, and correct our science.
30 pts - The notebook runs and does what you say it is doing. It should be relevant to the work we’ve done in class and make use of those tools and methods. It should provide evidence in the form of figures, equations (scanned from paper is ok), and graphs to clear statements of fact or claims about the system. Use these mathematical, computational, and graphical tools (from class) to provide evidence for the investigations you propose.
To get full credit here, you need to provide sufficient evidence for each step of the investigation; don’t skip challenging parts of derivations or explanations, make your best attempt or ask for help; provide properly documented and cited work, especially for code, derivations, and figures.
20 pts - The notebook and analysis is described thoroughly enough to be understood by someone who is looking to learn from this problem, think someone starting this class (e.g., support them with comments, explanations, and necessary derivations; really emphasizing the reproducible process).
Documenting the Analytical Process (20%)#
20 points total - You conduct the analysis for a reason, you are answering a question. How you present and discuss that analysis is important and is related to the evidence you generated through making models of the system. Think about your graphs, and figures; these lead to predictions and explanations you can make. Present a clear analysis for a particular question (or set of questions) you have formed. This can be done by:
comparing numerical and prior analytical results at boundaries and other limits in a thoughtful manner, and/or
analyzing and interpreting your results in a sufficient manner using plots, models, or simulations.
Just showing plots or stating what is on the plot will not receive full credit. There should be a comparison back to previous models/analytical results and describes implications of said results. We can help with that; these systems can be rich and complex. For example, in an analysis of a pendulum, you might consider these two statements about the same plot that as made.
“These are plots of theta vs time.”
“These plots show a pendulum with and without the small angle approximation, The numerical plot without the small angle approximation shows deviation from the purely harmonic motion and has an effective period of 2s compared to 1.5s.”
The second statement is more informative, definitive, and grounded in the analysis that was completed.
Sample Worked Problems#
A few students were generous in sharing their worked problems as samples. These earned high marks but not the same marks. They are meant to be examples of what a good analysis looks like. They are all a bit different.