You are here: start » courses » home » smfiles » diagnostics

Questions aked in the first two weeks of review, to check students background understanding.

Day 1: Exact differential

The purpose of this question was to see if students understood teh relation between partial derivatives and line integrals. Half of the eighteen students answered this question using the “murder mistery method” from the early paradigms. They typically got the correct answer, apart from trivial errors. Most other students integrated along a path. Half of those did take the correct path, the other half did not think about a path and obtained an asnwer that double counted terms.

Day 2: Chain rule

As it turns out, the two partial derivatives in the question were not consistent. The purpose of this question was to see if students remembered the chain rule, including the minus sign. Half the students remarked about a chain rule, using a division argument, but the minus sign was always forgotten. Some students tried to solve the equations, which can be done, but is much harder.

Day 3: Lagrange multiplier

Nobody remembered what a Lagrange multiplier is.

Day 4: Second law

The goal here is to see if students know the true basis for the second law, as opposed to a statement of probabilities. Some students did not remember, but most wrote down that entropy is a maximum. Nobody recognized that the second law is a thermodynamics principle, and that the maximum entropy is a consequence.

Day 5: "Free" energy

The goal is to see if students know/remember why we have different energies in thermodynamics, or which energy is free. General answer: no idea what is is!

Day 6: Ideal gas

Goal: what connections do students make. Ideal gas is a thermodynamics construct, and free particles are only a model for an ideal gas. Most students mix both. Good opportunity to say a few words about history of science, 200 years ago people were lookign for the ideal hidden by human imperfections.

Day 14: Double sums

Goal: what happens when we have a double sum with two independent dummy indices? Most students knew how to separate them. This was better than I expected, the graduate students often do have a problem here. The second part was changing a series, but most students thought it was an aplication of the first part, and ignored the fact that we now have only one independent index. This was not my intention to test, but the result came as a surprise. I checked quickly in class, and was able to discuss this right away, and students did see where they went wrong.