So, I am planning to cover sequences and series, then multivariable calculus. Probably I will continue on and discuss linear algebra. Differential equations are up in the air.
But I am entertaining the thought to take notes on classical physics. The structure of examples change, and more closely resemble Euclid’s Elements (c.f., Rodin’s “Doing and Showing” arXiv:1109.4298). What do I mean by this?
Well, solving a physics problem consists of four steps:
1. Identify the relevant concepts: Decide which ideas are relevant to the problem. Identify the “Target Variable,” i.e., the quantity whose value we’re trying to find.
2. Set up the problems: If it helps, draw a diagram. Choose the equations from the Identify step.
3. Execute the solutions: First list all the known and unknown quantities, and note which are the target variable (or target variables). Then “do the math”.
4. Evaluate your answer: Ask “Does this solution make sense?” This is tricky, because it requires some intuition. Usually we consider limiting cases.
We shorten these to Identify, Set-Up, Execute, Evaluate.
MIT’s Course 8.01 may be useful, as a reference…