Summer of Math Exposition

The explanation was generally easy to follow, but I think that it could’ve been improved by having a motivating example at the start and also explaining some of the algebra steps along the way. NIT: note η(A) = η(B) = 0, is this supposed to be \eta(0) = \eta(1) = 0 since the function takes in t-values not raw points?

Motivation - It’s not clear to me what the motivation is for this, aside from a study guide or reference sheet. More discussion about the equations or worked out examples could be provided to motivate someone to read through the document.

Clarity - There is little explanation aside from listing the formulas and variables. I’m not sure what the goal of this document is, the organization and presentation does not make it easy to read. It does not look like much time was spent on clarity, novelty, or memorability.

Calculus of variations is one of those things which I wish was talked about more in “regular” calculus classes because it’s one of those great conceptual settings that drove a lot of calculus’s development and solves all sorts of cool problems. So I am glad that there are things out there. That said, though, this could be a lot better organized with motivation moved up sooner (you mention, for example, “it is used in physics”), and perhaps a more worked out example to show its connection to more special cases. Like, for example, Newton’s 2nd Law for a single particle easily admits this formulation. That sort of context makes it easier to take in. Generally speaking Euler-Lagrange equations are one of my favorite topics, precisely because it can allow us to represent physical systems more like evolution in some kind of state space geometry. It’s really useful for modeling purposes to think of “space like things but not exactly space” and then putting some Lagrangians onto them. Having, say, an introduction that speaks of this type of modeling would be quite an improvement.