Math 150A — Prof. Rabin — Fall 2015 — Homework Assignments

Problems identified simply by numbers, e.g. 2.4.7, come from the course textbook Differential Geometry and Its Applications, 2nd edition, by John Oprea. Note that they are scattered throughout the text rather than collected at the end of each section or chapter. Assignment 0, discussed but not turned in on October 5: see separate document on website. Assignment 1, due Tuesday, October 13 by 5 PM: 1.1.17, 1.1.25, 1.2.7, 1.2.8, 1.3.12, 1.3.22, 1.3.27, 1.3.28. Problem 1.1.25 refers to “The Mystery Curve” given just above it. In problem 1.2.7, the “some point” where the end of the string is attached to the curve should be the same as the “some fixed point” from which arclength is measured, say t=0 in both cases. In problem 1.3.12 think of a small rectangular brick moving along the curve so that its three orthogonal axes are always aligned with the three orthogonal vectors T, N, B. It will have to rotate as it moves, and physicists describe this rotation by an angular velocity vector ω with the properties specified in the problem.