Multivariable calculus, class #27: Parameterized curves, and introduction to vector fields

Mathematician spotlight: Rachel Epstein

We look at a curve that lies on a paraboloid, and find its tangent line at a point. We show that if a particle's position and velocity are always perpendicular, it lies on a circle/sphere/etc. We introduce the idea of vector fields, sketch several examples, and discuss the Hairy Ball Theorem and some corollaries.