Search

21 Jan 2014: 7. Suppose γ : [a,b] R2 is a smooth curve parametrized by arc length. ... r cos z,r sin z,z).(c) U = (0, 2π) (0, 2π), σ(θ,φ) = ((a b cos φ) cos θ, (a b cos φ) sin θ,b sin φ).

21 Jan 2014: 7. Suppose γ : [a,b] R2 is a smooth curve parametrized by arc length. ... r cos z,r sin z,z).(c) U = (0, 2π) (0, 2π), σ(θ,φ) = ((a b cos φ) cos θ, (a b cos φ) sin θ,b sin φ).

4 Feb 2014: φ(s,v) = α(s) r(n(s) cos v b(s) sin v)where n = n(s) and b = b(s) are the normal and binormal vectors of α. ... 9. Consider a surface of revolution parametrized by φ : (0, 2π) (a,b) R3, whereφ(u,v) = (f(v) cos u,f(v) sin u,g(v)).

20 Oct 2014: 4. Let (fn) be a sequence of real-valued continuous functions on a closed, bounded interval [a,b], and. ... m=1 mam cos mx. (b) Show that f(x) =. m=1 am sin mx defines a continuous function on [π,π], but that the seriesm=1 mam cos mx need