Let M be the subset of R3 given by {(x, y,z) | x 2 + y2 6 z 4 x 2 y2}. Then M may be parametrized as a 3-manifold via X: DR3; X(u1, u2, u3)=(u1 cos u2, u1 sin u2, u3), where D = {(u1, u2, u3) R3 | 0 u1 5, 0 u2 < 2, u2 1 6 u3 4 u2 1}. (The parameters u1, u2, and u3 correspond, respectively, to the cylindrical coordinatesr, , and z. Hence, it is straightforward to obtain the aforementioned parametrization.) (a) Orient M by using the 3-form , where X(u)(a, b, c) = det abc . Show that the parametrization, when smooth, is compatible with this orientation. (b) Identify M and parametrize it as a union of two 2-manifolds (i.e., as a piecewise smooth surface). (c) Describe the outward-pointing unit vector V, varying continuously along each smooth piece of M, that is normal to M. Give formulas for it in terms of the parametrizations used in part (b).

Kyla Brinkley JOUR 3190 Spring 2015 Chapter 11 Notes Social Media and Journalism I. Introduction II. Changing Journalismâ€™s Formula a. Digital publishing changed the underpinnings of journalism b. Social media has changed its practice c. Originally journalism had a lot of flaws because of interviewed people having faulty memories, things are embellished, quotes may be altered d. Telephone made getting first word out easier and quicker e. Broadcasting and 24-hour cable news channels sped up the news cycle further f. With social media, the journalist is increasingly not the first witness to history g. Blogger or tweeter is just as likely to be an accidental witnes