Homework 4
Math 352, Fall 2011
A
Instructions: Solve all three of these problems. Your solutions must be written in L TEX.
Due Date: Friday, October 21
1. Let S 2 be the unit sphere in R3 . Given a point (u, v) R2 , let L be the line through
(u, v, 0) and
Types of Maps
Outline
1. Orientation-Preserving Maps
A linear transformation T : Rn Rn is called orientation-preserving if it satises any one
of the following equivalent conditions:
The n n matrix for T has positive determinant.
The vectors cfw_T (e1 ),
Homework 7
Math 352, Fall 2011
A
Instructions: Solve all ve of these problems. Your solutions must be written in L TEX.
Due Date: Wednesday, November 23
1. Let U = (0, ) (0, 2). Let C be the catenoid r = cosh z, and let : U C be the
surface patch
(u, v) =