MATH 113, FALL 2012
HOMEWORK 1
1. Let : I R3 (where I R is an interval) be a parametrized curve and let v R3 be a xed
vector. Assume that (t) is orthogonal to v for all t I and that (0) is also orthog
MATH 113, FALL 2012
HOMEWORK 2, DUE SEPTEMBER 13
1. Let f : R2 R be a C 1 function (i.e., f has continuous partial derivatives) such that the
gradient f (p) of f is nonzero for every p R2 .
(a) Show t
MATH 113, FALL 2012
HOMEWORK 6, DUE NOVEMBER 20
1. Exercise 8.1.9 from Pressley
2. Exercise 8.2.2 from Pressley
3. Show that at the origin of the hyperboloid z = axy we have K = a2 and H = 0.
4. Show
MATH 113, FALL 2012
HOMEWORK 4, DUE OCTOBER 18
1. Exercise 4.1.2 from Pressley.
2. Show that the antipodal map A : S 2 S 2 of the unit sphere S 2 dened by
A(x, y, z ) = (x, y, z )
is a dieomorphism.
3
MATH 113, FALL 2012
HOMEWORK 5, DUE NOVEMBER 1
1. Exercise 6.1.1 from Pressley
2. Exercise 6.1.3 from Pressley
3. Exercise 6.1.4 from Pressley
4. Let S be a surface of revolution with axis of revoluti
MATH 113, FALL 2012
HOMEWORK 3, DUE SEPTEMBER 27
1. Let : I R3 be a smooth curve parametrized by arc-length whose curvature is always
positive. Let (s) = (x(s), y(s), z(s). Suppose that 0 I, (0) = (0,
INTRODUCTION
FIELD colors TYPIEALLY focus on ora and fauna of the natural
world, assisting readers in identifying animals and owers, suggesting
how and where to nd them, and elaborating on what exactl