Homework 1, due Friday April 14: 2.1.24, 2.1.25, 2.1.26, 2.2.8, 2.4.6, 2.4.7, 2.4.9, 3.2.15, 3.2.16 (in 2.1.26 assume that delta has length 1 again).
Homework 2, due Friday April 21: 5.1.12, 5.1.13, 5.2.1, 5.2.2, 5.2.4, 5.2.11, 5.2.12, 5.2.13, 5.2.14.
Homework 3, due Friday May 5: 3.2.18, 3.2.22 (do not graph the surface), 3.2.23, 5.3.3, and
Exercises 2,3,4 from here, and
(1) Prove that the differential of a differentiable map of
surfaces is linear at every point.
(2) Prove that the composition of two differentiable maps F and G is
differentiable and compute its differential in terms of those of
F and G. What does this tell you about the differential of the
inverse of a differentiable map (when it exists)?
Homework 4, due Friday May 12: Oprea: 5.4.19, 5.4.20
O'Neill: Chapter 1 Section 5 #7, Section 6 #3, 5, 7, 8, 9, Chapter
7 Section 1 #4, 5
Homework 5, due Friday May 19: O'Neill: Chapter 1 Section 5 #10, Chapter 2 Section 7 #1, 2, 3, 4, Section 8 #1, 4, Chapter 4 Section 4 #4
Homework 6, due Friday June 2: O'Neill: Chapter 2 Section 8 #3, Chapter 4 Section 4 #5, Chapter 5 Section 6 #7, Chapter 6 Section 1 #1, 2, 3, Section 2 #1, 2
Homework 7, due Friday June 9: O'Neill: Chapter 7 Section 1 #1, 3, Section 2 #2, 9, 10, Section 3 #2, 5, 6