2007 April 20 / E-Mail Me

Math 206, Spring 2007 Schedule

This schedule is under construction; it will be updated as we go along. Unless otherwise noted, the readings and exercises are from Differential Geometry of Curves and Surfaces by Manfredo P. do Carmo.

Lecture	Day	Topic	Reading	Problems	Due Date
1	W	introduction
2	F	parametrized curves, dot product	1.2	#1, 2, 5	19 Jan
3	W	norm, regular curves, arc length	1.3	#4, 6, 10	26 Jan
4	F	cross product, curvature of curves	1.4	#10, 11, 12	26 Jan
5	M	Frenet frame	1.5	#2, 3, 4, 5	26 Jan
6	W	fundamental theorem of curves	1.5	Hmwk3, Lab1	2 Feb
7	F	isoperimetric inequality, calculus of variations	1.7
8	M	Euler-Lagrange equations	Mechanics	Hmwk4	9 Feb
9	W	action principle	Mechanics
10	F	curves as 1-manifolds	2.2
11	M	surfaces	2.2	Hmwk5	16 Feb
12	W	examples	2.2
13	F	inverse/implicit function theorems	2.2
14	M	coordinate changes, functions on surfaces	2.3	Exam1	20 Feb
15	W	Morse theory	Wikipedia
16	F	differentials	2.Appendix
17	M	tangent plane	2.4	Hmwk6	2 Mar
18	W	first fundamental form	2.5
19	F	pulling back inner products, arc length	2.5
20	M	integration, area vs. boundary length	2.5	#15	9 Mar
21	W	Gauss map	3.2	#6, 8	9 Mar
22	F	self-adjoint maps, quadratic forms	3.Appendix	Lab2	9 Mar
23	M	second fundamental form	3.2
24	W	Gauss/mean/normal curvatures	3.3	#6bc, 13	23 Mar
25	F	isometries, conformal maps	4.2	#7, 15, 18	23 Mar
26	M	Christoffel symbols	4.3	#2, 3, 8, and 4.2 #19	30 Mar
27	W	Theorema Egregium, vector fields	4.3	Lab3	30 Mar
28	F	covariant derivative	4.4	#4	30 Mar
29	M	geodesics	4.4	Exam2
30	W	parallel transport, holonomy	4.4
31	F	examples of abstract surfaces	Manifolds
32	M	abstract surfaces, change of coordinates	5.10
33	W	Riemannian surfaces	5.10
34	F	group project work
35	M	hyperbolic plane, non-Euclidean geometry	5.10
36	W	minimal surfaces, soap films	3.5
37	F	harmonic/holomorphic functions	3.5
38	M	geodesic curvature	4.4
39	W	local Gauss-Bonnet theorem	4.5
40	F	Gauss-Bonnet theorem
41	M	student talks
42	W	student talks