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.
1Wintroduction
2Fparametrized curves, dot product1.2#1, 2, 519 Jan
3Wnorm, regular curves, arc length1.3#4, 6, 1026 Jan
4Fcross product, curvature of curves1.4#10, 11, 1226 Jan
5MFrenet frame1.5#2, 3, 4, 526 Jan
6Wfundamental theorem of curves1.5Hmwk3, Lab12 Feb
7Fisoperimetric inequality, calculus of variations1.7
8MEuler-Lagrange equationsMechanicsHmwk49 Feb
9Waction principleMechanics
10Fcurves as 1-manifolds2.2
11Msurfaces2.2Hmwk516 Feb
12Wexamples2.2
13Finverse/implicit function theorems2.2
14Mcoordinate changes, functions on surfaces2.3Exam120 Feb
15WMorse theoryWikipedia
16Fdifferentials2.Appendix
17Mtangent plane2.4Hmwk62 Mar
18Wfirst fundamental form2.5
19Fpulling back inner products, arc length2.5
20Mintegration, area vs. boundary length2.5#159 Mar
21WGauss map3.2#6, 89 Mar
23Msecond fundamental form3.2
24WGauss/mean/normal curvatures3.3#6bc, 1323 Mar
25Fisometries, conformal maps4.2#7, 15, 1823 Mar
26MChristoffel symbols4.3#2, 3, 8, and 4.2 #1930 Mar
27WTheorema Egregium, vector fields4.3Lab330 Mar
28Fcovariant derivative4.4#430 Mar
29Mgeodesics4.4Exam2
30Wparallel transport, holonomy4.4
31Fexamples of abstract surfacesManifolds
32Mabstract surfaces, change of coordinates5.10
33WRiemannian surfaces5.10
34Fgroup project work
35Mhyperbolic plane, non-Euclidean geometry5.10
36Wminimal surfaces, soap films3.5
37Fharmonic/holomorphic functions3.5
38Mgeodesic curvature4.4
39Wlocal Gauss-Bonnet theorem4.5
40FGauss-Bonnet theorem
41Mstudent talks
42Wstudent talks