Differential Geometry (math 121A) Winter qtr 2009.

SYLLABUS

Lecture and reading schedule
HWs
HW for 3rd week. Due Thurs Jan 29: sec 3.2: 7, **9. sec 3.3: *1, 7, 19, 20
** HW due Feb 19 !! **


HW for Feb 26: from the Do Carmo text, ch 4.3 (p 237), problems: 2!, 3, 8!, 9. Extra Credit, 4 .

HW for Mar 5. Part A [10 pts] from text: p. 262-3 (sec. 4-4; parallel transp and geod.) 18! , 20 [for 10 pts]
Part B [10 pts] STATE (don't solve) a good problem around geodesics, space curves, surfaces of revolution, or Gauss-Bonnet.
(The problem you state may be used on the final.) ;
OR write a clear succinct question consisting of about a paragraph regarding one of these topics, or any other topic from class that has been bothering you.
*****************************************************************
last week of class

**** !! Mock Final ; REVISED VERSION (!) ! * ! ( preliminary version ) POSTED NOW !

HW for Mar 12. Ghomi, ch. 16. - some subset of these 11 problems. I recommend you do them all!

READING for remainder of class. On area: sec. 2-8. Gauss-Bonnet: sec. 4-5.
Gauss-Bonnet lecture (Montgomery)
Background to pf of G-B: forms; Stokes
On geodesic curvature (Ghomi ch. 15) .


REMAINING class lecture schedule:
** Mar 3. Clairut. Statement of Gauss-Bonnet. Some of Ghomi HW (see below)
** Mar 5. Understanding each term of Gauss-Bonnet. Start Pf via differential forms (a la Chern). Cte looking into HW for next week.
** Mar 10. Pf Gauss-Bonnet.
** Mar 12. HW due on Gauss-Bonnet. Some final review.
AND final review I.

HW SOLUTION NOTES relevant to Feb 19 and 26 HWs
feb 26: Deriving the Christoffel symbols using the Euler-Lagrange eqns
- application to finding the Christoffel symbols in the case of polar coordinates for the plane
feb 19 finding the curv. and tors. of the twisted cubic


****OLD STUFF *** Mock Midterm

Mid term solutions

Midterm solutions ct'd.


Ghomi lect notes --