Midterm solution suggestions. Note that most of the problems can be approached various ways; these are just the approaches that came to mind first.
Instructor: Debra Lewis
Office: 359B Baskin Engineering
Phone: 459-2718
E-mail: lewis at ucsc dot edu
(checked more often than voicemail or gmail)
and/or DebraKLewis at gmail dot com
TIMES AND PLACES
Lecture: MWF 2:00-3:10, 302 JBE
Office hours: Tuesday 6:00-7:00, location 360 JBE, Thursday 2:00-3:10 359B JBE new location!)
Course web page: http://people.ucsc.edu/~lewis/Math121
(here)
Elementary Differential Geometry, Second Edition, by
Barrett O'Neill
VERY TENTATIVE SCHEDULE
| Monday | Wednesday | Friday |
| January 9: tangent vectors, directional derivatives | January 11: curves in three-space | |
| January 14: 1-forms | January 16: differential forms | January 18: mappings |
| January 21: HOLIDAY | January 23: dot product, curves | January 25: Frenet formulas |
| January 28: arbitrary-speed curves | January 30: covariant derivatives | February 1: frame fields |
| February 4: connection forms | February 6: structural equations | February 8: isometries |
| February 11: orientation and Euclidean geometry | February 13: MIDTERM | February 15: congruence of curves |
| February 18: HOLIDAY | February 20: surfaces | February 22: computations on surfaces |
| February 25: functions on surfaces | February 27: differential forms | February 29: differential forms cont. |
| March 3: mappings of surfaces | March 5: the shape operator | March 7: normal curvature |
| March 10: Gaussian curvature | March 13: the fundamental equations | March 15: isometries revisited |
| March 17: Gauss's theorema egregium |
GRADING
Your overall score in the course will be the best of three weighted averages of your homework, midterm, and final exam scores. Your lowest homework score will be dropped. Your participation in the problem-solving sessions will influence your evaluation/grade, but there won't be a numerical score assigned to that component of your performance, or to your final project if you choose to do one.
HOMEWORK POLICIES
Late homework will be discounted and, at the discretion of the grader and/or the instructor, may not be accepted.
Your homework should be neatly written and well-organized, with the pages securely fastened together and your name on every page. Many of the exercises involve several nontrivial steps; make it clear to your readers (and yourself!) what it is you're doing at each step.
Clearly number the exercises and try to submit them in numerical order; if any problems are out of sequence, indicate that at the beginning of the assignment. (You don't need to solve them in order, just submit them in order.) The grader should not have to hunt through several pages to find a particular problem.
Computer difficulties do not justify late or incomplete assignments.