Differential Geometry:
Curves and Surfaces in R^3
Math 421, Spring Semester 2016
Physics 259, Mondays and Wednesdays, 1:25 - 2:40 p.m.
Professor
Hubert Bray
bray@math.duke.edu
189
Physics Building
(919)757-8428 (mobile)
Office
Hours: Mondays and Wednesdays, 4:30 - 5:30 p.m.
Announcements
Click on the above
link for course information. Your homework for the semester is
listed below, along with some practice exams which you will want to
study to prepare for the midterm and the final exam.
The final exam will be on Thursday, May 5, 2016 from 7 - 10 p.m. in our usual classroom.
Office hours are on Mondays and Wednesdays, 4:30 - 5:30 p.m. You are also
welcome to stop by my office anytime that I am in, or to make an
appointment.
Homework is due on Wednesdays in class, or by noon Thursday in my
mailbox in the mathematics department mail room (Physics 117). This is
so that you have the option to attend Wednesday office hours before
turning in your homework.
Homework
Homework #1 (due Wednesday, February 3, 2016)
1.1.2
1.1.3
1.1.4
1.1.6
1.1.13
1.1.25
1.1.26
1.1.27
1.2.2
1.2.5
1.3.2
1.3.7
1.3.11
1.3.19
1.3.22
1.3.23
1.3.24
1.3.26
1.3.27
1.3.28
Homework #2 (due Wednesday, February 10, 2016)
1.3.30 (after reading example 1.3.29)
1.4.6 (after reading this section, plugging into the
formulas)
1.4.7
2.1.1
2.1.6
2.1.7
2.1.8
2.1.11 (assuming h(u) and the speed of the curve (g(u),h(u)) are
both not zero)
2.1.12
2.1.13
2.1.15
2.1.16
2.1.19
2.1.20
2.1.21
2.1.22
2.1.23
2.2.5
2.2.6
2.2.7
2.2.9
2.2.11
2.2.14
2.2.15
2.2.16
Homework #3 (due Wednesday, February 17, 2016)
2.3.2
2.3.3
2.3.4
2.3.9
2.3.10
2.3.11
2.4.6
2.4.7
3.1.2
3.1.4
3.1.5
3.1.6
3.1.7
3.1.9
3.1.10
3.1.11
3.2.3
3.2.5
3.2.6
3.2.10
Homework #4 (due Wednesday, February 24, 2016)
3.2.12
3.2.13
3.2.14 (note similarity to previous problem)
3.2.15
3.2.16
3.2.18
3.2.19
3.2.26
3.3.1
3.3.3
3.3.4
3.3.5
3.3.6
3.3.7
3.3.8
3.3.10
3.4.2
3.4.4
3.4.5
3.4.6
Homework #5 (due Wednesday, March 2, 2016)
3.4.8
3.5.1
3.5.8
3.5.9
3.5.10
3.6.3
3.6.4
3.6.5
3.6.6
4.2.3
4.2.4
4.2.5
4.3.2
4.3.5
4.3.6
2013 Midterm Exam
and Solutions (This one is
easier, so you might do it first.)
The midterm was in class on Wednesday, March 9, 2016.
Homework #6 (due Wednesday, March 23, 2016)
Print out your midterm exam and submit solutions to each problem, beautifully written. Obviously
you could just copy the
answer
key. Please do not do this. I want you to truly understand the
solutions. Go through the solutions, spending the time to understand
them carefully, and then write up your version of the solutions as you
understand them, in your own words. Use this as an opportunity to
solidify your knowledge of the first half of the course.
Homework #7 (due Wednesday, March 30, 2016)
4.4.1
4.4.2
4.4.3
5.1.1
5.1.3
5.1.4
5.1.9
5.1.10 (Assume the curvature of the geodesic is never zero.)
5.1.11
5.1.12
5.1.13
5.2.1
5.2.2
5.2.4
5.2.10
5.4.2 (Conformal to the xy plane, so that E = 1/f^2 = G and F = 0.)
5.4.4
5.4.6
5.4.8
5.4.10
Homework #8 (due Wednesday, April 6, 2016)
5.4.11
5.4.14
5.4.15
5.4.19
5.4.20
5.5.6
5.5.7
5.5.10
5.5.12
6.1.1
6.1.2
6.1.4
6.1.5
6.1.9
6.2.1
6.2.2
6.2.3
6.3.1
6.3.3
6.3.4
Homework #9 (due Wednesday, April 13, 2016)
6.3.6
6.3.7
6.3.9
6.3.10
6.3.11
6.3.12
6.3.13
6.5.1
6.5.2
6.5.5
6.5.10
6.6.5
6.6.6
6.6.7
Homework #10 (due Wednesday, April 20, 2016)
Complete the practice final exam from 2013
and turn
in your solutions to be graded, mostly for completion. The solutions
are listed below - only look at them as needed after you've given each
problem a good try.
The final exam was on Thursday, May 5, 2016 from 7 - 10 p.m. in our usual classroom.