Differential Geometry:
Curves and Surfaces in R^3
Math 421, Spring Semester 2017
Physics 259, Tuesdays and Thursdays, 4:40 - 5:55 p.m.
Professor
Hubert Bray
bray@math.duke.edu
189
Physics Building
(919)757-8428 (mobile)
Office
Hours: Tuesdays, 9:45 - 11:45 a.m.
Announcements
The final exam will be on Saturday, May 6, from 7 - 10 p.m. in our usual classroom.
Office hours are on Tuesdays, 9:45 - 11:45 a.m. You are also welcome to
stop by my office anytime that I am in, or to make an appointment.
Homework is due on Tuesdays in class, or in my mailbox by noon the following day. 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.
2016 Midterm Exam and Solutions
2015 Midterm Exam and Solutions
2014 Midterm Exam and Solutions
2013 Midterm Exam and Solutions (easiest one, so you might do it first)
2016 Final Exam and Solutions
2015 Final Exam and Solutions
2013 Final Exam and Solutions
Homework
A few of the
homework problems in the book have typos, sign errors, and other
mistakes in them. In the most extreme cases, there are notes below
(next to the problem) identifying the errors for you.
Extra credit
will be awarded for identifying the typos, sign errors, and other
mistakes in the homework problems that are not already identified
below. I've left a handful of the smaller mistakes unlisted so that you
have to think critically about each problem and look for mistakes in
every problem. If you catch a mistake, attached a separate piece of
paper to the front of your homework identifying the mistake in the
problem for extra credit.
Homework #1 (due Tuesday, January 31, 2017)
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 Tuesday, February 7, 2017)
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 Tuesday, February 14, 2017)
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 Tuesday, February 21, 2017)
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 Tuesday, February 28, 2017)
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
The Midterm was in class on Thursday, March 2, 2017.
Homework #6 (due Tuesday, March 21, 2017)
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 Tuesday, March 28, 2017)
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 Tuesday, April 11, 2017)
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 Tuesday, April 18, 2017)
Bonus points: Identify the exercise below which has a sign error in the statement of the problem.
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 Tuesday, April 25, 2017)
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.