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.

Course Information

Announcements

The Midterm will be in class on Thursday, March 2, 2017. The final exam will be on Saturday, May 6, from 7 - 10 p.m. in our usual classroom. Mark these dates on your calendar now.

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

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 will be 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 4, 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 11, 2017)
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 18, 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.