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.


Course Information

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. 

2016 Midterm Exam, Solutions, and Grade Distribution

2016 Final Exam and Solutions



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.)

2014 Midterm Exam and Solutions

2015 Midterm Exam and Solutions

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.


2013 Final Exam and Solutions

2015 Final Exam and Solutions

The final exam was on Thursday, May 5, 2016 from 7 - 10 p.m. in our usual classroom.