Differential Geometry: 
Curves and Surfaces in R^3

Math 421, Spring Semester 2018
Physics 119, Wednesdays and Fridays, 10:05 - 11:20 a.m.

Professor Hubert Bray                     bray@math.duke.edu  
189 Physics Building                       (919)757-8428 (mobile)

Course Information

Office Hours with Professor Bray:
            Mondays and Wednesdays, 2:15 - 3:15 p.m., or by appointment, in Physics 189

Office Hours with the grader, James Wheeler:
            Wednesdays, 1 - 2 p.m., Physics 274A

Homework is due in class on Fridays, or by 5 p.m. in James Wheeler's mailbox in Physics 139.
Note that the mailroom closes at 5 p.m., so do not be late.


The Midterm will be in class on Wednesday, February 28, 2018.

The Final Exam will be on Tuesday, May 1, 2018 from 2 - 5 p.m. in our usual classroom, Physics 119.


Here are some practice exams which you will want to study to prepare for the midterm and the final exam.

2017 Midterm Exam and Solutions
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)

2017 Final Exam and Solutions
2016 Final Exam and Solutions
2015 Final Exam and Solutions
2013 Final Exam and Solutions

Homework is due on Fridays in class, or in my mailbox by 5 p.m. the same day. Your homework for the semester is listed below:

Homework

A few of the homework problems in the book have typos, sign errors, and other mistakes in them. There are notes below (next to the problem) identifying the errors for you, as well as giving you hints. Extra credit will be awarded for identifying the typos, sign errors, and other mistakes in the homework problems that are not already identified below.

Homework #0
(due Friday, January 19, 2018)
Write a 3 page, double spaced paper on any topic you like relating to either Special Relativity or General Relativity, such as black holes, the Big Bang, or gravitational waves. Bring good questions to class on the previous Wednesday to help you finalize the ideas for your paper.

Homework #1
(due Friday, January 26, 2018)
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 Friday, February 2, 2018)
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 Friday, February 9, 2018)
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 Friday, February 16, 2018)
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 Friday, February 23, 2018)
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 Wednesday, February 28, 2018.

Homework #6 (due Friday, March 9, 2018)
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 Friday, March 23, 2018)
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

No homework due on Friday, March 30, 2018.

Homework #8 (due Friday, April 6, 2018)
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 Friday, April 13, 2018)

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 Friday, April 20, 2018)
Complete the practice final exam from 2013 and turn in your solutions to be graded, mostly for completion. The solutions are listed above - only look at them as needed after you've given each problem a good try.

The Final Exam will be on Tuesday, May 1, 2018 from 2 - 5 p.m. in our usual classroom, Physics 119.