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)
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 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 (expressions for the shape operator in the book are off by a sign, for standard U)
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 was in class on Wednesday, February 28, 2018.
Homework #6 (due Friday, March 9, 2018)
Print out a blank midterm exam and submit solutions to each problem, beautifully written on the exam paper. 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.
Spring Break includes Friday, March 16, 2018.
Also no homework due on Friday, March 23, 2018.
Homework #7 (due Friday, March 30, 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
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.