Curves and Surfaces in R^3

Physics 119, Mondays and Wednesdays, 10:05 - 11:20 a.m.

Professor
Hubert Bray
bray@math.duke.edu

189 Physics Building (919)757-8428 (mobile)

Office Hours: After class, or by appointment

189 Physics Building (919)757-8428 (mobile)

Office Hours: After class, or by appointment

The Midterm will be in class on Wednesday, February 28, 2024.

The Final Exam will be in our usual classroom on Monday, April 29, 2024, from 9 a.m. - 12 noon.

Here are some practice exams (with solutions!) which you will want to study to prepare for the midterm and the final exam. Make sure you are an expert on these exams since problems, solution methods, and key ideas often get repeated

2018 Midterm Exam and Solutions

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

The lectures of this course were recorded in 2018 and may be accessed here.

Homework #0 (due Friday, January 19, 2024)

Watch Lectures 1 and 2. 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, 2024)

Watch Lecture 3 and work these problems:

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, 2024)

Watch Lectures 4 and 5 and work these problems:

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, 2024)

Watch Lectures 6 and 7 and work these problems:

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, 2024)

Watch Lectures 8 and 9 and work these problems:

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, 2024)

Watch Lectures 10, 11, and 12 and work these problems:

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 is in class on Wednesday, February 28, 2024.

Homework #6 (due Friday, March 8, 2024)

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.

(NOTE: Friday, March 15, 2024 is during Spring Break.)

Homework #7 (due Friday, March 22, 2024)

Watch Lectures 13, 14, and 15.

Homework #8 (due Friday, March 29, 2024)

Watch Lectures 16 and 17 and work these problems:

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 #9 (due Friday, April 5, 2024)

Watch Lectures 18 and 19 and work these problems:

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 #10 (due Friday, April 12, 2024)

Watch Lectures 20 and 21 and work these problems:

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

Bonus points: Identify the exercise above which has a sign error in the statement of the problem.

Homework #11 (due Friday, April 19, 2024)

Watch Lecture 22 and 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.

Not tested in course, but you may enjoy: Lectures 23, 24, and 25.

The Final Exam will be on Monday, April 29, 2024 from 9 a.m. - 12 noon in our usual classroom, Physics 119.