Math 241, Fall 2024, Section 009

Vector Calculus, Math 241

Frank Thorne - Fall 2024

University of South Carolina

Instructor: Frank Thorne, thorne [at] math [dot] sc [dot] edu, LeConte 447

Office Hours: Tue 9:30-11:00 and Wed 3:30-5:00, in LeConte 447.

Classroom: Currell 203, 12:00-12:50 MWF. (Don't go to Hamilton! The class was moved.)

Course objectives/learning outcomes:

Successful students will:

Understand the geometry of 2- and 3-dimensional Euclidean space, and be able to answer questions related to lengths, distances, and related topics.
Understand the concept of a vector, including dot and cross products, be able to explain its relationship to geometry, and work problems involving vectors.
Work problems involving derivatives and integrals in multiple variables.
Work problems involving derivatives and integrals of vector-valued functions.
Practice good mathematical writing. In mathematics, as indeed in everything else, it is important not only to be correct but to explain yourself clearly and as simply as possible.
Gain mathematical maturity, and be prepared to take more advanced math classes if desired.

Text:

Strang, Herman, et al., OpenStax Calculus, Volume 3. View or download it from that link -- freely and legally! Here is a direct PDF link. The book is OER.

A printed copy is not required, but you may buy one from the above link, from the campus bookstore, or from online book sellers. The color version is suggested over the black and white version.

The Thomas book is not required. (It is in most other sections of 241.) If you bought one for this course, please contact the bookstore for a refund.

Written Work:

Exams : There will be two in-class midterms; dates will be announced later in the term, at least a week in advance of the exam. The final exam will be given Monday, December 9, 12:30-3:00 as scheduled by the registrar.

At least half of all exam questions will be taken verbatim from the homework assignments. You should also be prepared for questions that ask you to explain the main concepts of the course and their relation to each other.

Crib sheets will be allowed: a 4-by-6 index card for each midterm, and an 8 1/2-by-11 sheet of paper for the final exam. You may write anything you like on these, front and back, as long as you prepare and handwrite them yourself, and you don't copy from any other student.

Homework : Homework will be assigned approximately weekly. You are not required to turn it in, but:

All quiz questions will be taken verbatim from the homework.
At least half of all exam questions will be taken verbatim from the homework.
If you turn in the homework with the corresponding quiz, then you can make up points lost on the quiz.

Quizzes: Quizzes will be given approximately once a week, and announced at least one class period in advance.

Survey: A survey, separate from the university course evaluations, will be distributed online at the end of the term.

Attendance Verification Quiz: You are also required to fill out an "attendance verification quiz" on Blackboard, by university policy. (Details will be announced.)

Grading:

Please note. You will be graded both on correctness and on quality of exposition. The standard is that someone who doesn't know the answer should be able to easily follow your work. In particular, you should write in complete English sentences and draw clear diagrams where appropriate. Any work that is confusing, ambiguous, or poorly explained will not receive full credit.

Grading scale: You are guaranteed at least the following: A = 88+, B+ = 83+, B = 76+, C+ = 71+, C = 64+, D = 50+.

Please note that my grading scale is more generous than the usual 10-point scale. However, I am a (slightly) stricter grader than most. This is intended to balance out.

Grade component % of grade

Quiz/Homework: 30%

Two midterm exams 20% x 2

Final exam 28%

End-of-class survey: 2%

Course Policies:

Academic honesty is expected of all students. Collaboration on homework is encouraged, but do not copy anyone else's writeup.
Attendance is expected of all students. Roll will not be taken. In case of excused absences, you are welcome to go through formal channels; alternatively, unless you are missing many classes or are asking to make up an exam, an email letting me know the circumstances will suffice.
Makeup quizzes and exams: Quizzes and exams may be made up in case of illness, emergency, or university-sanctioned absence (including religious observances). Barring extremely unusual circumstances, advance notice must be given (in case of university-sanctioned absence, at least a week in advance).
If you have difficulty seeing the board or hearing the lectures, or a related problem, let me know ASAP, and I will do something about it.
Harassment, bullying, racism, sexism, and homophobia will not be tolerated, and flagrant or repeated violations will be reported to the Office of Student Conduct. Please bring any incidents which I don't notice to my attention.
If you require disability-related accommodations, please talk to the Student Disability Resource Center as soon as possible. It is your responsibility to advise me of any needed accomodations a week in advance.
Please contact me if you have any questions about the course, about my expectations, about my lectures, about the homeworks, about the reading, or about anything else. The syllabus is demanding and it is my job to help you succeed. The best ways to get help are to come to office hours (no appointment necessary) or to e-mail me (during the week, I will almost always reply within 24 hours). If neither of these work for you then please e-mail me to set up an appointment.
You can also seek help at the Student Success Center. They offer peer tutoring in the subject matter, and can also give advice on time management and study skills.

Rough Course Schedule:

To be updated as the course progresses. Homeworks and other study materials will also be posted here.

Week 1 (8/21-23): Introduction, Vectors in the Plane (2.1)
Week 2 (8/26-30): Vectors in Space, Dot Products (2.2-2.3)
Homework 1, due Wednesday, September 4: Chapter 2: 1, 7, 10, 11, 13, 25, 26, 45, 46, 62, 63, 66, 70, 73, 86, 94, 99, 103, 126, 135, 136, 143, 145, 155, 167, 170, 171.
Week 3 (9/4-6): Cross Products (2.4)
Week 4 (9/9-13): Equations of Planes and Lines (2.5); Cylindrical Coordinates (2.7)
Homework 2, due Friday, September 13: Chapter 2.4-2.5: 184, 190, 193, 196, 208, 209, 212, 214, 230, 234, 244, 251, 254, 256, 258, 260, 262, 266, 268, 272, 275, 278, 282, 286, 288, 290, 292(a), 299
Week 5 (9/16-20) and 9/23: Vector-Valued Functions (3.1-3.4)
Homework 3, due Wednesday, September 25: (2.7) 364, 370, 372, 374; (3.1) 5, 6, 14; (3.2) 42, 52, 55, 58, 60, 63, 64, 67, 71, 78, 79, 97; (3.3) 102, 104, 115, 121, 127, 129, 130, 132, 135; (3.4) 158, 163, 165, 178, 179, 180, 181, 184.
September 25: Review and Questions.
September 27: Midterm Exam 1. (Postponed to October 2 due to Hurricane Helene; extra review held.)
Week 7 (9/30 and 10/4): Derivatives with Multiple Variables (4.1-4.3)
Weeks 8-9 (10/7-16): More on Derivatives (4.4-4.7)
Homework 4, due Wednesday, October 16: (4.1) 42, 44, 46; (4.3) 120, 121, 125, 135, 137, 150, 159, 160; (4.4) 170-175, 198, 199, 204; (4.5) 221-224, 230, 231, 251, 253-255.
Instructions: For 42, 44, and 46, checking with technology is a good idea but be aware that this won't be available on quizzes or exams. It's up to you to choose values of c to illustrate the behavior of the function. For 221-224, solve by whichever method you like; you don't need to solve twice, using each solution method once.
October 18: Fall Break!
Week 10 (10/21-25): Maxima, Minima, and Optimization (4.7-4.8)
Week 11 (10/28-11/1) and 11/4: Multiple Integration (5.1-5.2)
Homework 5, due Wednesday, October 30: (4.6) 263, 264, 280, 294, 295, 300, 306; (4.7) 318, 319, 322, 332, 344, 346, 348, 349, 350.
November 6: Review and Questions.
Homework 6, due Wednesday, November 6: (4.8) 358, 361, 377, 380, 382, 384, 385, 390; (5.1) 21, 22, 25, 26, 30, 33, 34; (5.2) 80, 81, 83, 96, 97, 98, 100, 101, 102, 108.
November 8: Midterm Exam 2.
Week 13 (11/11-11/15): Polar Coordinates (5.3) and Vector Fields (6.1).
Week 14 (11/18-11/22): Vector Calculus (6.2-)
Homework 7, due Friday, November 22: (5.3) 144, 146, 149, 150, 154, 155, 159, 160, 161; (6.1) 2, 3, 23, 24, and a special exercise , (6.2) 49, 50, 55, 56, 65, 66, 97.
Desmos Vector Field Calculator. Try it out!
November 25-29: Happy Thanksgiving!
Week 15 (12/2-6): Vector Calculus (6.3-6.4) and Review
Homework 8 (optional), due Monday, December 9: (6.3) 106, 107, 112, 130-133; (6.4) 162, 163, 164, 152, 154, 155.
December 9: Final Exam, 12:30-3:00.

The plan is to cover the following chapters from OpenStax:

Vectors In Space (2.1-2.7): 3 weeks
Vector-Valued Functions (3.1-3.4): 2 weeks
Differentiation in Multiple Variables (4.1-4.8): 3 weeks
Integration in Multiple Variables (5.1-5.7): 4 weeks
Vector Calculus (6.1-6.4): 2 weeks

Timing is approximate, and minor changes may be made if necessary. More details will be announced as the course progresses.

Unfortunately we won't have time to cover the following:

Parametric and Polar Coordinates (1.1-1.5): Hopefully this is familiar from previous coursework. We might do a bit of review, if necessary.
More Vector Calculus (6.5-6.8): This is beautiful material, covered in Math 550.
Differential Equations (7.1-7.4): Very important stuff, covered in Math 242 or 520.

Grade component	% of grade
Quiz/Homework:	30%
Two midterm exams	20% x 2
Final exam	28%
End-of-class survey:	2%