Kunkle's Syllabus, MATH 221, Spring 2022
last change: April 25, 2022

MATH 221 (Calculus III) Spring 2022

Section: 22862 - MATH 221 - 01
10:00 am - 10:50 am MWF MAYBANK HALL 117
10:50 am - 12:05 pm R MAYBANK HALL 112
Prerequisite(s): MATH 220
Instructor, Contact info: Tom Kunkle, 327 RS Small, k u n k l e t _at_ c o f c _dot_ e d u, 953-5921 (office), 766-0943 (home).
Instructor's Office Hours: M 9:00-9:50am, W 2:00-3:00pm, Th 1:45-2:45pm, F 12:00-12:50pm, or by appointment.
I'm happy to meet at other times that fit your schedule, if I'm available. Here's what my typical week looks like.

Here are my office hours for finals week this semester. If you'd like to see me but can't make these times, please ask for an appointment.

Tue Apr 26, 9:00-10:30, 12:00-1:50, 3:00-4:00
Wed Apr 27, 9:00-12:00, 3:00-4:00
Thu Apr 28, 9:00-11:00, 12:30-4:00
Fri Apr 29, 9:00-4:00
Sat Apr 30, 8:00-10:00 (possibly on Zoom)

Math Lab: Have a question and can't reach me to me for help? Try the CofC Math Lab.
Video review: To help you prepare for tests and catch up on classes you may have missed, I'm recording video summaries of each section of the text, which you can find at this link, following along using these review notes.
Course Objectives: MATH 221 is an introduction to multivariable calculus. We'll cover the calculus of geometry and motion in three-space, continuity and differentiability of functions of several variables, line integrals and multiple integrals, the theorems of Green and Stokes, and the Divergence Theorem.
Student Learning Outcomes: By the end of the course, students will be able to
  1. Identify, sketch and parametrize surfaces and space curves. Identify and plot vector fields.
  2. Algebraically manipulate vectors using the dot product, scalar product and cross product to answer geometric questions.
  3. Apply differentiation and integration to parametrized curves to draw conclusions about the geometry of the curve or about the trajectory of a particle.
  4. Compute, interpret, and apply various kinds of derivatives of multi-variable functions (whether scalar functions or vector functions).
  5. Solve multi-variable optimization problems, both constrained and unconstrained.
  6. Set up, evaluate, and apply integrals over two or three dimensional regions, using various coordinate systems and various orders of integration.
  7. Convert multiple integrals between different orders of integration and/or different coordinate systems.
  8. Evaluate and apply line integrals and surface integrals of both scalar functions and vector fields.
  9. Evaluate integrals by selecting an appropriate version of the Fundamental Theorem of Calculus (FTC for Vector Fields, Green's Theorem, Stokes' Theorem, or the Divergence Theorem) to transform the integral into an easier one with a domain of integration having a different dimension.
These outcomes will be assessed on the final exam.
Mathematics Program Student Learning Outcomes: Students will:
  1. use algebra, geometry, calculus and other track-appropriate sub-disciplines of mathematics to model phenomena in mathematical terms;
  2. use algebra, geometry, calculus and other track-appropriate sub-disciplines of mathematics to derive correct answers to challenging questions by applying the models from the previous Learning Outcome; and
  3. write complete, grammatically and logically correct arguments to prove their conclusions.
These outcomes will be assessed on the final exam.
Required Text: Calculus Early Transcendentals James Stewart, 8th ed.
As far as I can tell, your only option is buy this big book that covers all three semesters of calculus.

Read the book. Read it actively, with paper and pencil, following along with and working ahead of the author. Learning math by reading is an essential skill that will pay off in this course and any that follow. I strongly encourage you to obtain the version of our book you can best afford and read it.

It would be best for you to have your copy of the textbook by the first day of class, but everyone will have free online access to our book for the first two weeks of class through WebAssign. Students who purchase WebAssign will have online access to our book all semester. I find flipping through the pages online to be pretty clumsy and suspect most students without a hard copy of the text will simply not use the text (and that's bad).

Zoom: In case of emergency, we'll use Zoom.us for online class meetings. By logging on to our class via Zoom, you are granting me permission to record our class and post the recordings on Oaks for the remainder of the semester.
Oaks: This syllabus, your exam and quiz grades, and any course materials not contained on the syllaubs will be available on the College's learning management system, Oaks, a D2L/Brightspace product. For technical problems with Oaks, please contact the Student Computing Support Desk at 843.953.5457 or studentcomputingsuport@cofc.edu.
WebAssign: WebAssign is an online homework system that gives immediate feedback and extra help on many of the problems in our text. Some students find it useful, so I've put together optional WebAssign problem sets that match as much as possible the Assigned Problems listed below. These optional problem sets will not be used in the calculation of your grade. These WebAssignments will not be poasted on Oaks; to see them, you must log on to WebAssign. To set up your account, go to http://www.webassign.net, click on "Enter Class Key" (or "Students/I Have a Class Key"), and then enter our class key in the boxes:
cofc 3517 3945
You're allowed to use WebAssign for free for about the first two weeks of the semester, starting from the first day of class. You'll need to purchase a WebAssign access code if you want to use the system after that. (If you purchased one for a course that used the same textbook in an earlier semester, you might not need to purchase another.)
Exams and Grades: Note: The number of exams and quizzes, their dates and their point values may change in the event of an emergency, e.g., the college changing its schedule or delivery of classes during the semester due to weather or contagion. We'll have four (4) 75-minute midterm exams, a 2-hour final exam, and weekly one-question quizzes. See Schedule below for dates. All exams and quizes will be closed book: no notes, books, calculators, electronic devices, etc.

Although basic ideas we learn in this course can appear on several exams or quizzes, each weekly quiz will be based primarily on material covered since the time of the previous exam or quiz, and each midterm exam will be based primarily on material covered since the previous midterm. Our final exam will be weighted toward sections of the text that weren't covered on the miderms, but will otherwise be cumulative. Unless I specifically tell you otherwise, you should assume that any topic of this course could appear on the final.

The 75-minute exams are each worth 100 points, the final exam is worth 160 points, and the weekly in-class quizzes are worth 50 points altogether. I'll assign letter grades with this scale:
Letter grade: A A- B+ B B- C+ C C- D+ D D-
Minimum required score: 90% 87% 83% 80% 77% 73% 70% 67% 63% 60% 57%

I won't drop any exams, but if you do better on the final exam than on your worst 75-minute exam (excluding any on which you received a grade reduction for an honor code violation), I'll raise that (one) exam score by averaging it with your final exam (percentage) score. Then, at the end of the semester, I'll calculate your grade two ways--based on the percent you earned of the 560 possible exam points, and again based on the percent you earned of the 610 possible exam and quiz points--and give you whichever letter grade comes out higher.

Attendance Policy: Good attendance is a necessary first step towards a good grade. I strongly recommend that you attend class every day.

If you're absent on a non-exam day, I'll assume that you have a good reason for missing and will not require an excuse; however, I am unable to reteach the class to everyone who misses a day. Instead, I encourage you to catch up using the text, the videos and notes I've prepared for you, and notes from a classmate, if possible. Try homework for the day you miss, and then bring questions to me in my office. See Make-up Policy for absences on exam days.

Note: College of Charleston policy requires me to take roll during the first week after drop/add, until I determine that all of my students have attended at least once, and report the results to the College. Any student who has not attended class at least once during that week will be dropped from this class. These roll calls will not be used in my calculation of the remaining students' grades at the end of the semester.

Make-up Policy: Exams:
If you must miss an exam, I expect you to contact me (using all the numbers above) as soon as possible. Do not delay. Out of fairness to your classmates, I can allow you a make-up exam only if I determine that your absence at exam time (and every reasonable time until the make-up) is documented and excusable. If you've never seen a doctor for an illness causing you to miss the exam, it might be difficult for me to allow you a makeup. An unexcused exam will be given the grade zero, probably causing you to fail the course.

Quizzes:
At the end of the semester---starting from the date of the last in-class quiz and ending on the last day of final exams---I'll allow you to make up at most two (2) quizzes that you've missed for any reason. These makeups can only be used to replace quizzes that you've missed due to absences, not simply low scores.

The topic of the makeup quizzes can be from anything we've covered during this semester and will be taken outside of class at a mutually convenient time.

I'll drop your two (2) lowest quiz scores (after any makeups) before computing your quiz average.

Honor Code and Academic Integrety: Lying, cheating, attempted cheating, and plagiarism are violations of our Honor Code that, when suspected, are investigated. Each incident will be examined to determine the degree of deception involved.

Incidents where the instructor determines the student’s actions are related more to misunderstanding and confusion will be handled by the instructor. The instructor designs an intervention or assigns a grade reduction to help prevent the student from repeating the error. The response is recorded on a form and signed both by the instructor and the student. It is forwarded to the Office of the Dean of Students and placed in the student’s file.

Cases of suspected academic dishonesty will be reported directly by the instructor and/or others having knowledge of the incident to the Dean of Students. A student found responsible by the Honor Board for academic dishonesty will receive a XXF in the course, indicating failure of the course due to academic dishonesty. This status indicator will appear on the student’s transcript for two years after which the student may petition for the XX to be expunged. The F is permanent.

Students can find the complete Honor Code and all related processes in the Student Handbook at: http://deanofstudents.cofc.edu/honor-system/studenthandbook/.

How to get your best grade: Attend every class, practice lots of homework, and read the book!

After each class, do as many of the assigned problems as possible. There will be a short time to ask questions about these at the beginning of the next class. If you run into dificulty, really try; don't flit from one unsolved problem to the next.

Don't just do the homework until you get the right answer, but practice homework problems until you can do them reliably on an exam. Practice reading the instructions on homework problems. If you are able to do the homework only after looking at some answers in the back to figure out what the question is asking, then you're not prepared for the exams.

Begin extra studying well in advance for the tests, at least a week. Rework old problems that could appear on the test. Write (and rewrite) a special set of notes that summarize in your own words the important facts for the test. Include in these notes the different types of problems appearing in the homework and the steps you follow to solve each type. (For example, here are the notes written by an A student while studying for the first test in MATH 111 Precalculus.)

Calculators: Calculators will be excluded from all exams and quizzes but will be useful in some of the exercises. For those times when you want a grapher, Desmos.com works great. When you want a symbolic calculator, WolphramAlpha.com does everything but graph in 3 dimensions. Caution: Overreliance on tools such as these will leave you unprepared for the exams.
Inclement Weather and other emergencies: If in-person classes are suspended, faculty will announce to their students a detailed plan for a change in modality to ensure the continuity of learning. All students must have access to a computer equipped with a web camera, microphone, and Internet access. Resources are available to provide students with these essential tools.
Syllabus On Line: If it becomes necessary for me to change any part of this syllabus, you'll always find its most current version at http://kunklet.people.cofc.edu/. Look for the last change date at the top of this document, and the description of changes at the bottom.
Old Exams, Review: Here are my exams from the last time I taught this class. Because course content and the order of topics can change from one semester to the next, these exams might not always cover the material you should be studying for your exams. Check the solutions to see exactly which section each question was taken from.
Exam 1 Exam 2 Exam 3 Exam 4 Final Exam

I've prepared these review notes to help you study for the exams. You can read them on their own, or watch the accompanying videos. See also the math department's sample finals exams

Learning Disabled Students: Any student eligible for and needing accommodations because of a disability is requested to speak with the professor during the first two weeks of class or as soon as the student has been approved for services so that reasonable accommodations can be arranged. Center for Disability Services/SNAP.

Currently, SNAP requires students to schedule alternate testing arrangements at least one week before the exam date.

Assigned Problems: This is a list of all the problems worth doing in each section we'll cover. I won't collect these, but you should be doing them daily.

"5-25" means at least the odd numbered >roblems between 5 and 25, inclusive, and preferably the even numbered problems as well.
* indicates a challenging but worthwhile problem.
** indicates a very challenging problem for your enjoyment only. I won't put a ** problem on an exam, and I probably won't have time to do one in class.
"12.rev" refers to the review exercises at the end of Chapter 12.
[17] means to do problem 17 if time allows us to cover this topic in class. Ask me if you're not sure.
It is impossible to pass this course without good skills from Calculus I. Do the problems marked review in Chapter 3 to review differentiation. Do the problems marked review in Chapter 5 to review the Fundamental Theorem and substitution. Do the problems marked review in Appendix D to review trigonometry.

App.D: (review) 19-38. 3.1: (review) 3-35. 3.2: (review) 3-29.
3.3: (review) 1-15. 3.4: (review) 7-46. 3.5: (review) 49-58.
3.6: (review) 2-30. 3.rev: (review) 1-42. 5.3: (review) 19-40.
5.4: (review) 5-12, 14-16, 21-33. 5.5: (review) 1-35, 40-47, 53-60. 5.rev: (review) 11-35, 37, 38.

12.1: 5-7, 9-20, 23-40, 45. 12.2: 2-6, 9-31, 35, 41, 43. 12.3: 1-20, 23-25, 27, 39-44, 49-52.
12.4: 1-7, 13-15, 17-22, 27-36. 12.5: 1-41, 45-47, 51-61, 64-68. 12.6: 3-9, 11-28, 31-38, 43-46, 52*.
transformations on graphs of equations,
Clemson's conic section review,
conic section practice problems.
12.rev: 5, 6, 9, 11, 13-21, 23, 25, 27*, 28-37. 13.1: 1-27, 31, 32, 42-46, 49, 50. 13.2: 3-26, 33, 35-42, 49, 50.
13.3: 1-6, 15, 16**, 17-25, 30-31, [42-45], 47-50, 53, 59*. 13.4: 3-16, 19-20, 21*, 22*, [23-27], 37-42, 13.3.49, 13.3.50, 13.3.53, 13.3.55. 13.rev: 1-6, 9, 11, 12, 15, 17, 19, 22.
14.1: 1, 9-33, 36, 37, 41*-44*, 45-52, 55, 56, 61-70. 14.2: 25, 26, 29-36. 14.3: 1, 3, 5-8, 15-38 45-70, 97.
14.4: 1-6, 11-19, 21, 23-32. 14.5: 1-26, 35, 38, 39. 14.6: 1, 4-17, 21-27, 29, 33-34, 41-46, 49-50, 54-56, 57*, 59, 61*, 62*.
14.7: 1-15, 18-20, 31-38, 41-49, 50**, 51-54. more 14.8: 1-8, 13, [17-23], 29-42, 45. more 14.rev: 1-6, 9-17, 19-22, 25-29, 31-37, 51-56, 59-63.
15.1: 1-5, 7, 9-11, 15-43, 47-48. 15.2: 1-10, 15-32, 35-38, 39*, 40*, 45-56, 61, 62. 15.3: 1-27, 28**, 29-37.
15.5: 1-12. 15.6: 3-22, 27-36.
more triple integral practice problems.
15.7: 1-13, 15-24, 29-30.
15.8: 1-15, 17-27, 35-37, 41-43. 15.9: 1-19, 23-26, 27*. 15.rev: 3-15, 19-38, 47, 48, 53-56, 57*.
16.1: 1-18, 21-24, 25*, 26*, 29-32. 16.2: 1-15, 17-22, 39-41, 51. 16.3: 1, 3-26, [31-34], 35*.
16.4: 1-14, 17-19. 16.5: 1-20. 16.6: 1-6, 19-25, 33-36, 39-49.
16.7: 5-32. 16.8: 1-11, 13-15. 16.9: 1-13, 25-30.
16.rev: 1-14, 15*, 17, 18, 27-30, 32-34, 39.
Schedule: See CofC calendars and exam schedules for potential storm makeup days.
Content of exams and quizzes refers to topics in their order of appearance on this Schedule. For instance, "Exam 3 (15.1-15.8)" means all questions on Exam 3 will be selected from 15.1, 15.2, 15.3, 15.5, 15.6, 15.7, 15.8.
M 1/10 ( 1 ) : 12.1, 12.2 W 1/12 ( 2 ) : 12.2, 12.3 R 1/13 ( 3 ) : 12.3 F 1/14 ( 4 ) : 12.4
M 1/17 ( 5 ) : holiday W 1/19 ( 6 ) : 12.5 R 1/20 ( 7 ) : Quiz 1 (12.1-12.5) 12.6 F 1/21 ( 8 ) : 13.1
M 1/24 ( 9 ) : 13.2 W 1/26 ( 10 ) : 13.3 R 1/27 ( 11 ) : Quiz 2 (12.6-13.2) 13.3 F 1/28 ( 12 ) : 13.4
M 1/31 ( 13 ) : 13.4 W 2/2 ( 14 ) : Q&A R 2/3 ( 15 ) : Exam 1 (12.1-13.4) F 2/4 ( 16 ) : 14.1
M 2/7 ( 17 ) : 14.2 W 2/9 ( 18 ) : 14.3 R 2/10 ( 19 ) : Quiz 3 (14.1-14.3) 14.4 F 2/11 ( 20 ) : 14.5
M 2/14 ( 21 ) : 14.6 level curves and the gradient W 2/16 ( 22 ) : 14.6, 14.7 R 2/17 ( 23 ) : Quiz 4 (14.4-14.6) 14.7 F 2/18 ( 24 ) : 14.8
M 2/21 ( 25 ) : 14.8 W 2/23 ( 26 ) : Q&A R 2/24 ( 27 ) : Exam 2 (14.1-14.8) F 2/25 ( 28 ) : 15.1
Express II classes begin Feb 28. Mar 25 is the last day to withdraw from the course with a grade of W.
M 2/28 ( 29 ) : 15.1, 15.2 W 3/2 ( 30 ) : 15.2 intersection of two cylinders R 3/3 ( 31 ) : Quiz 5 (15.1-15.2) 15.3 level curves for r and Θ F 3/4 ( 32 ) : 15.3
M 3/7 ( 33 ) : holiday W 3/9 ( 34 ) : holiday R 3/10 ( 35 ) : holiday F 3/11 ( 36 ) : holiday
M 3/14 ( 37 ) : 15.5 W 3/16 ( 38 ) : 15.6 R 3/17 ( 39 ) : Quiz 6 (15.3-15.5) 15.6 F 3/18 ( 40 ) : 15.7
M 3/21 ( 41 ) : 15.8 W 3/23 ( 42 ) : Q&A R 3/24 ( 43 ) : Exam 3 (15.1-15.8) F 3/25 ( 44 ) : 15.9
M 3/28 ( 45 ) : 16.1 16.1 rough draft W 3/30 ( 46 ) : 16.2 R 3/31 ( 47 ) : Quiz 7 (15.9-16.2) 16.3 F 4/1 ( 48 ) : 16.4
M 4/4 ( 49 ) : 16.4, 16.5 W 4/6 ( 50 ) : 16.5 R 4/7 ( 51 ) : Quiz 8 (16.3-16.5) 16_6fig 16.6 F 4/8 ( 52 ) : 16.6, 16.7
M 4/11 ( 53 ) : 16.7 W 4/13 ( 54 ) : Q&A R 4/14 ( 55 ) : Exam 4 (15.9-16.7) F 4/15 ( 56 ) : 16.8
M 4/18 ( 57 ) : 16.8, 16.9 W 4/20 ( 58 ) : 16.9 R 4/21 ( 59 ) : review, Q&A F 4/22 ( 60 ) : review, Q&A
M 4/25 ( 61 ) : review, Q&A Saturday 4/30, 1:00-3:00pm, 117 Maybank : Final Exam
Changes:
01/08: changed some links from http to https 01/19: updated cofc attendance verification policy. 03/22: modified worst midterm policy in case of honor code violation. 04/21: added office hours during finals.
04/25: modified office hours during finals.