Kunkle's Syllabus, MATH 221, Spring 2018
last change: April 21, 2018

MATH 221 (Calculus III) Spring 2018

Section: 21108 - MATH 221 - 02
10:00 am - 10:50 am MWF MAYBANK HALL 223 and 10:50 am - 12:05 pm T MAYBANK HALL 224
Instructor: Dr. 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).
RS Small is item 23 on the campus map. It's a big pink building across from Maybank Hall on the Cougar Mall.
Instructor's Office Hours: Here are my remaining office hours this semester. If you'd like to see me but can't make these times, please ask for an appointment. As always, you're welcome to use my home number if you have a question.
Mon April 22, 11am-12pm
Tues Apr 24, 8:15am-12pm
Wed Apr 25, 11:00am-4pm
Thur Apr 26, 8:15am-4pm
Fri Apr 27, 8:15am-2:45pm

Math Lab: Have a question and can't reach me to me for help? Try the CofC Math Lab. (Opens Monday, January 22.)
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.
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.

Carefully save all receipts from the bookstore. If any of your books comes shrink-wrapped, DON'T unwrap it until you check with your instructor on the first day of class that you've bought the right book.

Students who are certain that they want to use WebAssign (see below) can probably save money by buying the book bundled with a WebAssign access code at our bookstore. Be aware that unbound "loose-leaf" texts are pretty delicate and will probably have no resale value at the end of the semester. Everyone else should try it for free first. Based on my limited experience, I think that the cheapest way to obtain the book only is probably to purchase it online and then sell it yourself on Amazon when you're through with it.

It would be good to have your copy of the textbook by the first day of class, but it's possible that everyone will have free online (but not down-loadable) access to our book for the first two weeks of class through WebAssign, and that students who purchase WebAssign will have online access to our book all semester. Even of that's true, I find flipping through the pages online to be pretty clumsy and an impediment to learning from the book. I think even those students who buy WA will want a hardcopy of the text, which can be bought online at a reasonable price.

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. 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:
cofc 3421 6012
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.)
These optional problem sets will not be used in the calculation of your grade.
Exams and Grades: We'll have four (4) 75-minute midterm exams, a 3-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, electroni c 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 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 200 points, and the weekly in-class quizzes are worth 50 points altogether. I'll assign letter grades by 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, 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 600 possible exam points, and again based on the percent you earned of the 650 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. Read the text and try the 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 two weeks 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 these two weeks 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) and the Absence Memo Office as soon as possible. Do not delay. 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 excusable. If you are not sick enough to see a doctor for your illness, then you are not sick enough to miss the exam. An unexcused exam will be given the grade zero, probably causing you to fail the course.

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, not simply low scores. No Absence Memo will be required for makeup quizzes.

The makeup can cover any topic from the course, not necessarily the topic of the quiz you missed, and will be taken outside of class at a mutually agreed upon time. Contact me after the last quiz to schedule a makeup.

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

Regrading Policy: I will never regrade something for a lower score. If you think I've overlooked something when grading your work and would like me to consider giving it a higher score, you must write, sign, and date the following statement on the exam or quiz in question. "Dear Professor Kunkle, Please regrade Problem(s) XYZ for a higher score. I have not altered my work on this paper in any way since it was first graded."
Academic Integrety: Students in this class will be held to the College of Charleston's Standards of Academic Integrity and Honor Code.
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 t he 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.)

"What do I need to get on the final?": In case you're wondering what grade you need on the final to get some particular grade in our course, here's the answer.

Let a, b, c, d be your scores on exams 1, 2, 3, 4. Make sure you use d to denote the lowest of these four. Let X be your desired score in the course overall. Represent these scores as numbers between 0 and 100. For instance, if you got a 75% on exam 1, represent that score as 75. To get an A in the course, X would have to be 90. See the syllabus for my grading scale. Let q be your quiz average (after dropping your two lowest quiz scores) multiplied by 5; q will be a number between 0 and 50. (You'll have to estimate q if you're planning to makeup a missed quiz or two before the semester's over.)

What percent do you need to earn on the final to get X in the course? The answer is tricky because: 1. I compute your grade with and without the quizzes and give you whichever letter grade comes out higher, and 2. I raise your worst midterm by averaging it with the final in case you do better on the final. Here's the answer.

  • If X > 2q, then:
    • If X > (a+b+c+3d)/6, then you need to earn (6X-a-b-c-0.5*d)/2.5 percent on the final.
    • If X ≤ (a+b+c+3d)/6, then you need to earn (6X-a-b-c-d)/2 percent on the final.
  • If, instead, X ≤ 2q, then:
    • If X > (a+b+c+3d+q)/6.5, then you need to earn (6.5X-a-b-c-0.5*d-q)/2.5 percent on the final.
    • If X ≤ (a+b+c+3d+q)/6.5, then you need to earn (6.5X-a-b-c-d-q)/2 percent on the final.
Calculators: A calculator is of limited use in learning the material in this class, so no specific model is required for this course. Calculators will be excluded from all exam and quiz questions.
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: Here are the midterm and final exams from the last time I last 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
Learning Disabled Students: Any student eligible for and needing accommodations because of a disability is requested to contact Disability Services (953-1431) and speak privately 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.
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 problems 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.
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 substition. 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, 39-44, 49-52.
12.4: 1-7, 13-15, 17-22, 27-36, 39, 41. 12.5: 1-41, 45-47, 51-61, 64-68. 12.6: 3-9, 11-28, 31-38, 43-46, 52*. 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, 15-25, 30-31, [42-45], 47-50, 53, 59*. 13.4: 3-16, 19-20, 21*, 22*, [23-27], 37-42. 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: 5-22, 25, 26, 29-41. 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: 1-20, 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. 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 also CofC calendars and exam schedules for potential storm makeup days.
M 1/8 : 12.1 T 1/9 : 12.2, 12.3 W 1/10 : 12.3 F 1/12 : 12.4
M 1/15 : holiday T 1/16 : 12.5, 12.6 W 1/17 : 12.6 F 1/19 : Quiz 1 (12.1-12.6), 13.1
M 1/22 : 13.2 T 1/23 : Quiz 2 (13.1-13.2), 13.3 W 1/24 : 13.3 F 1/26 : 13.4
M 1/29 : 13.4, 14.1 level curves T 1/30 : Quiz 3 (13.3-13.4), 14.1 W 1/31 : 14.2 F 2/2 : 14.3
M 2/5 : Q&A T 2/6 : Exam 1 (12.1-14.3) W 2/7 : 14.4 F 2/9 : 14.5
M 2/12 : 14.6 level curves and the gradient T 2/13 : Quiz 4 (14.4-14.5), 14.6, 14.7 W 2/14 : 14.7 F 2/16 : 14.7, 14.8
M 2/19 : 14.8 In-class example T 2/20 : Quiz 5 (14.6-14.8), 15.1 W 2/21 : 15.1, 15.2 F 2/23 : 15.2
M 2/26 : Q&A T 2/27 : Exam 2 (14.4-15.2) W 2/28 : 15.3 F 3/2 : 15.3, 15.5
M 3/5 : 15.5, 15.6 T 3/6 : Quiz 6 (15.3-15.5), 15.6 W 3/7 : 15.7, 15.8 F 3/9 : 15.7, 15.8
March 13 is the last day to withdraw with a grade of W.
M 3/12 : 15.9 T 3/13 : Quiz 7 (15.6-15.9), 16.1 W 3/14 : 16.2 F 3/16 : 16.2, 16.3
M 3/19 : holiday T 3/20 : holiday W 3/21 : holiday F 3/23 : holiday
M 3/26 : Q&A T 3/27 : Exam 3 (15.3-16.2) W 3/28 : 16.3 F 3/30 : 16.4
M 4/2 : 16.4, 16.5 T 4/3 : Quiz 8 (16.3-16.4), 16.5 W 4/4 : 16.6 F 4/6 : 16.6, 16.7
M 4/9 : 16.7 T 4/10 : Quiz 9 (16.5-16.7), 16.8 W 4/11 : 16.8, 16.9 F 4/13 : 16.9
M 4/16 : Q&A T 4/17 : Exam 4 (16.3-16.9) W 4/18 : Review F 4/20 : Review
M 4/23 : Review
M 4/30 : Final Exam 8-11am, 223 MYBK
01/17: omit problems 12.5.71-74 01/29: added link to level curves 02/12: added link to level curves and the gradient 02/19: added link to This day's last in-class example
03/05: Withdrawl deadline is March 13. 04/20: Final exam MYBK 223. 04/21: Posted office hours during finals week, and what you need on the final.