Kunkle's syllabus, MATH 220, Fall 2023

Tom Kunkle, 327 RS Small, kunklet@cofc.edu, (843)953-5921.
Hours: 12-1pm M, 1:45-2:45pm Tu, 9-9:50am W, 2-3pm Fri, or by appointment.
I'm happy to meet at other times that fit your schedule, if I'm available. Here's what my week looks like.

Either online access to Calculus, Early Transcendentals James Stewart, 8th ed.at Cengage.com
Or either of the following. The MATH 220 content is identical in both.

this book:

covers these courses:

Calculus, Early Transcendentals James Stewart, 8th ed.,

MATH 120, 220, 221.

Single Variable Calculus, Early Transcendentals James Stewart, 8th ed.

MATH 120, 220.

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.

If it becomes necessary for me to change any part of this syllabus, you'll always find its most current version at https://kunklet.people.cofc.edu/ Look for the last change date at the top of this document, and the description of changes at the bottom.

MATH 120 or HONS 115

Have a question and can't reach me for help? Free tutors are available at the CofC Math Lab.

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 quizzes. All exams will be in-person and closed-book: no notes, books, calculators, electronic devices, etc.

Although basic ideas we learn in this course can appear on multiple 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 slightly toward material covered after the last midterm but will otherwise be cumulative. Unless I tell you otherwise, you should assume that any topic of this course could appear on the final. When in doubt, please ask me.

Each of the midterm exams is worth 100 points, the final exam is worth 160 points, and the weekly in-class quizzes are worth 50 points altogether. Minimum required scores for letters grades are

A (90%)

A- (87%)

B+ (83%)

B (80%)

B- (77%)

C+ (73%)

C (70%)

C- (67%)

D+ (63%)

D (60%)

D- (57%)

I'll drop your two (2) lowest quiz scores (after any makeups) before computing your quiz average. I won't drop any exams, but if you do better on the final exam than on your worst midterm exam (excluding any on which you received a grade reduction for an honor code violation), I'll raise that (one) midterm exam score by averaging it with your final exam (percentage) score. Then, at the end of the semester, I'll calculate your course 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.

Here are the exams and solutions from the last time I taught this class under a format similar to this semester's. Since course content, exam dates, 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. You can see exactly which sections are represented on these old exams by searching in the solutions for the word "Source."

math dept sample finals

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. Caution: Overreliance on calculators will leave you unprepared for the exams.

I hope to see all of you every day in class. Good attendance is a necessary first step towards a good grade. 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. Any student who has not attended class at least once during that week will be dropped from this class by the registrar. These roll calls will not be used in the calculation of grades at the end of the semester.

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 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.

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 work through 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.)

You can watch some video lectures I recorded in 2021 at this link, working along with me using these lecture notes that I prepared.

Here are some review notes I wrote to help you study for the exams. The first 13 pages are a review of precalc and calc 1 for students in calc 2. For more review of precalc and calc 1, see my review notes for MATH 120. These notes aren't meant to take the place of the text and lectures.

All class announcements, your exam and quiz grades, and any course materials not found on the syllabus and will be available on Oaks, the College's learning management system. For technical problems with Oaks, please contact the IT Help Desk at 843.953.5457 or studentcomputingsuport@cofc.edu.

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 on this syllabus. 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:

cofc

8466

9103

You'll have free access to WebAssign for the first two weeks of the semester, starting from the first day of class. You'll need a WebAssign access code if you want to use the system after that. Contact WebAssign student support for help using or purchasing WebAssign.

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, unless it's a slow day, I probably won't have time to do one in class.
[17] means to do problem 17 if time allows us to cover this topic in class. When in doubt, please ask me.

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.

3.11: 1-4, 7-12, 15-19, 23, 24, 30-39.

4.4: 1, 2, 8-70, 73*, 74*, 75, 76.

6.1: 1-26, 29.

6.2: 1-34, 47-49, 54-61, 63**. more

6.3: 1-26, 37-43, 48**.

6.4: 1-5, 7-12 (Be careful with the units in 11 and 12.), 13-19 (On Earth's surface, an object of mass 1 kg weighs 9.8 N), [20-22].

6.5: 1-15, 17, 19, 21.

6.rev: 1-16, 23-25, 26*, 27-28, [29, 30], 31, 32.

7.1: 1-46, [49, 51-56], 57-58, 61-66, 69.

7.2: 1-49, 55, 61-64. more

7.3: 1-18, 19*, 20-28, 29*, 33-34, 37-38. (Hint for 22: use Example 8, §7.2.)

Euler: 1, 8, 9, 10.

7.4: 1-30, 31*, 32-54. more

7.5: 1-80, 82, 83. (Hint for 83: try p(x)e^x² for some polynomial p.)

7.7: Ignore all references to Midpoint Rule. 3-21, 27-30, 32, 37. more

7.8: 1-3, 5-46, 49-54, 57, 79*, 80*.

7.rev: TF:1-6, 11. Exercises: 1-52, 63-67, 71.

8.1: 1-22, 25-28.

8.2: 1-18, 27-28.

8.3: 21-35.

8.rev: 1-4, 7-8, 9*, 10.

9.1: 1, 2, 5, 9, 11*.

9.2: 1-8.

9.3: 1-20, 21*, 22*, [29-32], [45-48], [more]

9.rev: TF: 1-4. Exercises: 1, 3, [13,14], [18].

10.1: 1-24, 25*, 26*, 27*, 37-38.

10.2: 1-20, 23-24 (make signs charts for x' and y'), 29, 30, 41-48, 51, 52, 61-63, 65-66.

10.3: 1-12, 15-26, 29-44, 45*, 46*, 47-48, 52 (Hint: convert.), 55-64. polar graph paper

10.4: 1-12, 17-36, [37-42], [45-50].

10.rev: TF: 1-4, 7. Exercises: 1-5, 6*, 7-14, 17-18, 21-26, 31-32, [33-36], 37-40.

11.1: 1-8, 13-18, 19-22 (Use an online sequence plotter for 19-22.), 23-54, 55*, 69*, 70*, 71-78.

11.2: 3-8, 9-14 (Use an online series plotter for 9-14.), 15-48, 57-63, 67, 68, 75-76, 87*.

11.3: 1-28, [36-41, plus these more].

11.4: 3-28, 29* (easier with a later technique), 30-32, 39*, 40-41.

11.5: 2-18, 19* (easier with a later technique), 20-31. more

11.6: 1-20, 21*, 22*, 23*, 24*, 25-37, 43, 45.

11.7: 1-38. more

11.8: 3-26, 27*, 28*, 29-30.

11.9: 1-10, 13-33, 40.

11.10: 5-26, 31-48, 51, 53-65, 73-80.

11.11: 1-10, 13-22, 25-29, 31.

11.rev: TF: 1-20. Exercises: 1-8, 11-31, 33*, 40-55.

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 2 (7.3-8.2)" means all questions on Exam 2 will be selected from 7.3, 7.4, 7.5, 7.7, 4.4, 7.8, 8.1, and 8.2.

T 8/22 ( 1 ): 3.11, 6.1review

W 8/23 ( 2 ): 6.1, 6.2

F 8/25 ( 3 ): 6.3

M 8/28 ( 4 ): 6.4

T 8/29 ( 5 ): Quiz 1 (3.11-6.3), 6.4, 6.5

W 8/30 ( 6 ): 6.5, 7.1

F 9/1 ( 7 ): 7.1

M 9/4 ( 8 ): 7.2 Pascal's Triangle

T 9/5 ( 9 ): Quiz 2 (6.4-7.1), 7.2

W 9/6 ( 10 ): Euler

F 9/8 ( 11 ): Euler

M 9/11 ( 12 ): Q&A

T 9/12 ( 13 ): Exam 1 (3.11-Euler)

W 9/13 ( 14 ): 7.3

F 9/15 ( 15 ): 7.3

M 9/18 ( 16 ): 7.4

T 9/19 ( 17 ): Quiz 3 (7.3), 7.4 (7.5)

W 9/20 ( 18 ): 7.7

F 9/22 ( 19 ): 4.4

M 9/25 ( 20 ): 4.4

T 9/26 ( 21 ): Quiz 4 (7.4-4.4), 7.8

W 9/27 ( 22 ): 7.8

F 9/29 ( 23 ): 8.1

M 10/2 ( 24 ): Q&A

T 10/3 ( 25 ): Exam 2 (7.3-8.1)

W 10/4 ( 26 ): 8.2

F 10/6 ( 27 ): 11.1, FLESK

Express II classes begin Tuesday Oct 10. Oct 27 is the last day to withdraw from this course with a grade of W. Fix registration holds by this date.

M 10/9 ( 28 ): 11.1

T 10/10 ( 29 ): Quiz 5 (8.2-11.1), 11.2

W 10/11 ( 30 ): 11.2, 11.3

F 10/13 ( 31 ): 11.3

M 10/16 : holiday

T 10/17 : holiday

W 10/18 ( 32 ): 11.4

F 10/20 ( 33 ): 11.5

M 10/23 ( 34 ): 11.6

T 10/24 ( 35 ): Quiz 6 (11.2-11.5), 11.6, (11.7), 11.8

W 10/25 ( 36 ): 11.8, geometric partial sums, partial sums of another power series

F 10/27 ( 37 ): 11.9

M 10/30 ( 38 ): Q&A

T 10/31 ( 39 ): Exam 3 (8.2-11.8)

W 11/1 ( 40 ): 11.9

F 11/3 ( 41 ): 11.10

M 11/6 ( 42 ): 11.10, 11.11 Taylor's Theorem

T 11/7 ( 43 ): Quiz 7 (11.9-11.10), Taylor Polys of sin(x), 11.11

W 11/8 ( 44 ): 11.11, 9.3 slides

F 11/10 ( 45 ): 10.1, What's wrong with this picture?

M 11/13 ( 46 ): (9.3) 10.2

T 11/14 ( 47 ): Quiz 8 (9.3), 10.2, when x'=y'=0

W 11/15 ( 48 ): 10.3, where is r or θ constant?

F 11/17 ( 49 ): 10.3 logarithmic spiral

M 11/20 ( 50 ): Q&A

T 11/21 ( 51 ): Exam 4 (11.9-10.2)

W 11/22 : holiday

F 11/24 : holiday

M 11/27 ( 52 ): 10.3, 10.4

T 11/28 ( 53 ): 10.4

W 11/29 ( 54 ): Review, Q&A

F 12/1 ( 55 ): Review, Q&A

M 12/4 ( 56 ): Review, Q&A

W 12/6 : Final Exam 10:30 am-12:30 pm

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.

MATH 220 deepens the students' understanding of the definite integral by studying some of its various applications and the basic techniques of integration. We study sequences and series of real numbers, fundamental to any understanding of the real numbers and a stepping stone to the study of power series, the students' introduction to the important topic of the approximation of functions. Finally, we take our first steps towards multivariate calculus with the study of calculus on curves given parametrically.

By the end of the course, students should be able to

Represent the following as definite integrals: area between curves, volume of a solid of revolution, average value of a function, arc length of a curve.
Evaluate integrals by applying integration by parts, trigonometric substitution, trigonometric identities, and partial fraction decomposition.
Identify and evaluate improper integrals and apply the comparison test to determine whether an improper integral converges.
Identify properties of sequences (monotonicity, boundedness, convergence) and find the limits of sequences.
Determine whether an infinite series converges by choosing and applying a suitable convergence test.
Determine the radius of convergence of a power series.
Use Taylor Series to express functions as power series and to evaluate infinite series.
Represent plane curves as parametric equations, and recognize the plane curve that corresponds to given parametric equations.
Use derivatives and integrals to find slopes and lengths of parametric curves, and areas bounded by them.
Convert between Cartesian and polar coordinates, graph polar curves, and apply calculus to polar curves as for parametric curves.
Model mathematical questions with differential equations, and use basic methods for solving such equations.

This course can be used to satisfy some requirements of the undergraduate mathematics degree program, for which there are also some standard goals; students will:

use algebra, geometry, calculus and other track-appropriate sub-disciplines of mathematics to model phenomena in mathematical terms;
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
write complete, grammatically and logically correct arguments to prove their conclusions.

These outcomes will be assessed on the final exam.

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: https://deanofstudents.cofc.edu/honor-system/studenthandbook/.

If in-person classes are suspended, I'll announce 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.