2023 November 27,
Carleton College, Fall 2023, Joshua R. Davis, , CMC 324, x4095
Calculus has been a major driver of science and technology over the past few centuries. The material, that you learned in your first two calculus courses, is important but often not quite sufficient. Why? Because real problems often involve multiple variables. For example, a satellite orbiting Earth is not moving in a one-dimensional space with coordinate x but rather a three-dimensional space with coordinates x, y, z. A manufacturer trying to maximize its profit must consider not just one raw material but many materials, goods, and services. Therefore, our ability to apply calculus is greatly improved if we can handle several variables.
That's the point of this course: to extend the geometric and algebraic concepts of introductory calculus to functions that input or output multiple variables. Topics include partial derivatives, multiple integrals, and some vector calculus. Whenever we can, we explore applications in physics, engineering, economics, geology, computer science, and other fields.
The prerequisites are two Advanced Placement calculus courses or whatever our placement process regards as equivalent. (Students who have taken Math 120: Calculus 2 at Carleton should instead take Math 210: Calculus 3.) Talk to me if you are concerned about your background.
Our course meets in CMC 210 during period 3A. That's Monday 11:10-12:20, Wednesday 11:10-12:20, Friday 12:00-1:00. Our official final exam period is Sunday November 19 3:30-6:00 PM in CMC 210.
The College's accreditation says that a 6-credit course is 150 hours of work. That's about 15 hours per week or 5 hours per class meeting. Those 5 hours break down into about 1 hour for class itself and 4 hours for homework, reading, studying, etc. If you find yourself spending much more time, then talk to me.
You are expected to attend every class meeting promptly. You are expected to take notes on paper or a tablet. (Merely typing on a keyboard is inadequate, because of all of the pictures needed.) You are expected to participate in discussion and group work.
Some students don't like participating in class, because they are shy, they are not confident about their English, they are not confident about their math, etc. I urge those students to participate anyway. They can also compensate for a deficiency in class participation by working in office hours or generally demonstrating effort and interest.
Although class meetings may seem like the core of the course, homework assignments are actually where you learn the material. It is essential that you attempt each homework promptly, before the next class meeting. For then you better understand that next class meeting!
On homework, you are encouraged to figure out the problems with other students. However, you should always write/type your solutions individually, in your own words. You may not copy someone else's work — that includes artificial intelligence products — or allow them to copy yours. Presenting someone else's work as your own is an act of academic dishonesty. The College requires me to report you, if I suspect that you have not upheld its Academic Integrity standards.
Writing is not just for literature and history majors. Written and oral communication skills are essential to every academic discipline and are highly prized by employers. In this course, your written work is evaluated both for correctness and for presentation. (To help you, I might assign short writing exercises. I haven't decided yet.)
Homework is assigned at nearly every class meeting. Although you are expected to attempt the problems immediately, they are usually collected two meetings after they were assigned. This schedule tries to give you some flexibility.
But we all have bad weeks, where we can't get everything done, right? If you need to submit an assignment late, then do so. Put it in a separate pile from the on-time papers. If the grader hasn't graded the assignment yet, then they can grade your paper with the others for full credit. If the grader has graded the assignment already, then you might not get credit. There are limitations to how much delay and complication a grader can handle.
Please mark each assignment with the day that it was assigned (e.g., "Day 11"). Please staple multi-page packets. Paper clips don't work well.
Depending on time constraints in any given week, perhaps not all of your homework will be graded. In order to ensure full credit, do all of the assigned problems.
We have four exams. They are given roughly 1/4, 2/4, 3/4, and 4/4 of the way through the term. The last exam is given during our official final exam period.
Are the exams cumulative? No and yes. No, in that each exam is focused on the material that has not been tested yet. Yes, in that much of the material is inherently cumulative. For example, Exam D might ask you to compute a curl, which is covered around Day 27 of the course. But computing a curl requires you to compute partial derivatives, which are covered around Day 10 of the course.
For better or worse, we are required to measure your learning using grades. Your numerical grade is based on the responsibilities above: participation 5%, homework 10%, Exam A 20%, Exam B 20%, Exam C 20%, Exam D 25%.
Numerical grades are converted to letter grades only at the end of the term. Grades are not curved, so students are not in competition with each other. Grades are also not based on predetermined percentages (90%, 80%, 70%, etc.), because Math 211 problems are difficult to tune so precisely. (I could accidentally write a difficult exam and wreck everyone's percentages.) Rather, I assign grades by comparing the students to the course goals. For example:
Talk to me, if you are concerned about your grade.
I want all of my students to work hard and learn a lot. I try to give them all of the resources that they need. For starters, let's list some basic documents:
Those documents are a start, but if you're trying to do college alone, then you're doing it wrong! Remember that I encourage you to solve problems with classmates (even if the work that you submit must be your own). Consider working in the Math Skills Center on the second floor of CMC. There you'll find helpful tutors and probably classmates too. You might also be interested in the other arms of the Academic Support Center: Quantitative Resource Center, Writing Center, Assistive Technologies, etc.
I hold several office hours per week. They are essentially optional extra class meetings, where you pick the topic of conversation (usually homework problems). No appointment is needed for office hours; just drop in! Consult my weekly schedule for them. If you want to visit office hours but the times don't work, then consult my weekly schedule and e-mail me, listing several possible meeting times.
If a health condition or other personal matter affects your participation in class, homework, exams, etc., then please let me know as soon as possible. Depending on the situation, we might want to confer with Accessibility Resources, Assistive Technology, Student Health and Counseling, or Sexual Misconduct Prevention and Response. When you ask me to help, I do my best to help. :)
To help you decode the schedule, here is an example. Day 01 is Monday September 11. We discuss coordinate systems. Section 12.1 of the textbook covers that material; read it before or after class, if you wish, to get another treatment. You have seven homework problems, which are due at the start of class on Day 03. If you wish, you can review the Four Theorems worksheet that we used in class.
| Date | Day | Topic | Homework | Due | Reading | Notes |
|---|---|---|---|---|---|---|
| M 09/11 | 01 | coordinate systems | 12.1 #4, 8, 9, 15, 17, 40, 52 | 03 | 12.1 | four.pdf |
| W 09/13 | 02 | vectors | day02.pdf | 04 | 12.2 | |
| F 09/15 | 03 | dot product | 12.3 #1, 6, 7, 21, 31, 39, 45, 53, 54, 57 | 05 | 12.3 | |
| M 09/18 | 04 | cross product lines, planes | day04.pdf | 06 | 12.4 12.5 | |
| W 09/20 | 05 | parametrized curves polar coordinates | 10.1 #4, 24, 30, 57 10.3 #1, 3, 8, 10, 19, 26, 32 | 07 | 10.1 10.3 | parametrizedCurves.nb |
| F 09/22 | 06 | calculus with curves | day06.pdf | 08 | 13.1 13.2 | calculusCurves.nb curveProblems.pdf |
| M 09/25 | 07 | arc length motion in space | day07.pdf | 10 | 13.3 13.4 | curveProblemsMore.pdf |
| W 09/27 | 08 | functions of several variables | day08.pdf | 11 | 14.1 | severalVariables.nb |
| F 09/29 | 09 | Exam A | ||||
| M 10/02 | 10 | limits, partial derivatives | 14.2 #8, 14 (hint: polar), 52 14.3 #3, 6, 10, 18, 28, 50 | 12 | 14.2 14.3 | |
| W 10/04 | 11 | tangent plane, chain rule | 14.3 #69, 79, 84, 86, 89 14.4 #8, 30, 52, 54 | 13 | 14.4 14.5 | chainRule.pdf |
| F 10/06 | 12 | directional derivatives, gradient | day12.pdf | 14 | 14.6 | |
| M 10/09 | 13 | optimization | day13.pdf | 15 | 14.7 | optimization.pdf |
| W 10/11 | 14 | Lagrange multipliers | day14.pdf | 16 | 14.8 | multipliers.pdf |
| F 10/13 | 15 | double integrals | 15.1 #6, 12, 15, 19, 32, 34. 55 | 18 | 15.1 | integration.nb |
| M 10/16 | Midterm Break | |||||
| W 10/18 | 16 | double integrals | 15.2 #1, 5, 7, 11, 9, 20, 25, 36, 65 | 18 | 15.2 | |
| F 10/20 | 17 | polar integrals | 15.3 #7, 11, 18, 23, 38, 46 | 19 | 15.3 | accelerometer.pdf |
| M 10/23 | 18 | applications, triple integrals | day18.pdf | 20 | 15.4 15.6 | |
| W 10/25 | 19 | triple integrals, cylindrical | 15.6 #19, 55 15.7 #9, 15, 21, 22, 28 | 21 | 15.6 15.7 | cylSph.pdf |
| F 10/27 | 20 | cylindrical, spherical integrals | day20.pdf | 22 | 15.7 15.8 | |
| M 10/30 | 21 | vector fields | 16.1 #3, 13-18, 19-22 16.3 #3, 4, 5, 8 | 23 | 16.1 16.3 | vectorFields.nb |
| W 11/01 | 22 | potential functions, line integrals | day22.pdf | 25 | 16.3 16.2 | |
| F 11/03 | 23 | line integrals, fundamental theorem | day23.pdf | 26 | 16.2 16.3 | |
| M 11/06 | 24 | Exam C | ||||
| W 11/08 | 25 | fundamental theorem, Green's theorem | 16.3 #35, 42c 16.4 #1, 2, 3 | 27 | 16.3 16.4 | |
| F 11/10 | 26 | Green's theorem, divergence | day26.pdf | 28 | 16.4 16.5 | div.nb |
| M 11/13 | 27 | divergence, curl | day27.pdf | no | 16.5 | curl.nb gradCurlDiv.pdf |
| W 11/15 | 28 | review | review.pdf | |||
| S 11/19 | Exam D 3:30-6:00 |