Math 221 / Multivariable Calculus Spring 2016 Syllabus
Professor: Alex Kasman
kasmana@cofc.edu / 336 Robert Scott Small Building / 843-953-8018
Course and Section Number:MATH 221 SECTION 02
Office Hours: Mon 1-2, T 2-3, W 9-10

Please visit me in my office during these times if possible. I am often in my office at other times and do not mind at all if you drop by to talk, though I cannot guarantee that I will always be there or have time to meet. If you are unable to see me during my office hours and cannot find me at other times, just contact me by phone or e-mail and I will find an alternative time to meet with you.

NOTE: As part of a policy that has proven to be very effective, I will require every student in the class to meet me in my office for a short discussion at least once between the first test and the last day of class. The meeting can be during any one of my regular office hours or at another time either by appointment or drop-in. We can discuss the class or anything else you'd like to talk about. This meeting is not optional: you must meet with me in order to pass the class.

Math Lab: The ``Math Lab'' in the Addlestone Library provides tutors who can help you with your work in this class. In theory, you could go anytime that the Lab is open for help, but in my opinion some of the tutors are not familiar enough with the material from MATH 221 to be of much assistance. I will try to find out which tutors can best help and get you that information soon, but if you find out through your own experience, please let me know.
Class Meeting Times:We meet in room Maybank 223 four times per week: MWF 10:00-10:50AM and Tuesday 9:25-10:40AM.
Lecture Notes: I will prepare lecture notes for each class reviewing the key ideas and assigning homework problems. They will be available in the "Content" section on the course OAKS page.
Graded Work: Your grade in this class will be based on: tests, group projects, homework and the final exam.

Tests: A test in this class, as in any college level course, is an opportunity for you to demonstrate to me how well you understand the material we have covered. Consequently, there will be questions of varying levels of difficulty. Some questions could be answered correctly by anyone who has been paying attention, others cannot be done perfectly unless you have a good grasp of the subject and still others are so hard that only the top students in the class will be able to answer them at all. There will be tests in class on the following dates: February 9, March 1, March 29, and April 12.
Group Projects: During every class which takes place on a Tuesday (except the first) there will be either a test or a group project in class. The dates of the tests are listed above. Except on those dates, every Tuesday will be a group project. The questions on a group project will be more thought provoking than ordinary homework questions. Each student will work with one or two other students on the questions and they will turn in a single set of answers collectively. Any resource is available to you during a group project; you can use your notes, your textbook or even ask questions of other students in the class.
Homework: Many homework problems will generally be assigned at each class meeting. Two of these problems will be singled out as problems to be collected. Every Tuesday (except for the four test days), these (approximately 8) problems will be turned in and some (not all) of them will be graded. However, it should be noted that it will not be sufficient for you to do only those problems which are singled out for collection. It is expected that you will do all of the assigned problems. I believe that doing so is necessary for learning the material well enough to pass the tests.
Final Exam: Our final exam is scheduled for Monday April 25 from 8:00-11:00AM in 223 Maybank Hall. The final exam for this class will be approximately as long as two of the class tests. Questions on the final can and will test material covered throughout the semester.

Final Grade: Your final grade will be based on one of these two grading schemes. Both schemes add up to 100%. I will compute your grade both ways and give you whichever grade is higher.
Drop Lowest Test:
0% for your lowest test grade
45% for other tests (15% each)
45% for the final exam
5% for group project grade
5% for homework grade
Discount the Final:
65% for all four tests
25% for the final exam
5% for group project grade
5% for homework grade
Letter grade correspondences (what grade you need to get on a test in order to get an A or a C+, for example) are not determined in advance but rather will be determined by the class performance on that assignment. In other words, the grades are "curved" in such a way that the cutoff for a B- will be near the average grade and the top scores earned in the class will be given an A.
Attendance Policy: Of course, effort and attendance can affect how well you do on these graded assignments, but they will not have a direct influence on your grade. In particular, I do not keep a record of who attends or misses each class and do not take effort into account when determining grades.
"Make-up" policy:With very few exceptions, the policy in this class is that there is no way to make up a missed test, project or exam. If you miss a test, that test counts as your "lowest score" and is dropped even if it was missed for a valid reason such as illness or participation in an official College event. If you have a valid excuse for missing a group project, that also will be dropped so that it does not count against you, but you will not have an opportunity to make it up.
Textbook: The required text for the class is Calculus (Early Transcendentals) by James Stewart (Sixth Edition). You must buy the big version of the book with chapters going all the way up to Chapter 16. You cannot use the one that says "Single Variable" over the title because it does not contain the material we will cover in this class. If you find a copy of the book that does not say "Early Transcendentals" over the title or one that says "Multivariable" only you will be confused by the fact that chapter and question numbers will be different.
Material to be Covered: We will cover Chapters 12 through 16 in Stewart's book (possibly skipping a section here or there if we run out of time, and including some sections from Chapter 10 that might prove useful to us).

Since you all already know some calculus, I can easily explain the basic idea of this class to you. In your previous classes, you were always dealing with functions whose input and output were each just a single real number. For example, the function f(x)=2x+5 takes a number like 2 as input and gives the number 9 as output. However, in most realistic situations, functions are more complicated objects. In the real world, we have to deal with functions whose domain and range live in higher dimensional spaces. So, in this class we will learn a little about the geometry of these higher dimensional spaces, and then see that (with small modifications) the rules of calculus can be applied there as well. For instance, our ultimate goal in the class is to get up to learning about Stokes' Theorem and the Divergence Theorem (sections 16.8 and 16.9) which are higher dimensional generalizations of the Fundamental Theorem of Calculus that you learned about in Calc 1.

Specific Learning Outcomes Upon completing this class, students will be able to:
  • Identify, sketch and parametrize surfaces and space curves. Identify and plot vector fields.
  • Algebraically manipulate vectors using the dot product, scalar product and cross product to answer geometric questions.
  • Apply differentiation and integration to parametrized curves to draw conclusions about the geometry of the curve or about the trajectory of a particle.
  • Compute, interpret, and apply various kinds of derivatives of multi-variable functions (whether scalar functions or vector functions).
  • Solve multi-variable optimization problems, both constrained and unconstrained.
  • Set up, evaluate, and apply integrals over two or three dimensional regions, using various coordinate systems and various orders of integration.
  • Convert multiple integrals between different orders of integration and/or different coordinate systems.
  • Evaluate and apply line integrals and surface integrals of both scalar functions and vector fields.
  • 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.
Disability Accomodations: The College will make reasonable accommodations for persons with documented disabilities. Students approved for accommodations by the Center for Disability Services must notify Professor Kasman at least one week before they are required.
Mathematics Program Student Learning Outcomes 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.
WARNINGS AND ADVICE:
  • The material in this course is very challenging. Not only do some of the problems take a long time and a lot of technical skill to work out, there are some really big ideas. So, the course will not only develop your skills but also your ability to think logically about abstract mathematical concepts.
  • Even though we are not checking all of your homework, doing all of your homework is important. I will start each lecture by asking if there are any questions from the homework. I believe that your effort in doing the homework and this opportunity to ask questions about it are the most important part of the class. In fact, I think it is safe to say that unless you do your homework on-time and completely, your grade will suffer as a consequence. (Duh!)
  • Many students find themselves in trouble towards the middle of this course when the material gets much harder very quickly. In order to avoid this problem, I suggest that you do not get into the habit of "blowing off" the work in this class at the beginning when it is relatively easy. You can only get a good foundation upon which to understand the more difficult concepts if you spend some time and effort on really understanding the early stuff.
  • I will not have time to discuss all of the details in class. This does not reflect poorly on my teaching; it is simply a fact that in the chapters we are covering there is a lot of material. I will do my best to select the most important topics and make sure that those are fully discussed during lecture. In fact, I think you can probably pass the class knowing only those things I discuss in lecture. However, it is expected that you will be reading the book as we go through it. Reading the book (a difficult task in itself, which might require some learning on your part) will be necessary if you plan to do well in the class.
  • Expect to have to develop some new ways of working on and thinking about mathematics in this class. In many of your previous classes, it was probably possible to think of math as a series of steps to be memorized and performed. That method stops working at the higher levels of mathematics and this course is one in which many students first encounter this difficulty. Simply put, I believe the only way to succeed in this class is to learn the subject not as a list of techniques to remember, but as objects and deep facts about them that you must understand.
  • Cheating is not allowed. (Obviously.) But, it may not be clear what constitutes cheating in this class. Therefore, I have prepared a separate document (available under "Content / Resources" on the OAKS page) which explains in great detail what sort of activities will be treated as cheating under the honor code in this course.