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.

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 5, February 26, March 26, and April 16.

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 Wednesday May 1 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.

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.

• Identify space curves and surfaces given in the parametric or implicit form.
• Use the algebra of the dot and cross products to answer questions about geometry in 3-dimensional space.
• Decompose the acceleration of an object moving in 3-dimensional space into its tangential and normal components and physically interpret the results.
• Compute partial derivatives and directional derivatives and use them to analyze the qualitative behavior of a function of more than one variable.
• Identify solutions of a given partial differential equation.
• Find and classify local and global extrema of functions of two variables.
• Approximate double-integrals using Riemann sums.
• Use Fubini's Theorem to find the exact value of double and triple integrals.
• Construct iterated integrals whose value would answer given questions about volume and mass of an object occupying a specified region in space.
• Change coordinates to evaluate double and triple integrals (this includes both the ability to perform such computations and the ability to determine when it is necessary)
• Write and evaluate path integrals and surface integrals of vector fields to answer specified questions of physical or geometric significance.
• Compute the divergence and curl of a vector field and use them to answer questions about the qualitative behavior of that vector field.
• Find potential functions for conservative vector fields and recognize non-conservative vector fields.
• Use the higher dimensional versions of the Fundamental Theorem of Calculus (e.g. Green's Theorem, Stokes' Theorem and the Divergence Theorem) to convert an integral over an n-dimensional object into an integral over an n+1-dimensional object and vice-versa (this includes both the ability to perform such computations and the ability to determine when it is necessary.) Note that doing so will demonstrate an understanding of the theoretical relationship between the different types of derivatives and integrals in R³ separate from any particular application.
• Create higher dimensional mathematical models and use them to establish conclusions regarding the phenomenon being modeled.

• 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.