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.

• 25 August 2009 (Section 12.1, Space Coordinates)
• 26 August 2009 (Section 12.2, Vector: addition and scalar multiplication)
• 28 August 2009 (Section 12.3, Dot Product)
• 31 August, 2009 (Section 12.4, Cross Product)
• 1 September, 2009 (Section 12.5, Lines and Planes in Space)
• 2 September, 2009 (Section 12.6, Cylinders and Quadric Surfaces)
• 4 September, 2009 (Sections 13.1, 13.2, Vector Valued Functions: space curves and their derivatives)
• 7 September, 2009 (Sections 13.2, 13.4 Vector Valued Functions: space curves, tangents and velocity)
• 8 September 2009 (Sections 13.2 and 13.3, Integration and Arclength)
• 9 September, 2009 (Section 13.3, Arclength, Curvature and the Normal Vector to a Curve)
• 11 September, 2009 (Section 13.4, Physical Interpretation of Curvature, Tangent Vector, etc.)
• 16 September 2009 (Section 14.1 Functions of Two or More Variables)
• 18 September 2009 (Section 14.3 Partial Differentiation)
• 21 September 2009 (Section 14.4, Tangent Plane and Differentiability)
• 23 September 2009 (Section 14.2: Limits and Continuity / Section 14.4 Differentiability)
• 25 September 2009 (Section 14.5: Chain Rule and a better way to do Implicit Differentiation)
• 28 September 2009 (Section 14.6, Gradient Vectors and Directional Derivatives)
• 29 September 2009 (Section 14.7, Local Extrema)
• 30 September 2009 (Section 14.7, Global Extrema)
• 2 October 2009 (Section 14.8, Lagrange Multipliers)
• 7 October 2009 (Double Integrals: Section 15.1, Riemann Sums / Section 15.2 Fubini's Theorem)
• 9 October 2009 (Section 15.2, Iterated Integrals continued / Section 15.3, General Regions Part I )
• 14 October 2009 (Section 15.3, More General Regions)
• 16 October 2009 (Section 15.4, Double Integrals in Polar Coordinates)
• October 19, 2009 (Section 15.5, A Few Applications of Double Integrals / Section 15.6, Triple Integrals)
• October 20, 2009 (Section 15.6, Applications of Triple Integrals)
• October 21, 2009 (Section 15.7--15.8, Cylindrical and Spherical Coordinates)
• October 26, 2009 (Section 15.9, Change of Coordinates in Integrals)
• October 27, 2009 (Section 16.1, Vector Fields)
• October 28 and 30, 2009 (Section 16.2, Line Integrals)
• November 4, 2009 (Section 16.3, FTC for Line Integrals I)
• November 6, 2009 (Section 16.3, FTC for Line Integrals II)
• November 9, 2009 (Section 16.4, Green's Theorem)
• November 11, 2009 (Section 16.5, Div and Curl)
• November 13, 2009 (Section 16.6, Parametrized Surfaces)
• November 16, 2009 (Section 16.7, Surface Integrals - Part I)
• November 17, 2009 (Section 16.7, Surface Integrals of Vector Fields and Orientations of Surfaces)
• November 18, 2009 (Section 16.7, Some Examples of Flux Integrals)

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: September 15, October 6, November 3, and November 24

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 first and 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: The final exam for this course will be held on Friday December 11th from 8:00-11:00AM in our usual classroom. Note that this is the time scheduled for this course based on the time that we meet. There should not be any conflicts with this time since only exams for courses that meet at noon on Monday can be given at that time. This is the only time at which you will be able to take the exam for this course (not earlier or later).

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.

• 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.