OverviewThis course is a continuation of the topics covered in Calculus I and Calculus II. In Calc I and II, you dealt mainly with functions f(x) of one variable. As you may expect, in Multivariable Calculus we'll be studying functions f(x,y) of two variables, where things suddenly become much more complicated, and much more interesting. Many of the topics we will cover this semester allow us to solve many problems that do not seem to be immediately related to calculus. Here is one of my favorites:
Many small rectangles are combined to form one large rectangle. If each small rectangle has one pair of sides of integer length (but not necessarily both pair of sides), does the large rectangle have one pair of sides with integer length?
Reading the Text and Working with Other StudentsTwo of the goals of this course are that you learn to read a math text and that you learn to communicate mathematics. Mathematics is a very personal discipline that is best learned by doing rather than by observing. Many of the assignments this term will be group assignments where you will work in groups of two or three (of your choosing). Each assignment will receive a grade, and the group will determine how the points are allocated to each member. For example, if a group of three receives an 85 on an assignment, then the group will have 3 x 85=255 points to distribute among them. I will be available to mediate this process, if necessary. You will have a reading assignment for nearly every class meeting, and it is extremely important that you complete the reading before the next class meeting!
EvaluationYour final grade will be determined by
ExamsOn each of the two exams, there will be a short inclass part and a more substantial takehome part. The Final Exam will be entirely takehome. See the Tentative Syllabus for the dates of the exams.
Major ProjectsThere will be two group writing projects and an individual Maple project assigned during the semester. You will have one class period to work together on each group project, and your written report will be due about a week and a half later (see the syllabus for specific dates). I will give you the individual project with plenty of time to complete it. One of the main goals of the writing projects is that you learn to communicate mathematics precisely, both verbally with your group and in writing. The reports should be written in complete sentences explaining the results and major ideas involved. You may divide the writing of the report in whatever way is agreeable to the group, but everyone should completely understand the whole of the paper. Further, each member should proofread the entire paper for consistency and typos. I will give you a handout that explains my expectations for the written reports in more detail.
HomeworkHomework will be collected most Fridays, and I will grade four problems from each assignment. Each problem will be receive a score between 0 and 5, and I will give you solutions to the entire assignment. The homework assignments will vary between Individual assignments and Group assignments. For the Group assignments, each group will turn in one paper. On each assignment, one student will be designated as the primary author who writes-up the solutions. The role of primary author must rotate among the members of the group. For the Individual assignments, I encourage you to work with other students, but each person must turn in a separate paper. students, but each person must turn in a separate paper.
Here are a few guidelines for the presentation of your homework. If you do not follow these, I reserve the right to return your homework ungraded!
The text believes that you can think. There will not be an example worked exactly like every homework problem.
Reading AssignmentsI will put a copy of each reading assignment on the Math 236 homepage. Each assignment will indicate which parts of the section are especially important and which can be skipped. Each assignment will also have two or three questions that you should be able to answer after you have read the section.
See the Guidelines for Submitting Reading Assignments for more information.
Class AttendanceAlthough class attendance is not a specified percentage of your grade, I will keep a class roll to help me determine borderline grades at the end of the semester. If you do miss class, you are responsible for the material that was covered.
Getting HelpPlease come see me during my office hours! If you have a conflict and cannot make my office hours, please call or email me and we can set up an appointment for another time.
Hudson River Undergraduate Mathematics ConferenceThe HRUMC will be held on Saturday April 27 at Hamilton College. I would strongly encourage all of you to attend, and you should also consider giving a talk. This is a really nice day to be involved with mathematics with other undergraduates. A good time will be had by all. If you do give a presentation, you will receive an extra 5% on your final grade. Each talk is attended by anywhere from 10 to 50 people, most of whom are other mathematics students from around New England. Before you submit an abstract to give a talk, we will need to discuss your topic and make sure that it is at the appropriate level. I have very high expectations for the quality of these talks so you should expect to devote significant effort to your presentation. I will, of course, work with each of you on your talk. If you decide to attend without giving a talk, you will receive an extra 2% on your final grade.