Overview

One of the recurring themes throughout the semester will be the process of approximation: Although you may not be able to find a solution exactly, in most cases a good approximation serves just as well. One of the beautiful aspects of calculus is that quite often, by taking better and better approximations we can find a precise solution.

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 are just a few:

1. We will show that at any instant, there are two points on the equator which are exactly opposite each other and have exactly the same temperature. (It will not always be the same two points, but there is always at least one pair.)

2. One morning it begins snowing at a heavy and constant rate. A snowplow starts out at 8:00 a.m. At 9:00 a.m. it has gone 2 miles. By 10:00 a.m. it has gone 3 miles. Suppose that the snowplow removes a constant volume of snow per hour (which only seems reasonable). What time did it start snowing?

3. If you listen to the traffic reports in Chicago, they give times like ``It's 25 minutes from the junction to Touhy.'' Clearly there isn't a fleet of cars on the expressways with stop watches. How do they determine the travel times?

4. The Celtics are considering painting the parquet floor inside the 3-point line and outside the key in green (what else?). How much paint will it take?

Reading the Text and Working with Other Students

Therefore, the class will be structured with some lectures to emphasize particular topics, but much of the time will be spent on in-class work. The class meetings are not intended to be a complete encapsulation of the course material -- There will be material in the text for which you are responsible that we will not cover in class.

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 every class meeting, and it is extremely important that you complete the reading before the next class meeting! See the section below on Reading Assignments and the Guidelines for Submitting Reading Assignments for more information.

Evaluation

3 Exams	40%
Differentiation Exam	10%
Comprehensive Final Exam	15%
3 Group Projects	20%
Homework	10%
Reading Assignments	5%

Exams

The final will be a takehome exam and is due Thursday, December 18 at 12:00 noon.

Differentiation Exam

The Differentiation Exam will be given in class on October 29. If you pass the Exam (or any version of it) on or before November 17, you will receive the full 10% credit. After that date (until the end of classes on December 12), you will receive 5%. You are not allowed to take the exam after the end of classes!!

Group Projects

One of the main goals of the 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 ask each person to give a confidential evaluation of the contributions made by all members of the group. I will give you a handout that explains my expectations for the written reports in more detail.

Homework

The homework assignments will alternate 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.

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!

• Your writing must be clear and legible.
• Your homework should be well-written, using complete sentences to justify your results. A list of answers without explanation is not acceptable.
• Here is a good rule of thumb to follow when writing up your homework:

  Write your solutions so that you could hand them to another Calculus I student and they could understand your explanation.

• If you write in pen, there should be no scratch-outs.
• Do not turn in paper torn from a spiral notebook with ragged edges.
• Clearly label each problem.

Reading Assignments

See the Guidelines for Submitting Reading Assignments for more information.

Class Attendance

Getting Help

There will be a student who acts as a Calculus Assistant (CA) for this course. The CA be in class on Thursdays to help answer questions and will also be available in the evenings for two hours each week to answer questions. Please take advantage of this resource!

If you want to know check on your grade at any time during the semester, please ask me and I can give you a rough idea of your current standing.

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