### Overview

Very few things in this world are constant - Most things change: public opinion; your annual income; the speed of a car; your eating habits. Calculus is the language of change. It allows us to describe and predict the behavior of changing quantities.

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

Two of the goals of this course are that you learn to read a math text and that you learn to communicate mathematics with other students. Mathematics is a very personal discipline that is best learned by doing rather than by observing.

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 dates for the exams are given on the syllabus. I will give you a set of sample problems before each exam, and we will have a question and answer session before each exam to discuss the sample problems.

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

### Differentiation Exam

One of the fundamental skills you will learn this semester is how to differentiate, or find the derivative of a function (Don't worry about what this means. . . you'll find out soon enough). The Differentiation Exam will be a one page exam that is graded with no partial credit. You either get every problem correct, or you get no credit for the exam. However, you may retake a similar exam as many times as you need until you pass.

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

There will be three group projects assigned during the semester. You will have two class periods to work together on the project, and your written report will be due a week or so later (see the syllabus for specific dates).

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

Homework will be collected approximately 20 times during the semester (see the syllabus for the specific days that homework is due). Three or so problems will be graded from each assignment, with each problem graded fairly leniently and assigned a score of 0, 1, or 2. The most important aspect of the homework is that you make an effort on every problem!

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.
In order to give you some time to look over your assignment after you have asked questions, I will leave 10 minutes of class to answer questions on the homework during the class meeting \textit{before} the homework is due. For example, if homework is due on Wednesday, I will answer questions on Monday. The homework is due in my office by 4:00 on the due date. Be aware that
Late homework is not accepted! No exceptions!!
You will be allowed to drop two homework assignments at the end of the semester.

I will put a copy of each reading assignment on the Math 101 homepage Each assignment will indicate which parts of the section are especially important and which can be skipped. Each assignment will also have three (or so) questions that you should be able to answer after you have read the section.

### Class Attendance

Although 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 Help

Please 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.

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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Wheaton College, Norton, Massachusetts