Math 101 - Calculus I - Course Policies

    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. Our main tool will be the derivative function, f ', which tells us how a function f is changing.

    One of the recurring themes throughout the semester is 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 you can find a precise solution.

    We will begin the semester by reviewing some material on functions, graphs, and logarithmic, exponential and trigonometric functions. Next, we will study the very rich graphical relationship between a function f and its derivative f '. We will then begin the quest for finding algebraic expressions for f '. For example, if f(x)=(e^x)*sin(x), what is a formula for f '(x)? We will develop several important tools, called the product rule, the quotient rule, and the chain rule, that will allow us to calculate the derivative of almost every function we will encounter. Armed with these tools, we will be able to tackle several applications, such as finding the optimal size of a soup can to minimize cost or modeling the growth of a population and predicting its size in the future.

    We will take a brief break from finding derivatives to consider carefully what it means for a function to be continuous and what it means for a function to have a derivative. There are three very important theorems that will come out of these considerations: the Intermediate Value Theorem, the Extreme Value Theorem, and the Mean Value Theorem.

    Next, we will look at a question that is seemingly unrelated to the derivative. As a particular example, we will ask, what is the area of the region that is bounded by the curve y=sin(x) and the x-axis between x=0 and x=Pi?

    One of the most beautiful connections in mathematics is that this question is fundamentally related to finding a function whose derivative is sin(x).

    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.

    The class will be structured with some lectures to emphasize particular topics, but much of the time will be spent on in-class group 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.

    You will have a reading assignment for nearly every class meeting, and it is extremely important that you complete the reading before class!

    Evaluation

    Your final grade will be determined by
      3 Exams 40%
      Differentiation Exam 10%
      Comprehensive Final Exam 15%
      3 Group Projects 20%
      Homework & In-Class Worksheets 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.

    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 April 4. If you pass the Exam (or any version of it) on or before April 16, you will receive the full 10% credit. After that date (until the end of classes on May 6), 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 where you will work in groups of two or three. You will have one class period 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 within 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.

    All members of the group will receive the same grade on the project. I will ask each person to give a confidential evaluation of the contributions made by all members of the group. In extreme circumstances, I reserve the right to give different grades to members of the same group.

    I will give you a handout that explains my expectations for the written reports in more detail.

    Homework

    Homework will be collected approximately 17 times during the semester (see the syllabus for the specific days that homework is due). I will grade two or three problems 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, you will work in groups of two or three (of your choosing), each group will turn in one paper, and all members of the group will receive the same grade. 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 turns 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. (I will bring scissors to class so that you can cut off the edges.)
    • Label each page with the section number, and write down the problem number
    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 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.

    Reading Assignments

    I will put a copy of each reading assignment on 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.

    See the Guidelines for Submitting Reading Assignments for more information.

    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.

    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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