Below, I discuss
Calculus, from Graphical, Numerical, and Symbolic Points of View, Volume 1, by Ostebee and Zorn.
A calculator which is at least capable of evaluating exponential and trigonometric functions is helpful. A graphing calculator is not required.
The text, and a calculator if you have one, should be brought to class every day.
Most everything in the world changes: DNA, the orbits of the planets, weather, shopping patterns, and your annual income, to name a few. You can imagine how valuable understanding, predicting, and being able to affect how these quantities change would be! Calculus is the language of change; it allows us to describe and predict the behavior of changing quantities. In many of these situations, we of course can not predict the behavior exactly, but even a good approximation would be tremendously valuable. Calculus is all about using approximations. Often we can use better and better approximations until, by deducing what would happen if we continued this process ad infinitum, we find a precise solution!
This semester, you will begin to study this language of change. By the end of the course, you'll have the tools necessary to solve many fascinating problems. Many of the topics we will cover this semester allow us to solve problems that do not seem, at first glance, to be mathematical at all.
You will encounter a variety of topics and challenges. Most of the problems you will solve will not be solved by copying examples. Instead, you will be applying mathematical concepts to many different types of problems. You will also be faced with some open-ended questions that you and your colleagues will spend a week or more deciding how best to answer. These non-routine problems will require that you grasp mathematical ideas and communicate mathematics verbally and on paper. This course may present challenges which require more effort than you have previously experienced, but the rewards are far greater as well!
In this class, as with all others, how much you actually learn is entirely up to you. As you read through how the course is structured, you will see that a lot is expected of you. Plan to spend an average of 9 hours a week outside of class working on this course. As usual, some weeks you will spend more time on this class, especially when studying for exams while finishing up projects, while others will be less frenetic (relatively speaking).
Is This the Right Course for You?:
This course is of course intended for students who want to take it, or whose majors (or emphases) require them to take it: Calculus is not required for graduation. Those majors which require Calculus are: Math (of course), Physics, Chemistry, and Environmental Science. Calculus is also recommended for students who are Economics majors or who are Premed.
Students interested in other disciplines are of course welcome and encouraged to take Calculus, but be aware: if you are considering majoring in Economics or Psychology, you will be required to take Statistics. Statistics is also recommended for Sociology and Political Science majors. Early Childhood and Elementary Education minors are required to take Concepts of Mathematics.
Calculus I is intended to be your first exposure to Calculus! If you've had Calculus before, we encourage you to try Calculus II, whether you received credit for Calc I here or not!
Reading technical material is an extremely valuable skill, and is becoming more pervasive in all areas of our lives all the time. One of the goals of this class is that you become comfortable reading mathematical prose.
Before each class meeting, I expect you to have read the material that we will be discussing that day. Many of you have not read mathematics before, so to help you with this (and to give you credit for your efforts!) I will post questions on the web that cover each day's reading. You will send the responses to those questions by 8am of the day they are due.
You can get to the appropriate chapter's web page from the course's web page.
These reading assignments are required, and will be graded out of 2 points each: 2 points if you respond in full (whether correctly or not) and 1 point for a partial response. Late responses will not be accepted. I expect to drop each person's lowest score at the end of the semester.
Learning math is best accomplished through a combination of group and individual efforts. You will have problem sets due every Tuesday at 4pm. They will alternate between being done individually and done in groups.
For the individual problems sets, you may, of course, consult each other, but the final result must reflect your own understanding, word choice, and work!
For the group problem sets, you will benefit most from the experience if you have already made a sincere effort on every problem before your group meets. Points on the group homework will be based on each person's honest assessment of the effort and contribution made by each member. Groups also must make note of who was the primary author for each problem set, and the primary author must alternate.
Your assignments will be posted on the web. While they are posted in advance, make sure to check them each Tuesday, as they are ``subject to change''. The problems can be gotten to through links toward the bottom of the course web page.
Each Monday, I will set aside about 15 minutes to give hints on a few problems you have questions on. Help will also be available Monday nights in A102 (our classroom). Your solutions will be due by 4 pm each Tuesday. To ease the burden on the grader, I will tell her 3 or 4 problems to focus on. Those problems will each be graded out of 5 points (or 10 or even 15, depending on length). The rest of the assignment will be graded out of a total of 5 points.
Consult the Guidelines for Homework Presentation for information on how your problem sets should look.
|Late problem sets will not be accepted! No exceptions!|
I plan to drop the lowest non-zero problem set score at the end of the semester. If it is warranted, I may be persuaded to drop one zero instead.
One of the primary skills you will learn this semester is how to differentiate. The differentiation exam will be a one page exam that is graded with no partial credit. The bad news is, you must get every problem correct to get credit on the exam. The good news is, you may retake versions of this exam as many times as necessary until you pass. At that point, you get 100% on the exam, and that's the really good news.
The exam is scheduled for 4/3/01. If you pass it the first time you take it, or any subsequent time on or before 4/11/01 at 3pm, you receive 100% on the exam. If you pass it after 4/11/01 but on or before 4/16/01 at 3pm, you will receive 80%, and if you pass it after 4/16/01 but on or before 4/20/01, you will receive 50%. You may not take the exam after 4/20!
I will give three exams, to make sure throughout the semester that you have learned to solve problems which are somewhat different from those you have seen before, by putting together the concepts and skills we have covered.
Each of these will take an hour (or perhaps a little more) to complete. They may test some mathematical skills, but the primary emphasis will be to give you an opportunity to show me how well you've mastered the underlying mathematical ideas.
Each exam will be given during lab, and (as there are no classes between 12:30 and 1:00), you may begin taking the exam at 12:30, should you wish. All exams must be handed in at 1:55 ( no matter when you started taking the exam).
You will be allowed to bring one 8.5 x 11 sheet of paper, with handwritten (by you) notes, front only, to use during the exams and to turn in with the exams.
We will also, of course, have a cumulative final. This final will be a pre-scheduled exam, and will be given from 2 - 5pm on Wednesday May 9. I do not reschedule final exams.
Notify me in advance if you will be missing an exam, either by phone or by e-mail. If your reason for missing is acceptable, we will arrange that you take the exam early. If you miss an exam without notifying me in advance, I reserve the right not to give you a make-up exam. I will not give any individual more than one make-up exam during the semester.
Clearly, missing class is not a wise idea. If you do miss class, it is of course your responsibility to find out any assignments, and to get a copy of the notes and of any hand-outs.
I expect to use the weights below, although I reserve the right to change my mind if the semester does not go as expected.
I expect you to abide by the Honor Code. If I have any reason to suspect that perhaps a violation has occured, I will ask the Judicial Board to investigate the matter. Below are some guidelines on what constitutes violations of the honor code in this class.
Reading assignments: You may discuss the questions with your classmates, but you must enter the responses yourself, in your own words.
Homework and Projects: You may work with anybody you want. You may use any references that help you figure out how to do the problem on your own; you may not use any references (people, old projects, books, the web, for instance) which tell you how to solve it or lead you to the solution. You must understand how to do every problem, and you must cite references if you've received assistance from any source. When doing group projects or group problem sets, you may not divide it into different parts--you must do them all together, and you must make sure every member of your group understands every part. Exams: You may not use any notes, books, or colleagues as reference during the midterms and final, except for your ``cheat sheet'', which must conform to my stated rules. You may not use a calculator unless I specify that you may, and you may not use a graphing calculator.
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278