Below, I discuss
Course Materials: Calculus, from Graphical, Numerical, and Symbolic Points of View, Volume 2, 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.
This course picks up the study of Calculus where we left off in Calculus 1. Toward the end of Calculus 1, you learned the Fundamental Theorem of Calculus, which gives us the amazing result that antidifferentiation (related to velocities and tangent lines) is very closely tied to integration (finding the area under a curve).
We begin this semester by investigating integration and its applications, drawing on the the understanding of derivatives, tangent lines, and rates of change you developed in Calculus 1. Although the integral is defined to represent area (a 2-dimensional concept), we will learn how we can use integration to calculate volume (a 3-dimensional concept) and arclength (a 1-dimensional concept). We will learn techniques for calculating antiderivatives so that we can more effectively use the power of the Fundamental Theorem of Calculus. And because there are times when an antiderivative simply can not be found, we will investigate methods for approximating area and learn how to estimate the error that comes from these approximations.
In the second half of the semester, we will begin to consider the infinite. Interesting questions arise, many of which have unexpected answers. We will spend much of this portion of the class discussing sums of an infinite number of numbers: it turns out the sum can be finite! But under what circumstances? Wait and learn!
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. In order to get enough out of this course, you will need to spend an average of 9 hours a week outside of class on reading, homework, and projects!
Before each class meeting, I expect you to have read the material that we will be discussing that day. To help you continue to develop your mathematical reading skills, (and to give you credit for your efforts) I have posted questions on the web that cover each day's reading. Send the responses to those questions to me by 8am of the day they are due.
You can find the links to these web pages on the course 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.
You will have problem sets due every Friday. 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 recorder for each problem set, and the recorder must alternate.
I will assign several problems each Friday. The problems can be found through links toward the bottom of the course web page:
You are, of course, responsible for all of them, but you only turn in 3 or 4 of them, which I will specify. On Wednesdays, I will answer questions on a few of the problems I am not collecting. Solutions will be due by 4 pm each Friday.
Consult the Guidelines for Homework Presentation for information on how your problem sets should look.
I do not accept any late problems sets. I plan to drop the lowest problem set score at the end of the semester. Problems sets will probably be graded by a grader. I expect to drop each person's lowest score at the end of the semester.
The first half of the semester will be based upon your ability to antidifferentiate. In addition to using it constantly, we will develop methods for antidifferentiating more complicated functions than you could do in Calculus. Because antidifferentiation is so fundamental to your understanding and using the concepts of the semester, you will be taking an antidifferentiation exam. This 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.
While you may take the differentiation exam as many times as you need to, there is a deadline. The exam is scheduled for 3/7/00. If you pass it the first time you take it, or any subsequent time on or before 3/28/00, you receive 100% on the exam. If you pass it after 3/28/00 but on or before 4/4/00, you will receive 70%, and if you pass it after 4/4/00 but on or before the last day of classes on 5/5/00, you will receive 30%. You may not take the exam after May 5!
I will give three midterm exams, to make sure throughout the semester that you can put the concepts and skills together to solve problems which are somewhat different from those you have seen before.
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.
You will be allowed to bring an 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.
If you are disappointed with your score, you may rewrite the exam, to receive up to 1/3 the points you missed.
We will also, of course, have a cumulative final. This final will be a take-home exam, and will be due at Noon on May 11. Please do not plan on going home before then.
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 to not give you any 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.
Abide by the Honor Code. I take the Honor Code seriously, and will do my best to see that cheating results in a significantly lower grade. Why? Because cheating simply isn't right. Because cheating cheats a person of learning. Because it's not fair to the rest of the class, or to me.
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 (unless groups are assigned). 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 exams, 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