Below, I discuss
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 roughly where you 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. 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).
Reading technical material is an extremely valuable skill, and one that takes practice to maintain. One of the goals of this class is that you continue in the process of becoming comfortable reading mathematical prose.
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 will post questions on the web that cover each day's reading. You will send the responses to those questions to me 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 two scores at the end of the semester. People who do not miss any reading assignments will receive a small amount of extra credit.
Mathematics in the real world is usually done as a combination of group and individual efforts. In such situations, it is important that you are able both to work on your own and e to communicate complicated ideas to others. For that reason, your weekly problem sets will alternate between being done individually and in groups.
Problem sets will be due every Tuesday at 1:00pm at the latest (you may certainly turn them in earlier.)
Your assignments will be posted on the web. The assignments can be found through links toward the bottom of the course web page
Begin the week's problems on Wednesday -- they represent a week's worth of learning.
Consult the Guidelines for Homework Presentation for information on how your problem sets should look.
|Late problem sets will not be accepted!|
To give you an opportunity to solve problems that are more realistic--problems which do not necessarily have one ``right'' answer, or which can be approached in a variety of ways, and which take several days of pondering and working to solve to your satisfaction--you will work on three projects, in groups, this term.
You will have one or two days of class time to work on these projects; the rest of the work you will do outside of class. The project consists not only of the mathematical solution to the situation, but (equally importantly) your description of the solution and why it is true -- in the form of a letter.
Do I accept late projects?
Only in case of dire emergency! Because projects are worth a sizable chunk of your grade, I am reluctant to give all the members of a group a zero when the fault may have only been due to one person. However, unless the group has an irrefutable reason for turning in the project late, I take off significant points for each day the project is late. Even if your group does have a good reason, I may take off some points for each day the project is late, particularly as time goes on.
The first half of the semester will be focused on the theory and applications of integration and antidifferentiation. As a small part of this, we will develop methods for antidifferentiating more complicated functions than you could do in Calculus I. Because antidifferentiation is so fundamental to your understanding and use of 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. If you pass it before the deadline, you get 100% on the exam, and that's the really good news.
The exam is scheduled for 3/5/02. If you pass it the first time you take it, or any subsequent time on or before Tuesday 3/26/02 at 4pm, you receive 100% on the exam. If you pass it after 3/26/02 (at 4pm) but on or before 4/1/02 at 3pm, you will receive 80%. If you pass it after 4/1/02 (at 3) but on or before 4/22/02 (at 3), you will receive 50%. You will not receive any credit for passing the exam after 4/22/02 at 3pm.
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. The dates of these exams are fairly firmly scheduled, and are listed on the course syllabus.
Each of these will take an hour (or perhaps a little more) to complete and will be given during lab. 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 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 have two parts, a take-home component and an in-class component. The take-home component will be due at 2pm on Monday May 6, and the in-class component will be from 2-5 on Monday May 6. I will not reschedule final exams.
Notify me in advance if you will be missing a midterm 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. Unfortunately, it's not enough to simply ask me ``Did I miss anything?'' -- I can only keep one day's worth of events in my head and may not remember something important. So ask your friends as well!
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. Final Exam: You may only use your own notes and your own textbook for the take-home component. You may not discuss the final with anyone except me: neither a current classmate nor anyone else. You may not look at anyone else's exam of course. You may use Maple or a graphing calculator unless I have specifically instructed you not to.
Department of Mathematics and Computer Science
Science Center, Room 109
Norton, Massachusetts 02766-0930
TEL (508) 286-3973
FAX (508) 285-8278