Instructor: Fred Goodman
Office: 325G McLean Hall
Phone: 335-0791
Office Hours: To Be Arranged
A thorough knowledge of elements of differential and integral calculus, and applications; confidence and self reliance in problem solving and calculation.
Ellis and Gulick, Calculus with Analytic Geometry, 5th edition, required.
1. Classes on Mondays, Wednesdays, Thursdays and Fridays at 1:30, participation mandatory.
2. The Mathematics Tutorial Laboratory on the third floor of McLean Hall is available for tutorial help with the course material. The laboratory also has computer aided instruction material which may aid your understanding. Participation is optional, but highly recommended.
Mathematica and Maple are two general purpose mathematics programs which can do symbolic, numerical, and graphical computations which are useful for doing calculus. Both are available on university computers under a site license. I prefer Mathematica just because I'm used to it. I will provide some Mathematica demonstrations of calculus concepts with which you can experiment.
The Calculus Wiz is an add-on to Mathematica written by University of Iowa Professor Keith Stroyan. It is organized around calculus topics and can be used to solve most standard exercises in a standard calculus course. It is useful for checking your homework, and as a tutorial aid. It is available on some university computers, and is for sale for personal computers at the local bookstores. It is a much better value than the student answer book available with the text.
Some people like to use graphing calculators, but their capabilities are poor in comparison with a full featured program like Maple or Mathematica. Graphing calculuators will not be allowed for quizzes and tests.
Chapter 1 of the text contains a review of precalculus material, which will be of constant use in the course. You are expected to review this material on your own. I suggest that you do a substantial number of exercises from Chapter 1 to make sure that you have a ready grasp of the material. The staff at the Mathematics Tutorial Laboratory is ready to help you with precalculus material, and, of course, you may also ask me about it during office hours. You might also find other materials helpful, such as texts from previous mathematics courses, precalculus texts used at the University of Iowa or area community colleges, and commercial review books such as Schaum's outlines, etc. The primary responsibility is yours to make sure you do the necessary reviewing.
There are two big concepts in Calculus. The first is differentiation, which is the process of finding the rate of change of a changing quantity. The second is integration, which is the process of finding the accumulated change of a changing quantity. This course will introduce you to both concepts, the relation between them, and some elementary applications.
We will cover Chapters 2-5 and 11 in the text in class.
We will pay particular attention to exercises for which you have to set up and analyze a mathematical model for a verbally described situation. We will also pay particular attention to careful presentation, on paper and at the chalkboard, of exercise solutions.
We will begin by discussing the idea of differentiation (or the derivative) by examining two fundamental problems: that of finding the velocity of a moving object, and that of find the tangent line to a curve. These problems will lead to the general concept of the derivative. This introduction corresponds more or less to sections 2.1 and 3.1 in the text, but the presentation in class will be more visual, intuitive, and conceptual than that in the text. This introduction will take up the first 4-5 days of class time.
After that we will proceed with Chapters 3-5 and 11 of the text, with occasional forays into Chapter 2 (which logically ought to preceed the rest of the course, but pedagogically should come later).
Homework will be assigned weekly; many problems will be assigned, and among them a few will be singled out as "presentation problems." These are to be written out carefully and completely, with the logical steps explained. The criterion for having done this well is that a person who knows some calculus but has not done these problems should be able to understand completely how to do the problem by reading your paper. The examples in the text can serve as a model for your write-up of the presentation problems. In particular, what you hand in will not be the scratch paper on which you first figure out the problem. Some of these problems will be graded. The non-presentation problems will be spot checked for reasonable completeness.
The homework will be due on Friday each week in class.
There will be quizzes every second Friday in class. The material to becovered on each quiz will be announced ahead of time.
There will be two midterm exams on September 24 and October 22 (Fridays) in class.
There will be a two hour, comprehensive final exam at the time announced in the Fall 1999 course schedule.
Grades will be determined according to the following scheme: homework, 10%, quizes, 15%, two midterms, 30%, final exam, 40%.