Calculus, Fall, 1998
Instructor: James A. Davis Office hours: M-Th 10-11
206 Jepson Hall or by appointment
Math 211 is an introduction to calculus, the mathematical language of change. Calculus is used to model phenomena in a surprisingly wide variety of applications in such areas as the physical sciences, economics, epidemiology, and personal finance.
Students in Math 211 will be expected to develop skills in formulating problems, solving them, and communicating their solutions to others (usually in written form). Successful formulation of a problem often requires that the student recognize how the basic concepts of calculus are involved in the problem at hand, and be able to translate the problem into appropriate symbolic form. This process of formulation and solution helps students to develop analytical thinking skills applicable in a wide variety of situations. Some problems are designed to have students construct and analyze mathematical models of real world phenomena, while other problems help students make conceptual leaps from specific examples to general principles.
The main concepts in the course are the derivative and the integral, both of which require the underlying notion of limits. These ideas are amenable to both geometric and analytic interpretation, and both points of view will be stressed. Indeed, this course will emphasize the importance of being able to move easily back and forth between these two points of view. Students will be expected to develop some proficiency with techniques for evaluating derivatives and integrals, but only to provide the framework needed for solving problems.
The above quote is the rationale for Math 211 meeting the symbolic reasoning requirement, and it is a good description of what we will be studying this semester. Calculus is one of the greatest intellectual achievements of all time, and we will try to understand why it is so important.
Although many of the people in this class will have heard the words listed above, no prior experience in Calculus is required other than those listed in your freshman guide (if you have any questions about the level course that you should take, come talk with me as soon as you can). For those of you that have taken a calculus course, let me give you an important warning: this course will be different than the one most of you took in high school. We will be using some of the same words that you are familiar with, but the level of understanding that we expect in college is higher than what you are used to. In addition to this, we are using a textbook this year that will emphasize different aspects of the course than you are used to.
When approaching problems, we will use the ``rule of 3'' as described in the book. The rule of 3 asks you to view the problem algebraically (in terms of formulas), tabularly (in terms of tables), and geometrically (in terms of pictures). In addition to this, there is a 4th rule that I call ``verbal'': you must be able to express your answers in complete sentences that make grammatical sense as well as mathematical sense.
As often as possible, I will have you working in groups on problems. Part of your grade will be determined by how enthusiastically you work on these group work problems. Each time that we do this, I will choose one of the groups to report on their findings of the problem. Everyone else should be ready to discuss alternative ways to look at the solution. The idea behind this method of teaching is that you learn more when you are participating rather than observing. We will always have time for questions, and I will spend a little time lecturing on important topics.
We will use the book Calculus by Hughes-Hallett, Gleason, et. al. We will cover the first 6 chapters, including topics such as the derivative, the integral, and the Fundamental theorem of Calculus. At the beginning of the course, we will focus on building up a library of functions that will be used throughout the course. Our emphasis throughout the entire course will be to use these functions to model real world situations, and then use calculus to analyze those situations.
GRADING: Three hour exams (100 pts each) 300 pts
Exam dates: 9/24 10/27 11/24
Quizzes (20 pts each) 100 pts
Approximately 7 quizzes will be given; your
score will be the sum of the best 5. No
make-up quizzes will be given for any reason.
Homework grade 100 pts
You will turn in weekly homework assignments
Group work grade 50 pts
Final Exam (Tuesday December 15, 9-12) 200 pts
TOTAL 750 pts
(NOTE: You can get 10 bonus points for attending a lecture sponsored by the math and computer science department)