MC 21 -- Calculus I
Fall 1998
Moira McDermott

Calculus in many ways is the culmination of 17th century European mathematics. Problems in integral calculus (finding complicated areas) and differential calculus (finding instantaneous rates of change and tangents) date back to antiquity, but the genius of Newton and Leibniz was connecting differential and integral calculus with ``The Fundamental Theorem of Calculus''. The presentation of the material in the course does not represent the historical development of calculus which was piecemeal and halting. The topics are covered with the intention of building each new idea upon the previous ones, therefore keeping up with reading and homework is crucial.

The calculus is the greatest aid we have to the application of physical
truth in the broadest sense of the word. - W. F. Osgood

Office: OHS 313
Office phone: 933-7478
E-mail: mmcdermo

Web Page: http://www.gac.edu/~mmcdermo/mc21f98.html

I will post announcements, course information and assignments here.

Office hours: MTR 2:30-3:30, F 9:00-10:00 and by appointment.

I will be in my office and available for questions, discussion, and general conversation at the above times. If you can't come during any of these times, please call or e-mail and make an appointment. Please do not hesitate to come see me--in fact, I strongly encourage you to do so.

Prerequisites: Two years of high school mathematics beyond plane geometry, including trigonometry, or MC20.

Text: Single Variable Calculus, Early Transcendentals, Third Edition by James Stewart.

Exams: We will have three exams during the semester and a cumulative final exam. The exams during the semester will be given in the evening. They are tentatively scheduled for September 30, October 29, and November 24.
The final exam will be given December 14, 8:00-10:00 a.m., in OHS 103.

Evaluation: Your course grade will be determined using the following percentages as a guide:

Homework, Projects 30%

Class work, Labs 10%

Exams* 60%

*Final counts twice, drop lowest of five exam scores)

Academic Integrity: The academic honesty policy can be found on page 31 of the 1998-1999 college catalogue. I call your attention to the following excerpt: "In all academic exercises, examinations, papers, and reports, students shall submit their own work. Footnotes or some other acceptable form of citation must accompany any use of another's words or ideas."

Class Format: We learn by thinking and doing, not by watching and listening. Learning is an active process: it is something we must do, not have done to us. Class time will be a mixture of lectures, discussions, problem solving and presentation of solutions. At various times you will be asked to present problems, reflect on the reading and generate questions for your classmates. It is essential that you come to class prepared to do the day's work. In particular, you should read the text and attempt homework before coming to class. Class meetings are not intended to be a complete encapsulation of the course material. You will be responsible for learning some of the material on your own.

``A good lecture is usually systematic, complete, precise -- and dull; it
is a bad teaching instrument.'' -- Paul Halmos
``The best way to learn anything is to discover it by yourself... .
What you have been obliged to discover by yourself leaves a path
in your mind which you can use again when the need arises.''
-- George Polya

Homework: Weekly assignments will be due at the beginning of class on Fridays. I do not accept late homework. There are two types of homework in this course, daily practice exercises and weekly homework. The weekly homework problems will be carefully graded. Daily exercises will not be graded, but I will ask students to present solutions or ask questions about them in class. I reserve the right to collect them or to have quizzes if the need arises. You are allowed (even encouraged) to work together. However, ultimately you must work the problems and write up the assignment entirely by yourself.

I hear, and I forget;
I see, and I remember;
I do, and I understand.
-Proverb

Advice from Your Peers:
When asked what advice they would give a student about to take Calculus I, previous students most often responded with the following suggestions:

Study frequently, in small doses.
Work on calculus every night. Stay caught up with the homework.
Read the text sections to be covered before and after class.
Ask questions early and often. Don't just assume you'll figure it out later.

Course Objectives:

To reinforce prior understanding of functions.
To understand what a derivative is, how to find derivatives (limits, formulas), and how derivatives can be used.
To understand what definite integrals are (areas, accumulation of change, Riemann sums) and how to find them.
To develop critical thinking and problem solving skills.
To have fun doing mathematics.

Area D: Calculus I (MC21) satisfies the Quantitative Reasoning criteria of Area D.

Knowledge of the language of mathematics and logic. (understanding of the notion of function, limit, derivative and integral)
Familiarity with logical or algorithmic methods of symbolic reasoning (finding limits, derivatives, antiderivatives and definite integrals)
Knowledge of the practical applications of mathematical modeling and axiomatic systems (applications of derivatives in physical, biological and social sciences)
Appreciation of the role of the formal sciences in the history of ideas, and their impact on science, technology, and society (historical development of calculus)

Course Outline: We will proceed through most of chapters 1 through 5 in Stewart.

Tentative Schedule:

Week Dates Sections Topic Other Info

0 9/9 - 9/11 0.1 Introduction, Functions

1 9/14 - 9/18 0.5, 1.1-1.4 Tangents, Derivatives, Limits

2 9/21 - 9/25 1.5-1.7, 2.1 Limits, Continuity, Derivatives

3 9/28 - 10/2 2.2,2.3 Formulas, Applications, Trig Review Exam I,9/30

4 10/5 - 10/9 2.4, 2.5 Trig Functions, Chain Rule Nobel Conf.

5 10/12 - 10/16 2.6-2.8 Implicit Differentiation, 2nd derivatives

6 10/19 - 10/23 2.9, 2.10 Linear approximation, Newton's method Break 10/23

7 10/26 - 10/30 3.1 Exponential functions and their derivatives Break 10/26,
Exam2 10/29

8 11/2 - 11/6 3.2-3.5 Inverses, Logs, Exponentials

9 11/9 - 11/13 3.6, 3.8, 4.1-4.3 Inverse Trig, Mean Value

10 11/16 - 11/20 4.4-4.8 Concavity, Max-Min, Applications

11 11/23 - 11/27 4.9 Antiderivatives Exam 3 11/24
Thanksgiving

12 11/30 - 12/4 5.1-5.4 Definite Integrals

13 12/7 - 12/11 5.4-5.6 FTC, Substitution

Week	Dates	Sections	Topic	Other Info
0	9/9 - 9/11	0.1	Introduction, Functions
1	9/14 - 9/18	0.5, 1.1-1.4	Tangents, Derivatives, Limits
2	9/21 - 9/25	1.5-1.7, 2.1	Limits, Continuity, Derivatives
3	9/28 - 10/2	2.2,2.3	Formulas, Applications, Trig Review	Exam I,9/30
4	10/5 - 10/9	2.4, 2.5	Trig Functions, Chain Rule	Nobel Conf.
5	10/12 - 10/16	2.6-2.8	Implicit Differentiation, 2nd derivatives
6	10/19 - 10/23	2.9, 2.10	Linear approximation, Newton's method	Break 10/23
7	10/26 - 10/30	3.1	Exponential functions and their derivatives	Break 10/26, Exam2 10/29
8	11/2 - 11/6	3.2-3.5	Inverses, Logs, Exponentials
9	11/9 - 11/13	3.6, 3.8, 4.1-4.3	Inverse Trig, Mean Value
10	11/16 - 11/20	4.4-4.8	Concavity, Max-Min, Applications
11	11/23 - 11/27	4.9	Antiderivatives	Exam 3 11/24 Thanksgiving
12	11/30 - 12/4	5.1-5.4	Definite Integrals
13	12/7 - 12/11	5.4-5.6	FTC, Substitution