MCS 122 -- Calculus II
Spring 2000

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

This course is a continuation of the topics covered in Calculus I. One of the most fundamental, and most slippery, topics in mathematics is the relationship between the finite and the infinite. A recurring theme throughout the semester will be the relationship between an approximation and the exact value. We will spend quite a bit of time this semester trying to determine just how good any approximation is. One of the most beautiful aspects of calculus is that by taking better and better approximations and extending from the finite to the infinite, we will often be able to find a precise solution.

Web Page: http://www.gac.edu/~mmcdermo/mcs122/s00/mcs122s00.html

Announcements, course information and assignments will be posted here.

Prerequisites: MCS-121 or MCS-131 or placement exam.

Text: Calculus by Hughes-Hallett, Gleason, et. al. (John Wiley & Sons, New
York, Second Edition, 1998).

Calculators: You should have a graphing calculator available for use in class and on exams. If you do not own a calculator, please talk to your instructor. The department recommends the TI-83. You may use other calculators (especially other TIs, Casios, HP or Sharp) as long as you are able to enter a simple program into your calculator and you are comfortable with basic graphing features. Calculators with symbolic algebra capability will not be allowed during exams.

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

March 2
March 23
April 27

at 7:00 p.m.

The final exam will be given Saturday, May 20, 8:00-10:00 a.m.

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

Homework	20%
Prep Problems	5%
Exams (3)	60%
Final	25%

But wait, that adds up to 110%. Here's the deal. Basically, your lowest score will only count about half as much. If your lowest score is on one of the three exams or your homework, then it counts 10%. If your final ends up being your lowest score, then it will only count 15%.

Academic Integrity: The academic honesty policy can be found on page 31 of the 1999-2000 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: You may turn in one late assignment (by Thursday). In addition we will drop your lowest homework score.

There are two types of homework in this course, preparation problems and weekly homework. Preparation problems are meant to help you prepare for classes. Note that preparation problems for a section are assigned at the same time as the reading for that section. This means that you are being asked to read and digest a section and attempt problems before we discuss the material in class. This is intentional. These problems will often serve as the starting point for class discussions. The problems will be collected at the beginning of class and will be graded primarily on effort. Occasionally you will be asked to generate questions on the reading in lieu of preparation problems. Weekly homework is assigned for each section and is collected each Monday at the beginning of class. Only selected problems will be graded. You are allowed (even encouraged) to discuss both preparation problems and weekly homework problems with others. 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 II, 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 derivatives and how they relate to integration.
To be able to find antiderivatives systematically.
To be able to estimate definite integrals numerically and understand how to measure and compare error.
To be able to represent sums of physical quantities as definite integrals.
To be able to model with differential equations and to solve by separation of variables.
To understand how Taylor polynomials approximate functions and to be able to find and use Taylor polynomials.
To develop critical thinking and problem solving skills.
To have fun doing mathematics

Area D: Calculus II (MCS122) satisfies the Quantitative Reasoning criteria of Area D.

Knowledge of the language of mathematics and logic. (understanding of the notion of integral, series, differential equation)
Familiarity with logical or algorithmic methods of symbolic reasoning (finding antiderivatives, definite integrals, Taylor polynomials and solutions to differential equation)
Knowledge of the practical applications of mathematical modeling and axiomatic systems (applications of integrals s in physical, biological and social sciences, modeling using differential equation)
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 6 through 10 in Hughes-Hallett.

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