MCS 121 - Calculus I
Fall 2004

Course Description/Online Syllabus

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

### Web Page

Announcements, course information and assignments will be posted on the course web page.  The URL for this course is http://www.gac.edu/~mcs121/2004F/

### 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.

### Prerequisites

Two years of high school mathematics beyond plane geometry, including trigonometry, or MCS 120.

### Text

Calculus by Hughes-Hallett, Gleason, et. al. (John Wiley & Sons, New York, Third Edition, 2002).

This text is written specifically to aid you in understanding the concepts of calculus.  Our questions and problems will require you to invoke your understanding rather than to mimic template problems worked in the text, so you should read this text, both before and after each class. (Suggestions and more suggestions about how to read mathematics.)

### Calculators

You should have a graphing calculator available for use in class and on exams. If you are buying a new one, the department recommends the TI-83 or TI-86. 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 (e.g. TI-89 or TI-92) will not be allowed during exams.   A couple of calculators are on reserve in the library.

### Exams

We will have two in class skills tests, two exams during the semester and a cumulative final exam. The exams during the semester will be given in the evening. The tests and exams are tentatively scheduled for
• September 23 (in class)
• October 12 (evening)
• November 4 (in class)
• November 18 (evening).
The final exam is tentatively scheduled for Friday, December 17, 3:30 - 5:30 pm.

Please reserve these dates on your calendars. Make-ups will only be given for verifiable emergencies.   In particular, make-ups will never be given to accomodate travel plans.

We will provide you with a number grade on each assignment and on each test, so that you may keep track of your performance. As a guideline, the components will contribute in the following proportion to the final grade:
• 5% WeBWorK
• 15% Homework
• 12% Each skills test
• 18% Each intra-term exam
• 20% Final

The academic honesty policy can be found on page 31 of the 2001-2002 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.''

### Accessibility

Please contact your instructor during the first week of class if you have specific physical, psychiatric, or learning disabilities and require accommodations. All discussions will remain confidential. You can provide documentation of your disability to the Advising Center (204 Johnson Student Union) or call Laurie Bickett (x7027).

### 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.  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

### Prep Problems/Webwork

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.
• Prep problems, when assigned, must be done before the beginning of class, by the time deadline given.
• The prep problems must be done on WeBWorK, a web-based system that provides different, but equivalent, problems to each student, and allows correction of errors before final submission and recording.

### Homework

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

Homework is assigned for each section. Homework assignments will be collected about twice a week, but you are advised to do the problems from each section right after the class meeting on that section. A selection of the problems turned in will be graded. You are allowed and encouraged to discuss homework and prep problems with others, but (see the College Academic Honesty policy) ultimately you must work the problems and write up the assignment entirely by yourself. As a general rule, you must justify your answers: Explain, or show your work. Let the Golden Rule be your guide in preparing this homework: write it as if you were the person who would have to grade it.

Homework rules

• Acknowledge your sources (people and texts).
• Turn in neat, well-written solutions, not messy first drafts. Trim "fringes."
• Do not copy collaborative solutions; write up solutions in your own words.
• Turn in homework on time.  (Consult your instructor for their policy on late homework.)

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.

### Area D

Calculus I (MCS121) 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)