CALCULUS I MATH 119 SECTION 4 FALL, 2002
TEXT: Ostebee and Zorn, Calculus, vol. 1, 2nd ed., Harcourt, 2002; in SJU bookstore.
TEACHER: Tom Sibley OFFICE: Engel 243 (SJU) E-MAIL:
EXTENSION: 3810 HOME PHONE: 363-7359
OFFICE HOURS: 2:40 C 3:50 p.m. daily
I will be happy to arrange other times by appointment, or you may just stop by my office.
CLASS MEETINGS: ODD days 11:20 a.m. in Engel 229 (SJU)
LAB MEETINGS: days 2 and 4 2:40 p.m. in Engel 229 (SJU)
NOTE: On Sept. 2 and Dec. 6, we will meet in the Computer Lab, Engel 238.
OBJECTIVES:
(i)To understand and appreciate the concepts of calculus.
(ii)To acquire facility in the techniques of calculus.
(iii)To learn more about making and interpreting graphs.
(iv)To learn to read a mathematics textbook.
(v)To understand some of the historical and cultural aspects of mathematics.
TOPICS: We will study all five chapters of volume 1. I intend to spend 5 days on Chapter 1, 7 days on Chapter 2, 4 days on Chapter 3, 9 days on Chapter 4, and 7 days on Chapter 5.
DISTRIBUTION OF CREDIT:SCALE:
Homework and Lab work20% A 93% -- 100%
Test 1 (Sept. 19*)20% AB 88% -- 92%
Test 2 (Oct. 17)20% B 83% -- 87%
Test 3 (Nov. 14)20% BC 78% -- 82%
Final Exam (Dec. 16, 11 a.m.)20%C 69% -- 77%
(Comprehensive) CD 62% -- 68%
Extra Credit0% C 3% D 55% -- 61%
(See Handout) F 0% -- 54%
*Sept. 20 is the last day to drop without receiving a AW@ on your transcript. I won=t have the tests graded by then, so if you are worried about this course, talk with me before the test.
CLASS TIME: I welcome questions at any time as long as they relate to the class. I will start each class with some time to ask questions. (Note that there will be time in labs for your questions as well.) In addition to lectures, there will be time spent working individually and in groups. I will supplement the text in various ways, including some historical material.
LABS: Calculus requires consistent practice and reflection to master the concepts and techniques. Labs provide a structured way for you to practice individually and in groups and time for you to ask for help on your homework. There will be occasional quizzes during lab time. On Sept. 2 and Dec. 6 we will meet in the computer lab in ENGEL 238 to explore calculus with the aid of some computer software.
HOMEWORK: Consistent daily homework is vital to understanding in mathematics. Homework is due at the start of the class after it is assigned. Reading and pre-reading are part of the assignment, as are the DO problems, even though they will not be graded. You may work in groups on homework, except essays, as long as you are confident everyone in your group is really learning the material. Similarly, you may use the computer for homework, especially for essays. The essays will help you understand the concepts better. Each homework assignment is worth ten points, with the points given proportionally to the grading scale (10 corresponding to an A, 9 to an AB, 8 to a BC, etc.) The reading assignment corresponds to material talked about in the class prior to the assignment, and relates to the DO and TURN IN problems. The pre-reading assignment is to help you prepare for the next class.
I expect you to have a GRAPHING CALCULATOR whenever you work on calculus. I encourage you to use Mathematica on the computers for homework, essays, and exploration.
ATTENDANCE: I believe that you are mature enough to decide about attending for yourself, although I firmly believe the labs and classes are well worth your presence. I will take attendance until I learn all of your names. I will try to contact chronically absent students.
TESTS: An ideal test enables students to show their knowledge, integrate it and be challenged to go beyond it. Thus, in addition to standard problems, there will be challenging problems, essays to write and, as appropriate, items to prove. I do NOT require you to reduce your answers, but I do need to see ALL of your work. Please cross out work you do not want me to consider.
EXTRA CREDIT: Consult page 4 for details on the applications of calculus project.
FIRST HOMEWORK ASSIGNMENT (Due Aug. 30):
READ pages xvii-xviii, 1 - 8, 11 - 20, and 24 - 33. PRE-READ: 35 - 44.
(We will spend time on this material in the first two labs as well.)
DO page 9 # 33, 37; page 21 # 13, 57; page 35 # 43.
TURN IN page 9 # 36, 38; page 21 # 14, 56; page 35 # 44.
EXTRA HELP is available at the Mathematics Skills Center in HAB 004 at CSB (ext. 5236) and QUAD 151 at SJU (ext. 2061).
I look forward to working with you and getting to know you.
GOOD LUCK! HAVE A GOOD SEMESTER!
A[The universe] cannot be read until we have learnt the language
and become familiar with the characters in which it is written. It is
written in mathematical language... C Galileo Galilei (1564 C 1662)
AThe infinite! No other question has ever moved so
profoundly [the human] spirit.@C David Hilbert (1862 C 1943)
BIBLIOGRAPHY CALCULUS I MATH 119
The calculus books in the library have call numbers starting with QA303. Here are some other mathematics books you might find helpful or interesting for this class.
PRECALCULUS REVIEW
QA531 is the call number for trigonometry.
QA39 and QA248.3 are the call numbers for other precalculus topics.
PROBLEM SOLVING
QA11.P6(1957) George Polya, How To Solve It, Garden City, N. Y.: Doubleday, 1957).
This classic book can help you learn problem solving techniques.
QA43.L37(1983) Loren Larson, Problem Solving Through Problems, New York: Springer Verlag, 1983.
This good collection of problems and solutions has guides to understanding and discovery.
BROWSING ON PRECALCULUS AND CALCULUS TOPICS
QA7.S44 Apostol et al (editors), Selected Papers on Precalculus, Washington, D.C.: Mathematical Association of America, 1977.
Many interesting and unusual topics appear in over 100 short papers.
QA303.S398 Apostol et al (editors), Selected Papers on Calculus, Washington, D.C.: Mathematical Association of America, 1969.
Like the preceding book, this book contains short papers on interesting topics in calculus.
THEORY OF CALCULUS
QA303.S78 Spivak, Calculus, Reading, Mass.: Benjamin, 1967.
Analysis, the theoretical basis of calculus, is usually reserved for upper level mathematics majors. However, this calculus text really proves all of the standard results. Although it is well written and was intended for first year college students, it is hard reading.
HISTORY OF CALCULUS
QA303.B64 Carl Boyer, The History of Calculus and its Conceptual Development, New York: Dover, 1949.
This classic and readable history carefully interrelates many historical components.
QA303.E224 C. H. Edwards, The Historical Development of Calculus, New York: Springer Verlag, 1979.
This book gives a scholarly, readable presentation including more recent research than Boyer.
EXTRA CREDIT PROJECT CALCULUS I
Purpose: To enable interested students to find actual applications of calculus and to increase their ability to explain mathematics and its applications.
DUE: Any time on or before Dec. 9, 2002.
Because your project will probably be based on some article or book, it must be fully documented. You should consult a professor in an area of interest to you and me for guidance.
To receive the full 3% of extra credit, a project must:
1) be well written,
2) be fully documented,
3) be correct and illustrate a significant application of calculus to a real situation,
4) explain the mathematics and how it is used in the application, together with enough explanation of the applied area to understand the context,
5) give any assumptions of the model, including values of the constants, and explain how the assumptions were chosen,
6) conclude with an assessment of how successful the model was and any reservations you have,
7) use a mathematical model not presented in our text, in class, or in labs.
All models make assumptions. Some of these assumptions, such as constants, are found from experimental testing. Others come from a general understanding of the area investigated. The assumptions reveal much about the worth and generality of a model.
The application must be real in the sense that someone in that area actually used that particular model and the related mathematics to model something. Textbooks often give rather artificial functions for purposes of illustration. Real models tend to have constants particular to the situation considered. Compare, for example, the simplified high school level model below with an actual (non-calculus) model quoted below from Butler and Bobrow, The Calculus of Chemistry, New York: Benjamin, 1965, page 18.
In high school I learned the Ideal Gas Law: P = nrT/V described the pressure (P) of a gas in terms of volume (V), temperature (T), the amount of gas (n) and a constant (r).
AAs an example of a more complicated rule, consider the van der Walls equation. It gives the relation between pressure and volume of a dense gas. For 1 mole of CO at 250 C, the pressure in atmospheres is given as a function of volume in liters by the relation
P = 24.44/(V C 0.0427) C 3.59/V2.
When is this equation meaningful? Mathematically, V can take any value except 0 and 0.0427 .... [T]he validity of this equation is restricted to a much more limited range of values by the physical situation.... Both pressure and volume are inherently positive quantities. V is thus restricted to values greater than 0.0427, since if it is smaller, ... P would be negative.
AAre there any other kinds of restrictions? Yes, this equation is further restricted ... by the fact that it gives an accurate representation of the experimental pressure-volume relation only for V greater than 0.5 liter. This kind of restriction ... expresses the result of experiments.@
HINTS ON USING A MATHEMATICS TEXTBOOK
Mathematics texts are NOT simply problem sets and hints on how to solve them. If you read a text only when you are stuck on problems, you will probably find mathematics frustrating and add to your work by needing to undo some of your work. Consider the text as a guided tour of the material.
Read the assigned material at least once before attempting the homework. Read with a pencil, paper and a graphing calculator handy. You need to interact constantly with the text. On the first reading note the parts that puzzle you. When you come to a worked example, first cover the solution. Read the question carefully until you understand what is requested. Then try to solve the example yourself. After a short time, look at the first part of the given answer. If you are doing what the solution says, good! C keep working the problem out yourself. If you didn=t get anything at all or something very different, look back in the text to see if you can find why they thought to do it their way. (Sometimes the idea behind their way to solve an example is presented for the first time in the example.) Remember, the first step is often the hardest, so concentrate there and do not lose heart. Keep alternating between trying to do a step yourself and reading their solution.
Read the text a second time, which should be easier because you know what is coming. See if you understand the parts that puzzled you the first time. Reflect on the ideas in the text; remember calculus, like all college level mathematics, focuses on concepts. Ask lots of questions, and look for connections with what you have already learned. When your reading of a section feels comfortable, you are probably ready for the next section. Mathematics builds carefully on all previous material, so keep up with the class.
Discipline yourself to use notation correctly. Mathematical notation has been carefully honed to reflect exactly what is meant. In particular, only put an equals sign (=) between two numerical or algebraic expressions that are equal. (Don=t equate a function and its derivative, a common mistake.) Otherwise you will likely be confused when you look back at your work and those of us who read your work will certainly be confused.
Start working on the problems after the first reading of a section. Read the problem enough times so that you know what you are to do. If you know a step, write it down; it is amazing how that can clear your mind to figure out the next step. Draw diagrams and graphs whenever appropriateCmost people think visually much better than symbolically. In a word problem label what each variable means. Word problems are not devised in order to frustrate students. They are a pedagogical compromise because real world applications are usually far more difficult, seldom have a single clear answer and often present the solver with too little, too much or some irrelevant information. Use word problems to sharpen your reasoning and problem solving ability. The bibliography suggests two books on problem solving.
READING IS NOT A SPECTATOR SPORT!