CALCULUS II MATH 120 FALL, 1997



CALCULUS II MATH 120 FALL 2007

TEXT: Stewart, Calculus: Concepts and Contexts, 3rd ed., Pacific Grove, Cal.: Brooks/Cole, 2005. The text is available in the bookstore.

TEACHER: Tom Sibley OFFICE: Science Center 243 (SJU)

EXT. 3810 E-MAIL: tsibley@csbsju.edu HOME PHONE: 363-7359

Home Web page (for assignments): employees.csbsju.edu/tsibley

OFFICE HOURS: DAILY 2:30 - 4:00 pm in S243 (SJU), except when meetings conflict. I will be happy to arrange other times by appointment. Furthermore, I will usually be available at other times.

CLASS MEETINGS: 8:00 am on EVEN days in Engel 244 (SJU) (Section 01A)

LAB: 8:00 am days 3 and 5 in Engel 244 (SJU). T. A.: Stephanie Rothstein.

Note: Lab will meet in Engel 238 (SJU) on Sept. 10, Oct. 19 and Dec. 3.

OBJECTIVES:

i) To understand and appreciate the concepts of calculus.

ii) To acquire facility in the techniques of calculus.

iii) To learn some of the applications of calculus.

iv) To understand historical and cultural aspects of mathematics.

TOPICS: The topics and the approximate time on each are as follows: Chapter 5 - 5 days, Chapter 6 - 6 days, Chapter 7 - 6 days, Chapter 8 - 10 days, multivariable topics (selections from Chapters 9, 11 and 12) - 5 days.

DISTRIBUTION OF CREDIT: SCALE:

Homework and Labwork 20% A 94% - 100%

Quizzes (Sept. 12, Oct. 9, 16% AB 89% - 93%

Nov. 6, Dec. 5 (4% each)) B 83% - 88%

Test I (Sept. 28*) 16% BC 78% - 82%

Test II (Oct. 26) 16% C 69% - 77%

Test III (Nov. 19) 16% CD 62% - 68%

Final Exam (Dec. 19, 6-8 pm) 16% D 55% - 61%

(comprehensive) F 0% - 54%

Extra Credit 0%-3%

* Sept. 21 is the last day to drop without receiving a "W" ("withdrew") on your transcript. If you are worried about this course, talk to me before the test.

CLASS TIME: I welcome questions at any time as long as they relate to the topic. In addition, I will start each class with some time to ask questions. In addition to lectures, there will be time spent working individually and in groups to better understand the material. I will supplement the text with historical material.

LABS: There will be some time each lab for the TAs to answer your questions. However, most of the time will focus on students working in groups and presenting solutions. On Sept. 10, Oct.19 and Dec. 3 we will meet in the computer lab in Peter Engel 238 (SJU) to explore calculus another way. Quizzes will take place in lab.

HOMEWORK: Consistent daily homework is vital to understanding. Homework is due the class after it is assigned. Reading and problems not to be graded (DOs) are part of the assignment. I encourage you to work in groups on homework, except essays, as long as you are confident everyone in your group is really learning the material. You may use computers and graphing calculators.

GRAPHING CALCULATORS: I expect you to have a graphing calculator whenever you work on calculus. I may restrict the use of calculators on parts of exams and quizzes.

ATTENDANCE: I believe you are mature enough to decide for yourself, although I firmly believe you will find the labs and classes well worth your presence. I will take attendance until I learn all of your names. I will contact anyone whom my T.A. or I note for chronic absence.

TESTS and QUIZZES: An ideal test enables students to show their knowledge, integrate it and be challenged to go beyond it. Thus besides standard problems, there will be challenging problems, essays to write and perhaps items to derive. Questions on quizzes will be more straight forward, but will require mastery of the material. I do NOT require you to reduce your answers, but I need to see ALL of your work. Please cross out all work you do not want me to consider.

EXTRA CREDIT: See page 3 for details on the applications of calculus project.

I look forward to working with you and getting to know you.

GOOD LUCK! HAVE A GOOD SEMESTER!

"How can it be that mathematics, being after all a product of

human thought independent of experience, is so admirably

adapted to the objects of reality?" -- Albert Einstein

"The infinite! No other question has ever moved so

profoundly [the human spirit.] -- David Hilbert (1862-1943)

FIRST HOMEWORK ASSIGNMENT

Due: Monday, Sept. 3, 2007

READ: pages 366--392. PRE-READ: pages 393—398.

DO: page 374 # 15, 35; Page 383 # 5, 13; Page 392 # 27, 37, 53.

TURN IN: page 374 # 12, 36; page 383 # 6, 12; page 392 # 26, 30, 54.

EXTRA CREDIT PROJECT APPLICATIONS OF CALCULUS

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 December 7, 2007.

Projects generally use some article or book, so document yours carefully. Please consult a professor in an area of interest to you for guidance. Also I will be happy to help. Please seek my approval of your project before you start.

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, real application of Calculus II,

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 the 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.

The application must be "real" in the sense that someone in that area actually used that particular function and the related mathematics to model something. Textbooks often give artificial functions for purposes of illustration. Real models tend to have complicated expressions with 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 the Ideal Gas Law P = nrT/V describes the pressure (P) of a gas in terms of volume (V), temperature (T), the amount of gas (n) and a constant (r).

“As 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 - 0.0427) - 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. Are 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.”

BIBLIOGRAPHY CALCULUS II MATH 120

The calculus books in the library all have call numbers starting with QA303. There are too many standard texts to mention any.

QA303.S398 Apostol et al (editors), Selected Papers on Calculus, MAA, 1969. This book has numerous short papers on interesting topics, alternative presentation of standard topics and forgotten aspects of calculus.

PROBLEM SOLVING

QA11.P6(1957) George Polya, How to Solve It, Doubleday, Garden City, NY, 1957. This is a great book to help you better approach problems.

QA43.L37(1983) Loren C. Larson, Problem-Solving through Problems, Springer- Verlag, New York, 1983. This is a wonderful compendium of problems starting with a chapter on guides to understanding and discovery.

THE THEORY OF CALCULUS

QA303.S78 Michael Spivak, Calculus, Benjamin, Reading, MA, 1967. Analysis,

the theory of calculus, is a 300-level mathematics course. However, this is a rigorous, mathematically powerful presentation for freshmen. It is well written and covers the standard topics, although it is hard.

THE HISTORY OF THE CALCULUS

QA303.B64 Carl Boyer, The History of the Calculus and its Conceptual Development, Dover, New York, 1949. You should find this readable, although not light browsing. It interrelates many historical aspects well.

QA303.E224 Edwards, The Historical Development of the Calculus, Springer- Verlag, New York, 1979. This is a more scholarly, readable presentation.

THE HISTORY OF MATHEMATICS

QA21 .K516 (or QA21 .K53 SJU) Morris Kline, Mathematical Thought from Ancient to Modern Times, Oxford University Press, New York, 1972. This well respected book is an encyclopedic reference.

QA21 .S87 (or 510.9 ST8 SJU) Dirk Struik, A Concise History of Mathematics, Dover, New York, 1967. This is a good starting point on historical topics.

MATHEMATICAL MODELING

QA401.M63 Douglas Mooney and Randall Swift, A Course in Mathematical

Modeling, Mathematical Association of America, 1999. This textbook

introduces modeling and assumes calculus. For an extra credit project

you should probably consult a professor for a suitable topic first.

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