*Schedule*

Monday - Friday, 10:00am - 12:00noon, starting June 9,
1997; ILCC/ICN

*Instructor*

David Michael Burrow

*Home Phone/FAX*

515/295-5285

*ILCC Voice Mail*

800/242-5106 *301

*E-Mail*

DavidMBurrow@webtv.net

*Internet*

http://www.geocities.com/Heartland/Hills/3224/calculus.html

*Book*

Larson, Hostettler, and Edwards. *Calculus with Analytic
Geometry*. 5th Edition. Lexington, Massachusetts:
D.C. Heath, 1994.

*Calculator*

The best calculator for this class is a TI-85 graphing calculator,
which is available for around $100 in area stores. Other
graphing calculators, such as the TI-82 and TI-83 will also
work well. If the expense of a graphing calculator is
prohibitive, you *MUST* at least have a scientific
calculator, which should cost between $10 and $25.

*Other Supplies*

A small supply of graph paper may be useful for some
problems. You will also need to take organized notes
almost everyday. You will be asked to complete some
problems on computer, which may be accessed through the
ILCC labs.

*Description*

This course is a thorough introduction to single-variable
calculus. You will first review the basic properties of
functions and their graphs. Then you will investigate the
concept of limit and use it to understand derivatives and
antiderivatives. The course concludes with a basic
introduction to transcendental functions.

*Daily Assignments*

You will be given suggested assignments most days in class.
While these will not be turned in for a grade, it is
suggested that you do the problems. At the very least you
should look through them and make sure you know how to do
each type of problem. We will go through many of the
assigned problems in class.

*Tests*

You will be given five tests over the course of the summer.
We will review in class before each test. By the nature
of the course, each test will to some extent be cumulative,
reviewing what came before. Tests will be graded on a
straight point basis, with all tests (including the final)
worth approximately the same number of points.

*Special Assignment*

You will be required to complete a special assignment to
investigate the history, nature, or applications of
calculus. This may be done individually or as part of a
group of not more than three. Obviously more (in quantity
or quality) is expected from a group than from an
individual. The assignment will be worth approximately the
same as one test.

*Grades*

The standard grading scale applies: A = 90%+, B = 80%+, C
= 70%+, D = 60%+, and F = 59%-. There is generally no
"extra credit in this class.

*Monday, June 9*

Introduction to course

What is Calculus?

Using your calculator

*Tuesday, June 10* (Section 0.2)

Cartesian Plane

Distance and Midpoint

Circles

*Wednesday, June 11* (Section 0.3)

*Daryl Kohlhaas, guest instructor*

Graphing Equations

Mathermatical Models

*Thursday, June 12* (Section 0.6)

*Daryl Kohlhaas, Guest Instructor*

Introduction to Trigonometry

*Friday, June 13* (Section 0.6)

*Daryl Kohlhaas, Guest Instructor*

More on Trigonometry

*Monday, June 16* (Section 0.1)

*Greg Ahlers, Guest Instructor*

Real Numbers

Order

Distance

*Tuesday, June 17* (Section 0.4)

*Greg Ahlers, Guest Instructor*

Lines and Slope

*Wednesday, June 18* (Section 0.5)

*Greg Ahlers, Guest Instructor*

Introduction to Functions

*Thursday, June 19* (Chapter 0)

Review of Chapter 0

*Friday, June 20*

******TEST ONE == CHAPTER 0******

*Monday, June 23* (1.1)

The Concept of Limit

The Formal Definition of Limit

The Tangent Line Problem

*Tuesday, June 24* (1.2)

Properties of Limits

*Wednesday, June 25* (1.3)

Evaluating Limits

*Thursday, June 26* (1.4)

Continuity

*Friday, June 27* (1.5)

Infinite Limits

Vertical Assymptotes

*Monday, June 30* (Chapter 1)

Review of Chapter 1

*Tuesday, July 1*

******TEST TWO == CHAPTER 1******

*Wednesday, July 2* (2.1)

The Definition of Derivative

Tangent Lines

*Thursday, July 3* (2.2 - 2.3)

Rules for Differentiation

*Friday, July 4*

*NO CLASS == INDEPENDENCE DAY*

*Monday, July 7* (2.4)

The Chain Rule

*Tuesday, July 8* (2.5)

Implicit Differentiation

*Wednesday, July 9* (2.6)

Related Rates Problems

*Thursday, July 10* (Chapter 2)

Review of Chapter 2

*Friday, July 11*

******TEST THREE == CHAPTER 2*****
*****PROPOSAL DUE FOR SPECIAL ASSIGNMENT******

*Monday, July 14* (3.1 - 3.6)

Introduction to Curve Sketching

*Tuesday, July 15* (3.1 - 3.6)

More on Curve Sketching

*Wednesday, July 16* (3.7)

Applications of Derivatives

*Thursday, July 17* (3.10)

More Applications of Derivatives

*Friday, July 18* (Chapter 3)

Review of Chapter 3

*Monday, July 21*

******TEST FOUR == CHAPTER 3******

*Tuesday, July 22* (4.1 - 4.4)

Antiderivatives

The Fundamental Theorem of Calculus

*Wednesday, July 23* (4.2 - 4.3)

Area

Reimann Sums

*Thursday, July 24* (6.1)

More Area Problems

*Friday, July 25* (4.5)

Integration by Substitution

*Monday, July 28* (4.6)

Numerical Integration

Using Technology

*Tuesday, July 29* (5.1 - 5.2)

Logarithms and Integration

*Wednesday, July 30* (5.3 - 5.4)

Integrating Exponentials

Integrating Trigonometric Functions

*Thursday, July 31* (Sections 4.1 -
6.1)

Review for Final Exam

*Friday, August 1*

******SPECIAL ASSIGNMENT DUE*****
*****TEST FIVE == FINAL EXAMINATION******

1.

Investigate the history and development of calculus. Write
a 3 - 5 page paper summarizing what you discover.

2.

Write a 3 - 5 page biography of one of the developers of
calculus: Netwon, Leibniz, or Reimann.

3.

Do an Internet search on "Calculus". Find at least five
high-quality sites, and review each of them. The completed
set of reviews should be at least two pages long.

4.

Summarize any of the sections we skipped in this book.
Write a summary of the section in your own words. Explain
how the topic relates to those we have studied. Write an
example or exercise other than the ones found in the book.
Finally, explain why you think we might be skipping this
topic.

5

Re-create Isaac Newton's classic experiments showing the
effects of gravity on projectiles. Summarize your results,
and relate them to what we learn about derivatives in this
class.

6.

Answer the question: Why is calculus required for ...
(your major, or any particular major at the university
level)? Your answer should be approximately two pages
long.

7.

Find the equation for the standard normal curve used in
statistics. Using Mathematica or a
similar program, find the area between 0 and 1, 0 and 2,
and 0 and 3 standard deviations from the mean. How do
these areas relate to the proabilities used in statistics?
Summarize your findings in approximately one page.

8.

Write sample problems related to the applications of
derivatives. Obviously these must not be the ones found in
our book, nor should they be found in other calculus books.
You should come up with 8 - 10 problems, with answers.

9.

Write a "final exam" that you think would be appropraite
for Calculus I. Include at least twelve questions that you
think represent the major topics a student should learn in
the course, and explain why you included each problem.
(You do not need to actually answer the qurestions.)

10.

Explain in what situations you would do differentiation or
integration using each of these methods: formal
definitions, algebraic rules, numerical methods, graphing
calculator, computer. Your summary of when it is
appropriate to use each method should be 2 - 3 pages long.

. . . . . ???

Come up with any other idea you feel is appropriate for
this assignment. Submit it to Mr. Burrow, and after he
approves it, anything goes.

Links to other sites on the Web

Statistics Page

Mr. Burrow's ILCC Page

Mr. Burrow's Home Page

Official ILCC Home Page

The Integrator (Mathematica)

© 1997
*davidmburrow@yahoo.com*

The background music on this page is "Where Everybody Knows Your Name", the theme from the television show *Cheers*.