David Michael Burrow

Analytic Geometry & Calculus I (Summer, 1997)

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

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.

Tentative Schedule

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*****

Special Assignment Ideas

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)

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