Mathematics 10, Calculus IIFall 2004

Dr. Patti HunterOffice hours:WF 3:30-5:00 p.m.

Office: Math/CS BuildingM 9-10:20 a.m.(with

occasional exceptions)

Phone: 6076or by appointment

Email:

URL:

Prerequisites:Math 9 (Calculus I).

Text:

Calculus from Graphical, Numerical, and Symbolic Points of View, Vol. II, 2d ed., by Arnold Ostebee and Paul Zorn is a required text. (Of course, the combined Vol. I and II of the second edition may be used instead.) We will cover chapters 5 through 11.

Your textbook provides a clear, thorough, and engaging explanation of the material we will be studying. In short, it’s a good book. Read it.

Materials:

  • You will need to bring a graphing calculator to class every day. (The TI-83 is preferred, but others are acceptable. The TI-89 is not allowed on exams.) You will need your own graphing calculator during exams—sharing calculators during exams will not be allowed. Some notes on the use of the TI-83 will be provided. You may also find it helpful to have the user’s manual for your calculator, which may be available on-line.
  • We will make some use of Scientific Notebook, a mathematical word-processor with a built-in computer algebra system. This software is available in the PC lab in the basement of the library. I do NOT recommend that you purchase this software.
  • Some web-based graphing and computer algebra systems may also be useful throughout the semester. More about these later. Be prepared to work online (on your own computer or in the computer lab) from time to time.

Course Objectives:

The Big Picture

How fast is the AIDS epidemic growing in Africa? What force is exerted by the water behind Hoover Dam? Where’s the center of mass of a carbon monoxide molecule? What price should a trader charge for an option to sell 100 shares of Microsoft during the next three months at $40 per share? Calculus, with its mathematical models and quantitative methods, provides a language for asking such questions and a tool for answering them.

But calculus is more than a language and a tool. Like any subject in mathematics, it’s the study of certain abstract ideas and objects—things you can’t see or touch or measure. It is also a creative art, one that provides an outlet for both our reasoning and our imagination. And while it is useful as a tool, calculus as a creative process and as an abstract structure of concepts held together by careful axiomatic reasoning is, in the words of your textbook authors, “among our species’ deepest, richest, farthest-reaching, and most beautiful intellectual achievements.”

Of course our goals for the semester include the mastery of certain skills and facts along with the development of the ability to apply those skills and facts to problems in the sciences (more on those goals in a moment). But, as you acquire those skills, we will also look for opportunities to exercise our creativity as we solve problems and we will keep the broader, abstract structure of calculus in focus. Although this is not a course that emphasizes the details of the theory of calculus, you will find that a familiarity with those untouchable concepts and some experience with the abstract arguments and problems of this three hundred-year-old discipline will give you a deeper and more flexible mastery of this subject.

What’s the Point?

Reasoning about abstract structures and an ability to interpret, evaluate, and communicate quantitative ideas are useful skills—useful to scientists, voters, readers of the newspaper, anyone who wants to function in the 21st century. But these activities and abilities have a significance beyond their utility. God instilled them in us. Why? Perhaps the story of creation in Genesis suggests an answer. We’re stewards of God’s creation. Good stewards understand the stuff they’re taking care of. Carefully studying and understanding anything in this world often requires forming precise definitions, measuring, thinking logically about how things are and how they should be.[1] So the knowledge and abilities you will acquire in calculus can make you a better servant of the Master of the universe that calculus illuminates.

But even more than equipping you for service, I hope this semester of wrestling with new ideas, creating solutions to complex problems, and constructing in your own mind the central pillars and beams of the edifice of calculus will give you opportunities to experience, first hand, the order, beauty, and subtlety in this mathematical corner of God’s creation.

The Details

We do have some goals specifically associated with the content of Calculus II. This course focuses on the integral—defining it, applying it, and computing it. We also spend some time on the tangentially related topics of function approximation and infinite series. Here’s a list of our specific goals:

  • Gaining an understanding of the concept of the integral, both as an abstract structure and as a tool for modeling certain phenomena;
  • Learning how to use the integral and differential equations as tools for measuring and describing;
  • Acquiring the knowledge and skill necessary to do routine calculations of integrals (numerically and symbolically);
  • Learning how to approximate functions with Taylor and Fourier polynomials (and why you’d want to);
  • Becoming familiar with the abstract concept of infinite series.

What’s our plan for accomplishing these goals? How will we know if you’ve learned what you’re supposed to? Homework and exams (including a cumulative final) will be our main tools of learning and assessment. Your questions and comments in class will also provide some feedback. Here are the details.

Homework

Homework assignments will be posted on the course web page almost daily. These assignments will contain 2 types of exercises:

(1) Exercises for practice.(2) Exercises to turn in.

Homework assignments serve two purposes: (1) they give you opportunities to learn and (2)they enable me to measure how much you’ve learned.

In order to learn the material well, you should do all assigned problems. Most exercises to be turned in will be similar to at least one practice exercise. The answers to most practice exercises (odd-numbered problems) can be found in the back of your book. Use these exercises and their answers to help you understand how to do the other exercises.

As part of your homework grade, you will present some problems to the class. I will assign particular problems to particular students in advance. If you are assigned a problem, you should be ready to present it at the start of class. Sometimes you will simply write the solution on the board. At other times, you will need to be able to explain details and answer questions.

You may find some of the homework difficult. Persevere. When you get stuck, come for help.

In order to measure what you’ve learned, I will grade the homework you turn in. Perhaps this should go without saying, but I will base your grade on the correctness of your solutions. And I will often be looking for more than just the right number circled at the bottom of the page. How you arrive at the numbers will be important and, frequently, how you explain what you’ve done will also matter. Some problems will be straightforward calculations, but others will include instructions like, “Show that this approximation overestimates the integral,” or “Explain why is an improper integral,” or “Justify your answer.” Those questions will require more than numbers as answers.

One final note about homework—style matters. Assignments that receive full credit will be clearly and neatly written, carefully organized, appropriately illustrated, and grammatically correct.

I encourage you to work together on homework assignments, but you must be sure that you understand the ideas in the homework, and you must submit papers written in your own words. Any answers that appear to be substantially the same as another student’s will receive no credit.

Late homework will be penalized 10% per calendar day.

Your grade in the homework category will be based on a cumulative total.

Regular Exams

You will take exams on the following dates:

Exam IFriday, September 24

Exam IIFriday, October 22

Exam IIIFriday, November 19

If you cannot take an exam on the day scheduled, you may take it early at a time I will determine. See me at least one week in advance to sign up for the alternate time.

Final Exam

The final exam will be cumulative, covering chapters 5-11.

It is scheduled for Thursday, December 16, 8:00-10:00 a.m. Final exams can be rescheduled only by petition to the registrar; requests to reschedule exams to accommodate travel plans are rarely granted.

Participation and Attendance

Good participation and consistent attendance may result in a bonus of up to 5 percentage points in your final homework grade. Frequent absence and unimpressive participation may reduce your final homework average by up to 5 points.

Signs of good participation include the following: asking questions in class when confused, contributing appropriately to class discussions, and being a good sport about group and individual exercises. More than 3 unexcused absences will be considered excessive.

Evaluation: Your grade will be based on the following categories:

Homework and participation20%

Regular Exams (3)60%

Cumulative Final20%

I grade on the standard 90/80/70/60 scale.

Honesty

Dishonesty of any kind will result in loss of credit for the work involved. Major or repeated infractions will result in dismissal from the course with a grade of F.

Fine print:Syllabus is subject to change at the instructor’s discretion.

[1]For more on this idea, see Russell W. Howell and W. James Bradley, eds. Mathematics in a Postmodern Age, pp.4-5.