# Calculus III

## Syllabus

### Instructor: Dr. Art Duval

Please feel free to come by my office any time during scheduled office hours. You are welcome to come at other times, but in that case you might want to make an appointment, just to make sure that I will be there then. You can make an appointment simply by talking to me before or after class, by calling me at my office or at home, or by sending e-mail.

You may also ask any questions directly via phone or e-mail. If I'm not in when you call, please leave a message on the voice-mail or answering machine with your name, number, and a good time for me to call you back. I will try to respond to your phone or e-mail message as soon as possible.

### Course Objectives:

Upon successful completion of the course, you will be able to represent functions of two or three variables, and vector-valued functions, and their derivatives and integrals numerically, graphically, and symbolically, and be able to interpret such representations. You will be able to compute derivatives and integrals symbolically, and estimate them graphically and numerically.

Note that with functions of more than one variable, there is a greater variety of "derivatives'' (partial derivative, directional derivative, gradient vector) than there was with functions of one variable in Calculus I and II. Similarly, there are new wrinkles in integration, especially with setting up limits of definite integrals. Our study of vector-valued functions will culminate with the calculation of line integrals.

You will be able to set up and solve problems which require understanding and use of derivatives and integrals. You will be able to solve open-ended problems, problems which require written commentary rather than a string of symbols or numbers, and problems for which different answers may be equally correct.

### Textbook:

CALCULUS Single and Multivariable, 2nd ed., McCallum, Hughes-Hallet, Gleason, et. al., Chs. 11-18. We will skip sections 15.6 and 18.3,4. The textbook is required at all class meetings. A Student Solution Manual, consisting of solutions to approximately every other odd problem, is also available at the bookstore.

Required Reading: Preface: page xi. You may also want to read through the rest of the preface.

More Reading: Read each section that we cover in class, both before and after class. Skim the section before class, even if you don't understand it fully, to have some idea of what we'll be doing in class. Read it more carefully after class to clarify and fill in details you missed in class.

The textbook is written in a way designed to make it easier for you to read and understand than "traditional" textbooks. This doesn't mean that you can read the text as quickly as, say, a history text; you still need to work and do examples on your own. We will be spending some time in class learning how to effectively read a math textbook.

Warning: Sometimes, I will not "cover" all the material from a section, but instead focus on a particular aspect of the section. In such cases, I will point out in class (and at this website) which other parts of the section I expect you to read on your own.

### Technology:

We may occasionally meet in a computer lab for you to work on in-class projects using computer graphics. The emphasis will be on using the computers as tools, not learning any sort of programming. The computer lab has extensive open hours, so you may practice and explore outside of class. I will announce the open hours when I know them.

You may also have a graphing calculator, such as the TI-85 or HP-48 in class at any time, including during tests. A graphing calculator will only occasionally be useful, though, and you can probably get by without it. You will however, need at least a scientific calculator at all class meetings and during tests.

Homework (15%):
Individual homework will be assigned most class days and will generally be due at the next class (with exceptions as announced in class). You are allowed to work together on homework (in fact, I encourage you to do so), but the paper you turn in you must write yourself. Homework is due at the beginning of class (9:00 sharp); if you cannot make it to class, arrange to either deliver the homework to me early, or have someone else bring it to class for you. Your two lowest individual homework scores will be dropped.

Some homework may take the form of weeklong group projects and require a single written report. In this case, every group member will receive the same score. Each of these will count as two homework assignments.

There will also be in-class group assignments. These will each count as half a homework assignment, and cannot be made up if you are absent.

We will spend some time in class discussing how to work and learn effectively as a group.

Tests (15% each):
There will be three in-class tests on the following days:
• Chs. 11, 12: Thu. 21 Sep.
• Chs. 13, 14: Thu. 26 Oct.
• Ch. 15: Thu. 16 Nov.
Makeup tests can be given only in extraordinary and unavoidable circumstances, and with advance notice. (See also ``Exception'' below.)
Final (40%)
comprehensive (including Chs. 16, 17, 18)
Wed. 13 Dec., 10:00-12:45 p.m.
Exception
Your final exam score will be used in place of your lowest in-class test score, if this increases your overall class average. In particular, if you miss a test, your final exam score will replace it.

### Attendance Policy:

On-time attendance at all classes is required. If you have more than two unexcused absences, your overall course grade will be reduced by seven points; more than four, and you will be dropped with an F. Unexcused late arrivals or early departures will count as half an unexcused absence. I will usually excuse an absence if you tell me about it in advance, or, in cases of emergencies, as soon as possible afterwards.

### Drop date:

The deadline for student-initiated drops with a W is Mon. Oct. 23. (Note that the wrong date is printed in the class schedule.) After this date, you can only drop with the Dean's approval, which is granted only under extenuating circumstances.

I hope everyone will complete the course successfully, but if you are having doubts about your progress, I will be happy to discuss your standing in the course to help you decide whether or not to drop. You are only allowed three enrollments in this course, so please exercise the drop option judiciously.