Larry Riddle
Buttrick 327
LRiddle@AgnesScott.edu
Telephone #6222

Multivariable Calculus, by McCallum, Hughes-Hallett, Gleason, et al.

Maple 6

This is a powerful computer algebra system that is available over the network in all computer labs. The web site for Waterloo Maple is http://www.waterloomaple.com. Worksheets used in class and labs will be kept at W:\Students\Math\Math220.

Other class materials will be made available at our course web site on Ecademy:

http://ecademy.agnesscott.edu/~lriddle/courses/math220

Check there on a regular basis.

I do not have regularly scheduled office hours. Rather, you are encouraged to stop by my office at any time when you have questions or problems and if I am not too busy I will be happy to work with you. You may also stop by to make an appointment for a time that is mutually convenient. Another good way to contact me is through email, particularly during the evenings or weekends. I promise to respond to your email as quickly as I can.

Learn the tools and techniques of multivariable calculus, and their application in both mathematical and scientific contexts

Understand the development of differentiation and integration of functions of several variables

Develop an intuition for the geometry and properties of curves and surfaces

Enhance your analytic (problem solving) skills, your ability to think abstractly and to analyze critically, and your computational (algebraic) skills

Be able to use computer software as a computational tool for understanding and solving problems in multivariable calculus and its applications

Learn to communicate mathematics effectively, both verbally and in writing.

Functions of Several Variables (sections 1-6)

A Fundamental Tool: Vectors (sections 1-4)

Differentiating Functions of Many Variables (sections 1-7)

Optimization: Local and Global Extrema (sections 1-3)

Integrating Functions of Many Variables (sections 1-3, 5, 6)

Parameterized Curves and Surfaces (as time permits)

We will make frequent and important use of computer technology to help us learn about multivariable calculus. The use of the computer can reinforce concepts from class, contribute to the discovery of new concepts and make feasible the solution of realistic applied problems. The philosophy we will take can be summarized by the following quote adapted from Elementary Differential Equations, 5th Edition, by William Boyce and Richard DiPrima:

"For you, the student, these various computing resources have an effect on how you should study mathematics. It is still essential to understand how the various solution methods work, and this understanding is achieved, in part, by working out a sufficient number of examples in detail. However, eventually you should plan to delegate as many as possible of the routine (often repetitive) details to a computer while you focus more attention on the proper formulation of the numeric, graphic, and analytic methods so as to attain maximum understanding of the behavior of the mathematics and of the underlying process that the mathematics models. Our viewpoint is that you should always try to use the best tools available for each task. Sometimes this is a pencil and paper; sometimes, a computer or calculator. Often a judicious combination is best."

We will be using the computer algebra system Maple. This should be available over the network from any computer lab on campus or from your dorm room if you have a network card. If you want to access the program from your own computer over the network, run the program Setup.exe in W:\Students\Maple6\Client from your personal computer. If you have not used Maple before, you should start playing with it as soon as possible. A Maple tutorial called intro.mws can be found in the folder W:\Students\MapleEssentials. Either double click on the file from Windows Explorer or open it from within Maple.

The first and most important assignment is to regularly read the text and to work through and understand the examples in each section. You paid too much money to ignore it! You should try to spend time, no matter how short, on this every day. Do not just accept mathematical statements or examples discussed in the text, but try to verify these statements and examples yourself. Working with paper and pencil or with Maple while you read the text is a good way to do this. If you have questions, ask in class or stop by my office. Since the reading is so important, some hints on how to do it might be helpful. You may find that slight variations on the following scheme will work for you.

a. Plan on doing the reading more than once, and do not make it an essential goal to understand everything in the reading the first time through it. The first reading should be devoted only to getting a general overview of the material of the section.

b. After the first reading, stop for a few minutes and attempt to summarize to yourself, in your own words, what the section is all about. Then immediately reread the section.

c. During the second reading, make a serious effort to understand all of the material in the section. This does not mean to memorize it, but rather to understand all of the points before going on.

d. If you do not understand something during the second reading, put the book aside awhile and return to it later when your mind is fresher. If you still do not understand it after returning to it, ask me or some other members of the class about it. Do make sure you eventually understand all of the material. You will probably get tripped up in later reading, in doing the homework, or on tests if you treat material you don't quite understand as "probably not all that important."

e. Do not get discouraged if some points require some time to understand. It is not uncommon to have to think about a point in a math text for a day or even several days before it becomes clear what is really going on.

You will be given suggested problems to work on, which you will be expected to complete even though this work will probably not be checked unless you ask for help with it. The chapter problem sets can be found at our Ecademy web site. You are encouraged to work with others on these problems and check each other's work. I would like you to keep a notebook with your solutions. The notebook should be neatly organized and written. Please do not use it for scratch work. Each problem you work on should be clearly labeled to indicate which section of the text it comes from. The notebook should contain your work on the problems and comments you want to make about the problems to help you understand your solutions. I will occasionally ask you to submit solutions to some of these problems for me to grade.

Some assignments and exams may suggest extra credit work. Extra credit in this course will be tallied separately from regular scores. If you end up on a borderline between two grades at the end, extra credit will count in your favor. However, failure to do extra credit will never be counted against you, because grades are assigned on the basis of regular scores. You should do extra credit work if you find it interesting and think that it might teach you something. However, it never pays to skimp on the regular assignment in order to do extra credit problems.

I may send various kinds of information about homework problems and assignments by way of your Agnes Scott email address so I expect you to check your email on a regular basis.

You will have two take-home exams and a final exam. The final exam will be cumulative. The time to start preparing for it is now.

You are encouraged to work together on the problem sets for this course, but each student is always expected to write up (and understand) her own solutions. Working with someone else to understand an idea or a concept or even the requirements of an assignment is group learning and is encouraged. But once you understand what you were struggling with, you should complete the assignment individually, giving the work your own identity. Accessing or copying work of another student from a previous semester is a violation of the Honor Code.

Regular attendance for this class will be very important since much of our class time will be spent on discussing problems or working in small groups on problems or computing experiments. It is therefore expected that you will attend and be prepared for every class, but it is also recognized that circumstances may occasionally necessitate missing a class. However, you are still responsible for all material discussed in class whether you are there or not, and for submitting all work before the due date. Approval for extensions must be obtained in advance. Excessive number of missed classes may result in a reduction of your course grade.

Your grade will be determined by applying the most favorable of the following two weighting schemes (I reserve the right to make adjustments if necessary).