MATH 213 : Calculus III

TEXT : McCallum et al., Multivariable Calculus, Wiley 1997, New York.

INSTRUCTOR : David Lantz

• Office : McGregory 316, Extension : 7737
• Official Hours : MWF 9:30-10:20, TR 1:30-2:20
• Effective Hours: Weekdays, 9:00-5:00, except when I am teaching or in a meeting.
• E-mail: dlantz@mail.colgate.edu
• Home : 146 Lebanon Street, Hamilton
• Phone : 824-0965 (Please do not call after 10 p.m.)

HOMEWORK : Assigned and collected daily. The list of assignments will be available at

TESTS : The three hour exams, worth 100 points each, will be 7:30-9:30 p.m. on Tuesday evenings, February 20, March 20 and April 24, in Lawrence 105 (the Ho Lecture Room). There will be no "makeups" for any of these exams -- if you cannot come at the appointed time, please see me in time to schedule an alternate time to take the exam early. The final will be comprehensive, emphasizing the material covered after the last hour exam, and will also be worth 100 points. Remember that there will be a common time for the final exam for the sections of Math 213; when the finals schedule is published, look for Math 213, not for 8:30 or 10:30 MWF.

GRADING : The sum of four exam grades and homework points will be divided by 4 and the result will be put on a 90-80-70-60 scale. An added + or - will be subjective.

WEB SOURCES: As the solutions homework exercises are completed, they will be linked to the corresponding section on the assignment page (see the link above). They are in .pdf format, so you will need a reader for this format on your browser. One free source for such a reader is from Adobe Acrobat:

It is likely that you will find it useful initially to have a computer program to draw graphs in three dimensions (though you will need to be able to picture them for yourself at least to some degree for the exams, because you will not have access to a computer). One such program for Windows is "Winplot", which is available as freeware from Peanut Software:

I have made a list of links to all the graphics that I use in class. Some are just the graphics themselves, and will display in a browser window. Others are Winplot files; when you click on the link, it will download to your computer -- be sure you notice where -- and you can open it with Winplot and manipulate the image (rotate it, etc.). Here is a link to that list:

You should also be aware that there are many free resources for calculus on the Web. A long list of links to such sources is

SUGGESTIONS :

1. If you see an error at the board, or if you do not understand something, stop me and ask (even if everyone else seems to understand).
2. Calculus III is probably the easiest part of the calculus sequence for the students who enroll in it, i.e., who have learned most of the manipulations earlier. The most challenging part of the course is the ability to picture graphs in three dimensions. The computer can help with this initially, but you must be prepared to do it on your own to some degree during exams. Do not believe that the "meat" of the course is memorization of the many formulas, many involving partial derivatives. Though they are certainly important, it is more important to learn to visualize the graphs and what they can tell you about the functions. (Indeed, in the "real world", many functions are given by table data or even just by a picture of the graph, not by algebraic expressions, so the formulas are often useless.)
3. Doing the homework, regularly and thoughtfully, will contribute greatly to your success in the course.
4. It is a common practice, and a great mistake in mathematics courses, to spend a week working only on, say, English (especially when a paper is due), history the next, calculus the next, etc. Mathematics courses rely on all that has come before; the next lecture may be incomprehensible if you do not understand the last one.