Math 211 Multivariable Calculus

Semester: Spring 2010

Newton's diagram from Principia
Lecture 001
Inst : Dr. Asher Auel
auel AT mathcs*emory*edu
Time : Tue Thu 2:30 - 3:45 pm
Loct : MSC W201
Office: MSC W425
Phone: (404) 727-5356
Mon 1 - 2 pm
Tue 1 - 2 pm
 Catalogue listing Math 211.
Text : Calculus: Multivariable, 5th ed.,
McCallum, Hughes-Hallet, Gleason, et al,
John Wiley & Sons, 2008. ISBN: 978-0-470-13158-9.

Publisher's website.
Course syllabus (updated 29 Apr 2010)
Homework assignment posting page (updated 29 Apr 2010)

Description of course: This course is about the investigation of multidimensional spaces (actually, usually only 1, 2, and 3 dimensional spaces). We'll build on a solid foundation of 1 dimensional calculus, where we had the notions of derivative and integral, linked by the Fundamental Theorem(s) of Calculus (FTC). Multivariable functions (often called vector fields) on multidimensional spaces also have derivatives, but now there are derivatives in many different directions, hence the local properties of functions are more complicated. Multivariable functions can also be integrated, though the generalization of "area under the curve" to multiple dimensions is more subtle. There is also a FTC, rather, many of them: Greens theorem, Divergence theorem, and Stokes's Theorem. To understand these deep and beautiful theorems, we'll need to investigate the notions of circulation, divergence, path-independence, and conservative vector fields.

Homework 25%
Quizzes  9%
Midterm exam 1 (Feb 18)   18%
Midterm exam 2 (Mar 25)   18%
Final exam (Apr 30) 30%
Grades: Your final grades will be based on several components. Notice that more emphasis is placed on exams than on weekly homework assignments in computing your final grade. On the other hand, completing your homework on a weekly basis is the most sure way to success on the exams.
Group work, honestly: Working with other people on mathematics is highly encouraged and fun. You may work with anyone (e.g. other students in your section, in the course, not in the course, bums on the street, ...) on your homework problems. If done right, you'll learn the material better and more efficiently working in groups. The golden rule is:
Work with anyone on solving your homework problems,
but write up your final draft by yourself.
Writing up the final draft is as important a process as figuring out the problems on scratch paper with your friends, see the guidelines below. Mathematical writing is very idiosyncratic - I will be able to tell if papers have been copied - just don't do it! You will not learn by copying solutions from others! Also, if you work with people on a particular assignment, please list your collaborators somewhere on the top of the paper. Make the process fun, transparent, and honest.


(or otherwise the small print)

Homework: You will be assigned a weekly problem set, which will be due on Friday (except for the first Friday of the semester, January 15th), and posted on the course web-site the Thursday of the week before it's due.

{Late or improperly submitted homework will not be accepted.} Period. If you know in advance that you will be unable to submit your homework at the correct time and place, you must make special arrangements ahead of time (e.g.\ religious holidays or trapped on a desert island).

In general, even if you haven't completed all the homework problems for the week, it is advisable to hand in what you have. In keeping with the guidelines below, it's advisable to hand in a selection of problems with complete solutions rather than shaky and poorly written-up solutions to all the problems.

Your homework must be stapled, with your name clearly written on the top. Consider the pieces of paper you turn in as a final copy: written neatly and straight across the page, on clean paper, with nice margins and lots of space, and well organized. If it's not readable, it won't be graded. Your lowest homework score will be dropped.

Homework guidelines: Generally, a homework problem in this course will consist of two parts: the creative part and the write-up.

  • The creative part: This is when you "solve" the problem. You stare at it, poke at it, and work on it until you understand what's being asked, and then try different ideas until you find something that works. This part is fun to do with your friends. If you're having trouble, even in understanding what the problem's asking, you should come me for hints, either in person during office hours, or by email. Ask for help as early as you can! This part should all be done on "scratch paper."

  • The write-up: Now that everything about the problem is clear in your mind, you go off by yourself and write up a coherent, succinct, and nicely written solution on clean sheets of paper. Consider this your final draft, just as in any other course. This part you should definitely NOT do with your friends.

Please note that a fully correct solution requires both parts: having "figured out" the problem, but not having written it up (or having written up something incoherent that does not express what you know) or conversely, having written up many pages of beautiful prose that still fail to solve the problem, don't count for very much. You will be graded accordingly.