UNDER CONSTRUCTION. Suggestions welcome.
Math 324 is taken by many engineering majors, some science majors, most math majors, and a sprinkling of others (e.g., economics mojors). Most will be listed on your classlist as juniors or seniors (though in many cases that is by credits, and they are actually sophomores or juniors, repectively). Some take 324 immediately after 126, but most wait a year or even two. Be sure to review ideas from 126, or direct the students to, as they come up during the course.
This course presents multiple challenges to the students, depending on their interests, abilities, and background. Most find 3D visualization and drawing difficult. Parametrization and change of variables challenge almost all of them. Vector fields and the various ways we use them in the course are quite mysterious for many. Even more than most math courses, this course is "end-loaded", with all the themes and major new ideas tied together in Chapter 16. Some suggestions for dealing with these challenges are included below with the discussion of various sections of the course.
Departmental syllabus for 324.
Textbook. The official text is "Multivariable Calculus - Custom Edition (Early Transcendentals)", 6th Edition by James Stewart. This contains part of Chapter 14 and all of Chapters 15 and 16 of Stewart's 7th edition "Calculus --Early Transcendentals". In the past, sometimes the bookstore also stocked the full text, which confused students. Be sure to make clear that they don't need both. If a student has the regular (not Early Transcendentals) version of the 7th edition, that will work but the chapter numbers will 15, 16, and 17 (instead of 14, 15, and 16), and the page numbers will be different. I do not know how much the 7th edition differs from the 6th (please let me know if you do). The 5th and earlier editions aren't feasible for students to use.
Homework. Choosing homework problems carefully is particularly important in this course because there are so many small variations in problem types. Students need practice in all the kinds of problems you plan to test them on. On the other hand, it's very easy to get too enthusiastic and assign homework that is too long and/or too difficult. Remember this is only a three-credit course. While in principle they should be able to do all kinds of integration, doing a particularly difficult integration by parts, or multiple substitutions, probably doesn't teach them much about 324 topics. Use the complete solution manual for instructors (available in C-36) to check how complicated the calculations are in the problems you assign. Unless the problems are very short, about 12 problems a week is a good number.
The students need some feedback on their work. WebAssign, which gives students individual variations of the problems and checks every final answer, may be used in 324. However, a certain number of students take 126 elsewhere (especially students taking 324 in Autumn, but also in other quarters) and so don't already have WebAssign access, and may object to its cost for a single quarter. If you don't use WebAssign, you may be able to get a grader. (Ask in C-36.) Unless you are very lucky, your grader won't give much feedback to you or the students, but at least some of the students' work will be checked. I usually tell the grader three problems to look at "in detail". These are given 0 to 2 points: 2 = all correct or only a minor (e.g. +/-) error; 1 = correct approach, not finished, or student got through the problem, but with one or two significant errors; and 0 = skipped, barely started, or many errors. In addition the grader gives 0 to 4 "completion" points for do the rest of the problems assigned. I've had to specifically instruct the grader to indicate clearly which problems were looked at "in detail" and to mark where the errors are for which points are deducted. I also tell the students, "The grader is paid to spend less than 5 minutes on each paper (seven weeks only)."
Judith Arms's course page from Autumn 2011.
Carto Wong's course page from Spring 2010.
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Most recently updated on December 5, 2012