Math 11 Accelerated Multivariable Calculus

Term: Fall 2019

diagram of a sphere
Lecture 01 (91107)
Inst : Prof. Asher Auel
asher.auel AT dartmouth*edu
Time : Mon Wed Fri 10:10 - 11:15 am
X-hour Thu 12:15 - 1:05 pm
Loct : Kemeny 008
Office: Kemeny 339 240
Phone: No office phone yet!
Office
hours: 		Mon 02:00 - 04:00 pm
Thu 12:15 - 01:15 pm
Text : Multivariable Calculus, 8th ed., James Stewart,
Cengage Learning, 2015. ISBN: 978-1305266643.
Alt : Calculus, vol. 3,
OpenStax Consortium, 2016. ISBN: 978-1947172166.
The course Canvas site contains the syllabus and all other information.

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 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: Green's theorem, Divergence theorem, and Stokes's Theorem. To understand these deep and beautiful theorems, we'll need to investigate the notions of divergence, path-independence, and conservative vector fields.

WeBWorK 10%
Homework 10%
Midterm exam 1 (10 Oct)   25%
Midterm exam 2 (29 Oct)   25%
Final exam (22 Nov) 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.

Additional notes

X-hour: The X-hour will usually consist of office hours. As it lands the day after homework is due, it is primarily an opportunity to get general advice, discuss previous material, or get a head start on the next week's written homework. On the occasional week when the X-hour will serve another purpose, I'll reschedule office hours.

Homework: 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.