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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, pathindependence, and conservative vector fields.
Work with anyone on solving your homework problems,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. Policies(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 20th), and posted on the course website 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 writtenup 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 writeup.
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. 
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