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Unformatted text preview: MATHEMATICS 218 ANALYSIS IN SEVERAL VARIABLES FALL TERM, 2009 COURSE SYLLABUS Instructors: R. C. Gunning (902 Fine Hall) and K. Hughes (311 Fine Hall) Classes: MWF 10-10:50am, Fine 214 and Th 7:30 -7:50pm, Fine 214 Course Description The course covers differentiation and integration in several variables, covering both the theoretical results, with fairly detailed proofs, and the applications, providing practice in explicit calculations and applications. The course meets four times a week, and it is expected that all students will attend all four hours of the course weekly. Required Texts: Math 218 , R. C. Gunning and L. B. Pierce (course notes available for down- loading at the course web site on Blackboard Advanced Calculus , G. Folland (Prentice Hall, 2002) Optional Texts for Reference , on reserve in Fine Library: Calculus on Manifolds , M. Spivak (Benjamin, 1965) Vector Calculus , J. Marsden and A. Tromba (Freeman, 1996) Prerequisites Prerequisite is a background knowledge of calculus in one variable from a fairly rigorous and abstract point of view, such as in MAT 215, and a basic knowledge of the properties of vector spaces and linear transformations, such as in MAT 204 or 217. Assignments Weekly reading and problem assignments will be distributed on Mondays, with the solutions generally due the following Wednesdays. If it is helpful you may work together on the weekly problem sets; but you should make all necessary efforts to understand the work and be sure that you can solve problems similar to those in the homework assignments, on your own. Grading Problem Sets 15% Midterm In-class Quiz 15% Midterm Take-home Exam 25% Final In-class Quiz 15% Final Take-home Exam 30% 1 MATHEMATICS 218 ANALYSIS IN SEVERAL VARIABLES FALL TERM, 2009 First Assigment, due Wednesday September 30, 2009 READING: Read Chapter 1 of the course notes, pages 1 -12. This covers background material, dealing with the geometry of the spaces R n as described by various norms, some basic topological notions such as those of open, closed, compact and connected sets, and the basic properties of continuity of functions and mappings. Much of this may be familiar, from a rigorous course in calculus of one variable, such as MAT 215; but there are some aspects that involve func- tions of several variables, so be sure that the material is clear. Many of these topics are discussed from a slightly different point of view in Folland, Chapter 1. PROBLEMS: The weekly problem assignments have two groups of problems. Group 1 contains fairly straightforward problems and basic calculations; these problems should be relatively easy. Group 2 contains some more challenging theoretical problems and more difficult calculations. You should complete both sets of problems each week....
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