Simon Fraser University Department of Mathematics
Spring 2005
Course Information
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Vector Analysis The mathematical description of much of physics and engineering, including mechanics, continuum and fluid mechanics, and electromagnetism, depends heavily on the language of vectors, particularly in three dimensions. In this course we will develop the theory of vector analysis, the differential and integral calculus of scalar and vector functions in one and several dimensions, leading us to the great theorems of Green, Gauss and Stokes and some of their applications. We will aim for an appreciation both of the underlying mathematics as well as of some of the applications that have historically motivated this theory. As time permits, we will explore how one can extend the linear structure of vector algebra to more general vector spaces of polynomials and functions, including an introduction to Fourier series. Course Policies and General Information:Prerequisites: The essential prerequisites for this course are the differential and integral calculus of a single variable, multivariable calculus (Math 251), and linear algebra (Math 232). Homework: Homework problems will be assigned weekly; they will be posted on the web by Wednesday, and due the following Wednesday at 5pm in the Mathematics Homework Box 5a, b, or c (depending on your tutorial section) on the 9000 level of Shrum Science Centre. You are encouraged to work together and discuss problems with each other (or use the WebCT discussions utility), but solutions must be worked out and submitted individually; you are responsible for your own homework. Please work neatly and clearly and explain your reasoning, and produce neat and clearly labelled graphs when appropriate. A selection of the problems will be marked every week. The lowest score will be dropped before computing the homework average, and all homework assignments will count equally toward the final homework grade. There will be weekly tutorial sections held by the teaching assistant on Tuesdays. You are encouraged to use these times to discuss the course material and problems, and give feedback on the course. Please also make use of office hours (or make an appointment) if you are having difficulty with any of the material. In addition to the homework problems, I may suggest additional exercises. These are optional, but I encourage you to look at them; they are usually chosen as a review, a simpler introduction to the basic ideas of a section, an alternative perspective to the ideas discussed in class, or additional practice. Exams and Grading: There will be an in-class midterm exam, provisionally on Friday, February 25; the final exam date is scheduled for 12:00-3:00pm, Tuesday, April 19. The (tentative) overall grading policy is as follows:
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