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Unformatted text preview: Math 241, Final Exam Information. Saturday, May 2, 2 - 5 pm, LC 115. Review: April 30, 6 pm, LC 112. The Final Exam will be based on: • Sections 12.1 - 12.6, 13.1 - 13.3, 14.1 - 14.3, 14.5 - 14.9, 15.1 - 15.3, 15.5, 15.7, 15.8. • The corresponding assigned homework problems (see http://www.math.sc.edu/ ∼ boylan/SCCourses/241Sp09/241.html). At minimum, you need to understand how to do the homework problems. Useful materials: • Exams 1, 2, 3 and their solutions. • Quizzes 1- 9 and their solutions. New Topic List (not necessarily comprehensive): (Consult review handouts for Exams I, II, III for a list of old topics.) You will need to know how to define vocabulary words/phrases defined in class . § 15.5 : Triple integrals: Be able to set up and evaluate triple integrals in rectangular coor- dinates: ZZZ G f dV = ZZ R Z g 2 ( x,y ) g 1 ( x,y ) f ( x,y,z ) dz ! dA Note that the limits on the inner integral are functions of (at most) the outer variables x and y . We typically try to view G as a simple xy-solid. In particular, we try to identify: • The ”top” of G : z = g 2 ( x,y ) ; the ”bottom” of G : z = g 1 ( x,y ) . We must have g 1 ( x,y ) ≤ g 2 ( x,y ) for all x,y . • The projection R (or ”shadow”) of G on the xy-plane. We try to find equations for the boundary of R ....
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- Spring '08
- Math, Spherical coordinate system, Polar coordinate system, xyz-space, S. One, §15.3