Outcomes List for Math 200-200935 Multivariable Calculus (9thedition of text) Spring 2009-2010 The purpose of the Outcomes List is to give you a concrete summary of the material you should know, and the skills you should acquire, by the end of this course. As an overall summary, you should be able to, after completing this course: Do basic calculations with vectors and related geometric shapes (lines and planes), using dot products, cross products, and vector calculations Do calculus with space curves, including finding velocity and equations of tangent lines Work with plots of multivariable functions, including the computation of level curves and level surfaces Use partial derivatives, including chain rule formulas Compute tangent planes to surfaces, find critical points, and check for max/min Work with cylindrical and spherical coordinates Work with parametric surfaces Do basic multivariable integrals Do change of variables in multivariable integrals This outcomes list will be updated with specific review problems and topics for each exam of the quarter.The following information is for reviewing for the “new” material since Exam 3. The final exam is COMPREHENSIVE. It will cover the “old” material from the Outcomes Lists for Exam 1, Exam 2, and Exam 3. In addition it will cover this “new” material from Chapters 14.1, 14.2, 14.3, 11.8, 14.4, 14.5, 14.6, and 14.7. Approximately 60-70% of the final exam will come from this new material. 14.1 Compute double integral calculations over rectangular regions using partial integration. Inspect an integral, and decide if the order of integration is easier one way (y first, x second) or the other (x first, y second). Interpret a double integral as the volume under a surface.
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