Outcomes List for Math 200-200935
Multivariable Calculus (9
th
edition 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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