MAC 2313 - Section 04 - Spring 2008
Related Pages: Course Home Page | Syllabus | Homework
As stated in class, you are allowed to bring to the test one 8.5x11 inch
page, written on both sides. You can write whatever you want on this page:
eg. definitions, formulas, examples, etc. Calculators will be allowed for
the test.
Chapter 14 - Partial Derivatives - Sections 14.5 (from page 936 on implicit differentiation), 14.6-14.8
Applications
implicit differentiation
equation of tangent plane: using partial derivatives and also gradient
directional derivative: definition, interpretation, compute numerically
and algebraically
gradient vector: definition, interpretation
Critical Points and Optimization Problems
types of critical points
finding critical points algebraically
second derivative test
local vs. global extrema
Lagrange multipliers
applications: solving unconstrained and constrained optimization
problems (i.e. word problems)
Review Homework for Chapter 14, pg 975: #11b, 27, 29,
42, 43-47 odds, 51-55 odds, 59-65 odds
More problems from Section 14.7: 39, 41, 49
More problems from Section 14.8: 11-17 odds, 29, 33
Chapter 15 - Multiple Integrals - Sections 15.1-15.5
Double Integrals
definition
interpretation
compute numerically and algebraically
change limits of integration
applications of double integrals: volume, area, average value,
density, mass, moments, center of mass, moments of inertia, probability
Change of Variables in Integration
polar coordinates
Review Homework for Chapter 15, pg 1050: #1-5 odds, 9-21 odds, 35, 41
More problems from Secton 15.3: 23, 31, 39, 41
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