MAC 2313 - Section 04 - Fall 2011
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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 (pg 895 from differentiability) - 14.8
Partial Derivatives
differentiability of a function
chain rule
implicit differentiation
gradient vector: definition, interpretation
directional derivative: definition, interpretation, compute numerically and algebraically
Applications
differential
equation of tangent plane: using partial derivatives and gradient
maximum rate of change of a function
direction of maximum rate of change of a function
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 (covers 14.4 from pg 895 - 14.8), pg 945: #11b, 25b, 27, 42, 43-47 odds, 51-55 odds, 59-63 odds
More problems from Section 14.7: 41, 43, 51
More problems from Section 14.8: 11-17 odds, 29, 31, 35
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 (covers 15.1-15.5), pg 1022: #1-21 odds, 29, 35, 39, 43
More problems from Secton 15.3: 31, 49, 55
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