Exam 2
Review Sheet
August 31, 2012
The exam will cover sections 2.6, Chapter 3 and 4. Sections labelled optional that
we did not cover will not be covered. (This also includes the moving frame and torsion
from Section 3.2.) Below lists topics/questions you are likely to see. Please plan on one
“take-home” question. I also expect to include some True/False questions.
•Be able to prove Theorem 6.3 of section 2.6, and be able to use it.
•Be able to calculate the velocity, speed and acceleration of a path.
•Be able to calculate the length of a path
•Be able to calculate flow lines, sketch a vector field.
•Be able to calculate the gradient, divergence and curl and be able to use them.
•Find the first order and second order Taylor polynomial of a multivariable function
•Be able to identify critical points of a multivariable function, and determine their
nature
•Be able to use Lagrange multipliers to identify critical points of a function subject
to a given constraint(s). (It would be too cumbersome a test question to ask you to
use the second derivative test for constrained local extrema.)
•Be able to use these techniques to solve regression problems (don’t memorize formulas,
please!) and basic utility problems in economics.
Definitions to know:
•directional derivative of fat ain the direction of v, and know how to compute it
using the dot product
•path, speed, acceleration
•vector field, flow line
1
