Math 223 (Vector Calculus), Spring 2007
Review Information for Test #2 (4/12/07)

The test will be in class on Thursday, April 12. Class on Tuesday 4/10 will consist of a Q&A review session (you bring the Q's, I'll supply the A's).

Bring a calculator and a supply of loose-leaf paper to the test.

You are responsible for the following topics:

• Parametrized curves, velocity, acceleration and speed (pp. 177--181)
• Arclength (pp. 190--192)
• Vector fields, gradient fields, potentials, flow lines (pp. 208--213)
• Gradient, divergence, curl, and the ∇ operator (pp. 214--218)
• Multivariable Taylor series (pp. 230--235, 238--242)
• Unconstrained optimization and the Hessian criterion (pp. 245--252)
• Lagrange multipliers with one constraint (pp. 259--264); you don't need to know the Hessian test on p. 268
• Finding areas and volumes with iterated integrals (pp. 289--291)
• Double integrals (pp. 292--303)
• Changing the order of integration (pp. 309--311)
• Triple integrals over boxes (pp. 312--314)

You are also responsible for all material covered on the first midterm test that is necessary for the topics above.

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