Date: Sun, 13 Mar 2005 15:58:49 -0600 (CST)
From: Ilya Krishtal <krishtal@math.wustl.edu>
To: victor@kirk.wustl.edu
Subject: test 2 (fwd)

List of skills for exam 2.

01. Compute the limit of a vector function.
02. Differentiate and integrate vector functions.
03. Find equations of the tangent line to the curve.
04. Find the arc length function and the length of the curve.
05. Reparametrize a curve with respect to the arc length.
06. Find the curvature.
07. Compute the TNB-frame.
08. Find position/velocity/acceleration of the point.
09. Find the normal/tangential component of acceleration.
10. Match the surfaces with the verbal description of their level curves.
11. Find the limit of functions of 2 or more variables or show that it does not exist.
12. Find the partial derivatives of functions of 2 or more variables.
13. Find the equation of the tangent plane to the surface (best linear approximation of a function).
14. Use differentials to estimate the error of the linear approximation.
15. Use the Chain rule to evaluate partial derivatives of composite functions.
16. Use the Chain rule to perform implicit differentiation.
17. Evaluate the gradient of a function.
18. Evaluate the directional derivative of a function using its definition and/or gradient.
19. Find the direction of the most rapid rate of change of a function and its magnitude.
20. Find the equations of the tangent plane and the normal line to the level surfaces.
21. Find local max/min of a differentiable function.
22. Find an absolute max/min of a function on a closed bounded set.
23. Find an absolute max/min of a function subject to constraints.