Washington University in Saint Louis
			    Math 233 Calculus III

		  LIST OF SKILLS FOR THE FINAL EXAMINATION
		      (Friday, May 6th, 2005, 10:30am)

Approximately equal numbers of final examination questions will be taken from
each of these three parts of the course.

List of skills for Part I (Midterm Exams 1 and 2, Homeworks 1-6)

 1. Find the distance between two points.
 2. Find the radius and the center of the sphere given its equation.
 3. Perform basic vector operations (addition, subtraction,
      multiplication by a scalar) both geometrically and algebraically. 
 4. Compute the dot product of two vectors (geometrically and algebraically).
 5. Find the angle between to vectors.
 6. Find the work performed by a given force while moving an object in a given direction.
 7. Find the scalar and vector projections.
 8. Compute the cross product of two vectors (geometrically and algebraically).
 9. Find the area of the parallelogram or triangle with given vertices.
10. Find vector(s) orthogonal to given one(s).
11. Compute the scalar triple product.
12. Compute a volume of a parallelepiped.
13. Determine whether 3 vectors are coplanar.
14. Write down different equations of lines and planes.
15. Use the equation(s) of the line (plane) to find vectors parallel or
      orthogonal to it and points which lie on it. 
16. Determine whether two lines are parallel, intersect or are skew. 
17. Find equations of the line that is the intersection of two planes.
18. Find the distance between a point and a line, a point and a plane, a
      line and plane, two lines, and two parallel planes.
19. Convert between any two: rectangular, cylindrical and spherical coordinates.
20. Match the standard surfaces with their equations.
21. Compute the limit of a vector function.
22. Differentiate and integrate vector functions.
23. Find equations of the tangent line to a curve.
24. Find the arc length function and the length of a curve.
25. Reparameterize a curve with respect to the arc length.
26. Find the curvature.
27. Compute the TNB-frame.
28. Find position/velocity/acceleration of a point.
29. Find the normal/tangential components of acceleration.
30. Match surfaces with the verbal description of their level curves.
31. Find the limit of a function of two or three variables or show that it does not exist.
32. Find the partial derivatives of functions of two or three variables.
33. Find the equation of the tangent plane to a surface (best linear approximation of a function).
34. Use differentials to estimate the error of the linear approximation.
35. Use the chain rule to evaluate partial derivatives of composite functions.
36. Use the chain rule to perform implicit differentiation.
37. Evaluate the gradient of a function.
38. Evaluate the directional derivative of a function using its definition and/or gradient.
39. Find the direction and magnitude of the most rapid rate of change of a function.
40. Find the equations of the tangent plane and normal line to the level surfaces.
41. Find local maximum/minimum of a differentiable function.
42. Find an absolute maximum/minimum of a function on a closed bounded set.
43. Find an absolute maximum/minimum of a function subject to constraints.


List of skills for Part II (Midterm Examination 3, Homeworks 7-10)

 1. Approximate the double integral using Riemann sums.  
 2. Evaluate iterated integrals.
 3. Calculate the volume under a given surface.
 4. Compute double integrals.
 5. Evaluate double integrals by reversing the order of integration.
 6. Evaluate double integrals using polar coordinates.
 7. Find the average value of a function of two variables.
 8. Compute mass, moments, and the coordinates of the center of mass of a lamina.
 9. Compute the moments of inertia of a lamina.
10. Solve problems involving the joint probability density function of two random variables.
11. Find the surface area of a parametric surface.
12. Find the surface area of the solid of revolution.
13. Evaluate triple integrals.
14. Find the volume using triple integrals.
15. Find the average value of a function of three variables.
16. Evaluate triple integrals using cylindrical or spherical coordinates.
17. Evaluate the Jacobian of a transformation.
18. Determine the image of a region under a given transformation and compute its area.
19. Make a change of variables in double/triple integrals.
20. Compute line integrals with respect to the arc length.
21. Compute line integrals of vector fields.
22. Determine whether a region is open, connected, and simply connected.
23. Determine whether a vector field in two dimensions is conservative.
24. Find the potential function of a vector field.
25. Compute line integrals using the corresponding FTC.
26. Compute work using line integrals.
27. Find mass, moments, and center of mass of a thin wire.
28. Compute line integrals using Green's Theorem.
29. Compute the area of the region enclosed by a curve.
30. Compute the flux integral.


List of skills for Part III (Homeworks 11 and 12)

1.  Compute the divergence of a vector field.
2.  Compute the curl of a vector field.
3.  Understand relations between grad, div, and curl.
4.  Determine whether a field is incompressible, irrotational or neither.
5.  Compute surface integrals of scalar fields.
6.  Find the surface area via surface integrals.
7.  Find the flux of a vector field across an oriented surface.
8.  Use Gauss' law to find the charge enclosed by a surface.
9.  Determine the net rate of fluid/heat flow across the surface.
10. Use Stokes' Theorem to evaluate line integrals.
11. Use Stokes' Theorem to evaluate flux integrals.
12. Use the divergence theorem to find the outward flux of the vector field.