Math 32B Sample Problems
You might find these problems useful when studying for the final. Answers to
the odd numbered problems are provided. These problems are taken from a slightly
old edition of Stewart's calculus text. If you have a copy (from 31A/B or your
high school calculus class) of Stewart, or Thomas/Finney, or Larson/Hostetler/Edwards,
you might want to look there for lots of exercises to try.
Triple Integrals
(Answers)
Spherical Coordinates (ignore the
problems about centroids, moments of inertia, etc.)
(Answers)
Change Of Variables
(Answers)
Line Integrals
(Answers)
Conservative Vector Fields (testing
whether a vector field is the gradient of a function, finding a function whose gradient
is the given vector field, etc.)
(Answers)
Surface Integrals and
More Surface Integrals
(Answers)
Stokes' Theorem
(Answers)
The Divergence Theorem
(Answers)
Will Conley, Graduate Teaching Assistant
Mathematics Department
UCLA