Exams are grouped by topic; to access the exams/quizzes click on the "down arrow" to expand the group.

## Comprehensive Final

Comprehensive Final

- Spring 20 [online format]
- Fall 19 (solutions)
- Spring 19 (solutions)
- Fall 18 (solutions)
- Spring 18 (solutions)
- Fall 17 (solutions)
- Spring 17 (solutions)
- Fall 16 (solutions)
- Spring 16 (solutions)
- Fall 15 (solutions)
- Fall 15(M) (solutions)
- Spring 15 (solutions)
- Fall 14 (solutions)
- Fall 13 (solutions)
- Fall 13(M) (solutions)
- Fall 12 (solutions)
- Spring 12 (solutions)
- Spring 12(M) (solutions)
- Fall 10 (solutions)
- Spring 10 (solutions)
- Spring 09 (solutions)

## Quizzes

Quizzes

The following contain are a set of quiz banks. In addition to a collection of 10 problems there are also some selected additional problems from old exams and reviews. The more problems that you are able to answer, the better you are doing; so try and answer as many as possible!

- Quiz 1 -- Review material
- Quiz 2 -- Coordinate systems; spheres; vectors
- Quiz 3 -- Dot product; angles; work; cross product; areas; volumes
- Quiz 4 -- Lines/planes; quadric surfaces; parametric curves; tangent lines; derivatives of vector-valued functions
- Quiz 5 -- Integration of vector-valued functions; arc length; decomposing motion; osculating plane; curvature
- Quiz 6 -- Multivariable functions; level curves/surfaces; limits; partial derivatives
- Quiz 7 -- Tangent planes; chain rule; implicit differentiation; gradients; directional derivatives
- Quiz 8 -- Taylor polynomials; critical points; second partials test; absolute max and min on closed and bounded set; Lagrange multipliers
- Quiz 9 -- Basics of multivariable integration; iterated integrals; changing order of (2D) integration; integration in polar coordinates
- Quiz 10 -- Triple integrals; changing order of (3D) integration; applications of integration
- Quiz 11 -- Integration in cylindrical/spherical coordinates; Change of variables (Jacobian); vector fields; curl; divergence
- Quiz 12 -- Line integrals; work; line integrals of conservative functions; Green's Theorem; surface integrals; flux through a surface
- Extra material -- Stokes' Theorem; Divergence Theorem