## Learning expectations for Quiz 4

- You should know all the learning expectations from Quiz 1, Quiz 2, Quiz 3, and the midterm in addition to the following...
- Be able to use Green's theorem to compute area in terms of a line integral.
- Be able to use Green's theorem to compute line integrals: primarily around closed loops, but also possibly for non-closed curves (where you must add a curve or curves to make a loop).
- Apply Green's theorem to domains with both interior and exterior boundaries.
- Know the definitions of divergence and curl and their basic properties.
- Be able to derive various product formulas for divergence, gradient, and curl.
- Be able to find parameterizations of surfaces, including surfaces contained in a plane and parts of spheres.
- Know and understand the standard parameterization of the sphere
- Use a surface integral to compute surface area of a parameterized surface.
- Be able to compute the integral of a function over a surfaces.