# Exam reviews

Exam reviews

(Note coverage of topics has moved a bit over the years)

### Major topics include:

Major topics include:

- Cartesian, cylindrical, and spherical coordinate systems
- Using vectors: addition, scaling, component form
- Dot product; angles between vectors; projection
- Cross product; finding perpendicular vectors; areas/volumes
- Planes and lines
- Parametric equations for curves; tangent line
- Velocity and acceleration; decomposition of acceleration
- Length of parametric curves
- Cylinders and quadric surfaces

### Major topics include:

Major topics include:

- Functions of two (or more) variables as graphs; level curves and level surfaces
- Compute partial derivatives
- Find tangent plane to functions of two variables
- Chain rule; implicit differentiation
- Gradient vector and its geometrical properties; tangent planes to implicit surfaces
- Directional derivatives
- Linear approximation
- Second-order Taylor polynomials for multi-variable functions
- Finding critical points; classifying critical points using second partials test
- Absolute max and min of a continuous function on closed and bounded set
- Lagrange multipliers method for optimization with constraint

### Major topics include:

Major topics include:

- Iterated integration; changing order of 2D integrals
- Integration in polar coordinates
- Triple integrals over 3D regions; changing order of 3D integrals
- Using integration to find area, surface area, volume, mass, moments, center of mass, and inertia
- Integrate in cylindrical and spherical coordinate systems
- Change of variables (Jacobian)
- Vector fields; curl and divergence of vector fields
- Line integrals; work along a line; conservative line integrals
- Green's Theorem
- Surface integrals; flux through a surface
- Stokes' Theorem
- Divergence (Gauss') Theorem