## Exam reviews

(Coverage of topics has moved a bit over the years)

### 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:

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:

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