## 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

### 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