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