Exam reviews

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

Geometry of space; vectors

Spring 2020

Fall 2019

Spring 2019

Fall 2017

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

Multivariable differentiation

Spring 2020

Fall 2019

Spring 2019

Fall 2017

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

Multivariable integration

Fall 2019

Spring 2019

Fall 2017

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

Final Exam (comprehensive)

Spring 2020

Fall 2019

Final exam "unboxing"