* Syllabus
* Week 1
* Dylan
* Cartestian coordinates
* Polar coordinates
* Graphing in polar coordinates
* Converting between polar and cartesian
* Slop in polar coordinates
* Week 2
* Dylan
* Area in polar coordinates
* sin(k theta) for k even and odd
* parametric equations
* parametric curves
* the cycloid
* calculus with parametric curves
* area with parametric curves
* Week 3
* Dylan
* parametric curves
* orientation of parametric curves
* arclength
* the coordinate system on R^3
* the dot product
* lines and planes
* normal to a plane
* parametric equations for lines in space
* functions of several variables
* domain of functions of several variables
* cross sections
* level sets
* Week 4
* Dylan
* limits and continuity
* continuity at a point
* partial differentiation
* partial derivatives
* tangent planes
* the multivariate chain rule
* implicit partial differentiation
* Week 5
* directional derivatives
* unit vectors
* gradient vector
* higher order partial derivatives
* Clairaut's theorem
* maxima and minima
* critical points
* Hessian matrix
* multivariable second derivative test
* reducing number of variables in optimization
* Week 6
* Lagrange multipliers
* test review
* Week 7
* test review
* Week 8
* integration
* order of integration
* Fubini's theorem
* changing order of integration
* sketching regions of integration
* first octant
* volume in polar coordinates
* Week 9
* integration in polar coordinates
* area as volume of prism
* surface area
* line integrals
* force fields