* Week 1
* Kostya
* Shrijan
* vectors
* lengths
* angles
* standard basis
* i,j,k basis
* parametric equation of lines
* dot product
* orthogonal
* parallel
* parametrix equation of a plane
* normal form of a plane
* Week 2
* Shrijan
* Eric
* Kostya
* matrix multiplication
* transpose
* inverse of a matrix
* determinants
* volume of parallelpipeds
* co-factor expansion
* determinant and row operations
* det(AB) = det(A)det(B)
* the cross product
* Week 3
* Kostya
* vector geometry
* geometry and dot products
* limits
* delta-epsilon limits
* contour plots
* continuity
* the circle-box argument
* open sets
* open disks
* partial derivatives
* Week 4
* directional derivative
* differentiability
* gradient vector
* paths in space
* total derivatives
* the chain rule for R^n --> R
* the chain rule for R^n --> R^n
* Week 5
* Thanusun
* Taylor series
* Euler's identity
* Week 8
* Tabeeb
* critical points
* the Hessian matrix
* Clairaut's theorem
* relative minima and maxima
* cup, cap, and saddle
* multivariable second derivative test
* optimization
* Week 9
* Shrijan
* Tabeeb
* constrained optimization
* open sets
* closed sets
* bounded sets
* extreme value theorem
* Lagrange multipliers
* Week 10
* Shrijan
* Tabeeb
* integration
* fundamental theorem of calculus
* Cavalieri's principle
* Archimede's theorem: cone + semi-sphere = cylinder
* double integrals
* x-simple regions
* y-simple regions
* simple regions
* area and integrals
* Fubini's theorem
* Week 11
* Tabeeb
* changing order of integration
* upper and lower bound inequalities
* triple integrals
* applications of integrals
* averages
* mass and density
* Week 12
* change of variables
* onto functions
* one-to-one functions
* domain and range
* linear transformations
* fundamental theorem of linear algebra
* Jacobian matrix
* polar coordinates
* polar to cartesian
* "r dr dtheta"
* integrating in polar coordinates