* Week 3
* financial math
* present value
* future value
* principal
* effective continuous rate
* effective annual rate
* annuities
* Week 4
* bonds
* perpetuities
* linear systems
* types of linear systems
* input/output models
* Week 5
* solving linear systems with matrices
* parameters
* row echelon form
* reduced row echelon form
* Gaussian algorithm
* Week 6
* matrix operations
* algebra with matrices
* linear combinations
* matrix products
* strange phenomena with matrix multiplication
* inverse matrices
* matrix inversion algorithm
* Week 7
* linear algebra
* geometry of matrix multiplication
* eigenvalues and eigenvectors
* Week 8
* probability and counting
* basic counting principle |A x B| = |A||B|
* permutations
* power sets
* factorial
* permutations with repeated elements
* combinations
* Poker
* Week 9
* independence
* inclusion/exclusion
* total probability
* conditional probability
* Week 10
* conditional probability
* conditional total probability
* Bayes' law
* expected value
* expectation
* limits
* one sided limits
* existence of limits
* Week 11
* limits and asymptotes
* limit laws
* continuity
* Week 12 (doc cam)
* slope and tangent lines
* secant lines
* tangent lines
* derivatives
* product rule
* quotient rule
* one-sided continuity
* toolbox of continuous functions
* types of discontinuities
* Week 13
* derivatives
* examples of derivative calculations
* differentiability
* natural exponentials
* cusps, vertical tangent lines, and jumps
* types of non-differentiability
* Week 14
* the chain rule
* asymptotes
* "designer" functions
* derivatives of inverses
* logarithmic differentiation
* implicit differentiation
* Week 15
* shape and derivatives
* strictly increasing/decreasing
* sign charts
* critical points
* concavity and the second derivative
* points of inflection
* Week 16
* optimization
* extreme value algorithm
* first derivative test
* second derivative test
* applied optimization
* Week 17
* approximation
* linear approximation
* approximating area
* power series for exp(x)
* Riemann sum setup
* Week 18
* Riemann sums
* Fundamental Theorem of Calculus
* anti-derivatives
* total area
* signed area
* substitution
* Week 19
* substitution
* integration and the product rule
* integration by parts
* iteratred integration by parts
* bounds and parts
* Week 20
* vertical slices
* horizontal slices
* dividing a region in to two parts of equal area
* area between curves
* differential equations warm-up
* Week 21
* differential equation
* simple differential equations
* seperable equations
* linear equations
* integrating factors
* Week 22
* differential equations
* growth/decay model
* second order constant coefficients
* second order constand coefficients with repeated roots
* multivariate functions
* partial derivatives
* tangent planes
* contour plots
* Week 23
* hessian matrices
* second derivative test
* unconstrained optimization
* Week 24
* optimization over regions
* volume calculations
* dxdy and dydx