* Week 1
* exponent laws
* n'th roots
* logarithms
* exponential functions
* Week 2
* piecewise functions
* the absolute value function
* inequalities
* sigma notation
* geometric series
* functions
* composition of functions
* domain and range
* inverse functions
* symmetry
* even and odd functions
* Week 3
* financial math
* simple compound interest
* annual percentage rate
* continuously compounded interest
* effective continuous rate
* annuities
* future value
* present value
* compound interest worksheet
* Week 4
* future value of an annuity
* present value of an annuity
* Week 5
* review of financial math
* linear systems
* types of linear systems
* parameters
* effective annual rate
* matrix form
* row echelon form
* reduced row echelon form
* the Gaussian algorithm
* Week 6
* matrix operations
* column vectors
* sum of matrics
* transpose
* linear combination
* product of matrices
* economic example of matrices
* identity matrix
* inverse matrix
* matrix inversion algorithm
* Ax = b
* Week 7
* one sided limits
* infinite limits
* existence of limits
* continuity of polynomials
* Week 8
* limits to infinity
* horizontal asymptotes
* vertical asymptotes
* horizontal asymptotes of rational functions
* continuity
* composition of continuous functions
* one-sided continuity
* continuous from the right
* continuous from the left
* types of discontinuities
* removable discontinuity
* jump discontinuity
* essential discontinuity
* Week 9
* slope of lines
* tangents
* secant line
* derivative
* Leibniz notation
* Newton notation
* the product rule
* the quotient rule
* derivatives and competing companies
* Week 10
* types of dicontinuities
* differentiable => continuous
* failures of differentiability
* vertical tangent lines
* cusps
* discontinuities
* Leibniz notation
* the chain rule
* writing functions as compositions
* tables of values
* inverse functions and derivatives
* logarithmic differentiation
* Week 11
* implicit differentiation
* increasing and decreasing functions
* critical points
* concavity
* concave up and down
* points of inflection
* Week 12
* optimization
* local maximum
* global maxmimum
* the first derivative test
* the second derivative test
* optimization algorithm
* the curve sketching algorithm
* Week 13
* linear approximation
* factorials
* n'th order polynomial approximation
* Week 14
* definite integrals
* approximating the area under a curve
* integrable functions
* summation formulas
* Riemann sums
* anti-derivatives
* Week 15
* anti-derivatives and area
* initial value problems
* displacement
* velocity
* speed
* acceleration
* the Fundamental Theorem of Calculus
* sketch of proof of the Fundamental Theorem of Calculus
* signed area
* total area
* Week 16
* integration by substitution
* substitution for definite integrals
* integration by parts
* integration by parts for definite integrals
* Week 17
* area and integrals
* signed area
* total area
* area between curves
* horizontal slices
* vertical slices
* review of integration techniques
* Week 18
* improper integrals
* convergence
* divergence
* integrating unbounded functions
* divergence tests
* direct comparison
* limit comparison
* Week 19
* differential equations
* seperable equations
* linear differential equations
* integrating factors
* second order differential equations
* Week 20
* partial derivatives
* tangent planes
* gradient vector
* marginal productivity
* competing and complementary goods
* Week 21
* higher order partial derivatives
* Clairaut's theorem
* Hessian matrix
* multivariate chain rule
* unconstrained optimization
* critical points
* two variable second derivative test
* cup, cap, and saddle
* Week 22
* constrained optimization
* reducing variables
* Lagrange multipliers
* Lagrange with multiple constraints
* Week 23
* volume and iterated integrals
* cross sectional area
* Fubini's theorem
* density and mass
* Week 24
* functions f : R^n --> R^k
* coordinate systems
* chain rule
* change of variables
* Jacobian matrix
* linear maps and change of area
* exam review