* Week 1:
* functions
* one-to-one
* onto
* graphs
* transformations
* function composition
* inverses
* intervals
* inequalities
* absolute values
* distances
* Week 2:
* Exponential functions
* logarithms
* the unit circle
* radians
* degrees
* trigonometric identities
* quantifiers
* implication
* logic
* counter-examples
* proofs with quantifiers
* proofs with inequalities
* proofs as essays
* Week 3:
* limits
* limits to infinity
* existence of limits
* uniqueness of limits
* vertical asymptotes
* horizontal asymptotes
* Week 4:
* Delta-epsilon proofs
* Delta-Epsilon Examples
* Delta-Epsilon Story
* discontinuous functions
* bounding delta
* infinity limits and quantifiers
* estimation
* Week 5:
* Bounds
* upper bound
* lower bound
* least upper bound (lub)
* greatest lower bound (glb)
* completeness of the reals
* continuitty
* continuity of linear functions
* continuity of f(x) = x^2
* intermediate value theorem
* Week 6:
* Uniqueness of limits
* squeeze theorem
* continuity of polynomials
* Week 7:
* Slope
* the slope function
* secant lines
* tangent line
* left derivative
* right derivative
* derivative
* physics of falling objects
* Week 8:
* Scaling
* adding
* power rule
* product rule
* quotient rule
* composition
* chain rule
* higher order derivatives
* anti-derivatives
* Week 9:
* Logarithms
* exponentials
* logarithmic differentiation
* differentiation of piecewise functions
* power series for e^x
* derivatives of inverse functions
* Week 10:
* maxima and minima
* curve sketching
* local extrema
* global extrema
* critical points
* Fermat's theorem (extrema are critical)
* Rolle's theorem
* closed interval method
* mean value theorem
* equivalence of mean value theorem and Rolle
* first derivative test
* Week 11:
* curve sketching algorithm
* concavity
* Week 12:
* l'Hopital's rule
* logarithms and limits
* anti-derivatives
* anti-differentiation
* integration by substitution