* Week 1
* Functions
* Domain
* Range
* Simple graphs
* Vertical line test
* Piecewise functions
* Week 2
* Essential functions (line, parabolas, and trig)
* sine and cosine
* transforming graphs
* horizontal / vertical shift
* horizontal / vertical translation
* horizontal / vertical stretch
* horizontal / vertical compression
* reflections about x-axis and y-axis
* exponential functions
* one-to-one functions
* inverse functions
* natural logarithm function
* Week 3
* inverses and logarithms
* trigonometry
* radians
* inverse trig functions
* sin(sin^{-1}(x))
* unit circle diagram
* Week 4
* limits
* one-sided limits
* calculating limits visually
* limit laws
* squeeze theorem
* continuity
* left continuous
* right continuous
* intermediate value theorem
* Week 5
* showing solutions exist with the IVT
* limits to infinity
* asymptotes
* horizontal asymptotes
* derivatives and rates of change
* secant lines
* tangent lines
* instantaneous rate of change
* average rate of change
* physics of falling objects
* differentiability
* cusps
* derivative as a function
* higher derivatives
* Week 6
* derivatives of polynomials and exponentials
* the power rule
* tangent lines
* derivative of e^x
* limits as derivatives
* product and quotient rule
* tangent lines passing through a given point
* Week 7
* derivatives of trigonometric functions
* high order derivatives of trig functions
* lim sin(x)/x
* the chain rule
* derivatives from tables of values
* Week 8
* implicit differentiation
* chain rule and inverse functions
* derivatives of inverse trigonometric functions
* logarithmic differentiation
* higher-order implicit differentiation
* Week 9
* natural growth law
* natural decay law
* half-life
* Newtonian heating / cooling
* related rates
* related rates solving strategy
* growing shadow
* falling ladder
* draining cone