* 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
* Week 10
* max and min values
* extreme value theorem
* closed interval method
* derivatives and graphs
* first derivative test
* Week 11
* rolle's theorem
* the mean value theorem
* Week 13 (hand written)
* area and the definite integral
* sub-intervals
* sample points
* riemann sums
* sigma notation
* the definite integral
* fundamental theorem of calculus
* Week 14
* indefinite integrals
* anti-derivatives
* net change theorem
* area calculations
* chain rule and integration
* substitution
* definite integrals and substitution
* Week 15
* area and integration
* signed area and total area
* volume
* Week 16
* volume
* bodies of rotation
* Cavalieri's principle
* average values
* integration and the product rule
* integration by parts
* iterated parts
* cyclic parts
* Week 17
* trig integrals: sin^k(x)cos^l(x)
* trig integrals: sin(kx)cos(lx)
* trig substitution
* Week 18
* ratios of polynomials
* polynomial long division
* partial fractions
* irreductible quadratic terms
* Week 19
* general strategy for partial fractions
* improper integrals at infinity
* improper integrals at discontinuities
* p-test
* two sided infinite limits
* convergence and divergence
* comparison for integrals
* Week 20
* sequences
* convergence / divergence of sequences
* L'Hopital and squeeze theorem for sequences
* increasing and decreasing sequences
* monotonicity
* boundedness
* monotone convergence
* factorials
* Week 21
* convergence and divergence
* integral test
* the Riemann zeta function
* harmonic series
* telescoping series
* monotone convergence and series
* direct comparison of series
* Week 22
* direct comparison
* limit comparison
* alternating series
* Week 23
* absolute convergence
* root test
* ratio test
* power series
* Week 24
* power series
* maclaurin series
* taylor series
* euler's identity
* review