* 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