* 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