* Week 3 * financial math * present value * future value * principal * effective continuous rate * effective annual rate * annuities * Week 4 * bonds * perpetuities * linear systems * types of linear systems * input/output models * Week 5 * solving linear systems with matrices * parameters * row echelon form * reduced row echelon form * Gaussian algorithm * Week 6 * matrix operations * algebra with matrices * linear combinations * matrix products * strange phenomena with matrix multiplication * inverse matrices * matrix inversion algorithm * Week 7 * linear algebra * geometry of matrix multiplication * eigenvalues and eigenvectors * Week 8 * probability and counting * basic counting principle |A x B| = |A||B| * permutations * power sets * factorial * permutations with repeated elements * combinations * Poker * Week 9 * independence * inclusion/exclusion * total probability * conditional probability * Week 10 * conditional probability * conditional total probability * Bayes' law * expected value * expectation * limits * one sided limits * existence of limits * Week 11 * limits and asymptotes * limit laws * continuity * Week 12 (doc cam) * slope and tangent lines * secant lines * tangent lines * derivatives * product rule * quotient rule * one-sided continuity * toolbox of continuous functions * types of discontinuities * Week 13 * derivatives * examples of derivative calculations * differentiability * natural exponentials * cusps, vertical tangent lines, and jumps * types of non-differentiability * Week 14 * the chain rule * asymptotes * "designer" functions * derivatives of inverses * logarithmic differentiation * implicit differentiation * Week 15 * shape and derivatives * strictly increasing/decreasing * sign charts * critical points * concavity and the second derivative * points of inflection * Week 16 * optimization * extreme value algorithm * first derivative test * second derivative test * applied optimization * Week 17 * approximation * linear approximation * approximating area * power series for exp(x) * Riemann sum setup * Week 18 * Riemann sums * Fundamental Theorem of Calculus * anti-derivatives * total area * signed area * substitution * Week 19 * substitution * integration and the product rule * integration by parts * iteratred integration by parts * bounds and parts * Week 20 * vertical slices * horizontal slices * dividing a region in to two parts of equal area * area between curves * differential equations warm-up * Week 21 * differential equation * simple differential equations * seperable equations * linear equations * integrating factors * Week 22 * differential equations * growth/decay model * second order constant coefficients * second order constand coefficients with repeated roots * multivariate functions * partial derivatives * tangent planes * contour plots * Week 23 * hessian matrices * second derivative test * unconstrained optimization * Week 24 * optimization over regions * volume calculations * dxdy and dydx