Infinite sequences and series of numbers, power series, tests for convergence; Taylor's theorem and Taylor series for functions of one variable; planes and quadratric surfaces; limits, continuity, and differentiability; partial differentiation, directional derivatives and gradients; tangent planes, linear approximation, and Taylor's theorem for functions of two variables; critical points, extreme value problems; implicit function theorem; Jacobians; double integrals, iterated integrals and change of variables.