Finding specific antiderivatives using initial conditions, including applications to motion along a line. Solving separable differential equations and using them in modeling. Solving logistic differential equations and using them in modeling. Use of Riemann sums and the Trapezoidal Rule to approximate definite integrals of functions represented algebraically, geometrically, and by tables of values. Series are defined as a sequence of partial sums, and convergence is defined as the limit of the sequence of partial sums.
Technology is used to explore convergence or divergence of various examples.
Motivating examples including decimal expansion. Geometric series with applications. The harmonic series. Alternating series with error bound. Terms of series as areas of rectangles and their relationship to improper integrals, including the integral test and its use in testing the convergence of p-series.