1.Arc length, area of a surface of revolution and its applications
2.Modeling with differential equations and its applications
3.Curves defined by parametric equations, calculus with parametric curves, polar coordinates
4.Areas and lengths in polar coordinates
5.Sequences, series
6.Strategy for testing series, power series, representations of functions as power series
7.Taylor and Maclaurin series, applications of Taylor polynomials
8.Vector functions and space curves, derivatives and integrals of vector functions
9.Arc length and curvature, motion in space: velocity and acceleration
10.Functions of several variables
11.The chain rule, directional derivatives and the gradient vector
12.Maximum and minimum values, Lagrange multipliers
13.Double integrals over rectangles, iterated integrals, double integrals over general regions
14.Double integrals in polar coordinates, applications of double integrals
15.Line integrals