1. Inderteminate forms and improper integrals (inderteminate forms of type 0/0, other inderteminate forms, improper integrals: infinite limits of integrations, infinite integrands)
2. Infinite series (infinite sequences and series, positive series: integral test and other test, power series, Taylor and McLaurin series, alternative series,Taylor approximation to a function)
3. Parametric Equations and Polar Coordinates (the parabola, ellipses and hyperbolas, translation and rotation of axes, parametric representation of curves in plane, the polar coordinate system, graphs of polar equations, calculus in polar coordinates)
4. Geometry in space and vectors (Cartesian coordinates in three spaces, vectors, the dot and cross products, vector-valued functions and curve linear motion, lines and tangent lines in three spaces, curvature and components of acceleration, surfaces in three spaces, cylindrical and spherical coordinates)
5. Derivatives for functions of two or more variables (functions of two or more variables, partial derivatives, limits and continuity, directional derivatives and gradients, chain rules, tangent planes and approximation, maxima and minima, the method of Lagrange multipliers)
6. Multiple integrals (double integrals over rectangles, iterated integrals, double integrals over nonrectangular regions and polar coordinates, application of double integrals, surface area, triple integrals in Cartesian coordinates, cylindrical and polar coordinates, change of variables in multiple integrals)