TECHNIQUES OF INTEGRATION.

Integration by Parts. Trigonometric Integrals. Trigonometric Substitution. Integration of Rational Functions by Partial Fractions. Strategy for Integration. Approximate Integration. Improper Integrals.

FURTHER APPLICATIONS OF INTEGRATION.

Arc Length. Area of a Surface of Revolution. Center of Mass.

DIFFERENTIAL EQUATIONS.

Modeling with Differential Equations. Direction Fields and Eulerâ€™s Method. Separable Equations. Linear Equations.

PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Curves Defined by Parametric Equations. Calculus with Parametric Curves. Areas and Lengths in Polar Coordinates.

INFINITE SEQUENCES AND SERIES.

Sequences. Series. The Integral Test and Estimates of Sums. The Comparison Tests. Alternating Series. Absolute Convergence and the Ratio and Root Tests. Strategy for Testing Series. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials.