COURSE NUMBER AND TITLE: MATH 2012 Calculus and Analytic Geometry II

CREDIT HOURS: 4

CATALOG DESCRIPTION: A continuation of calculus including applications of integration, techniques of integration, improper integrals, sequences, series, and polar coordinates.

SUGGESTED TEXT(S):
Calculus, by Salas, Hille, Etgen
Calculus, by Rogawski
Essential Calculus, by Stewart

COURSE OUTLINE:

1. Techniques of Integration
• Integration by Parts
• Integration of Powers and Products of Trigonometric Functions
• Integration using Partial Fractions
• Numerical Integration
2. Applications of the Integral
• Area
• Volume by Parallel Cross-Sections; Discs and Washers; the Shell Method
• The Centroid of a Region; Center of Mass
• Work
3. Conic Sections; Polar Coordinates; Parametric Equations
• Parabolas, Ellipses, and Hyperbolas
• Polar Coordinates
• Parametric Equations of Curves
• Arc Length
• The Area of a Surface of Revolution
4. Infinite Series
• The Integral Test; the Comparison Test; the Root Test; the Ratio Test
• Absolute and Conditional Convergence; Alternating Series
• Taylor Series; Power Series
• Binomial Series