• Learning Outcomes for 3450:222 Analytic Geometry and Calculus II

Students are expected to be able to:

• Communicate mathematical results through the proper use of mathematical notation and words
• Use basic integration techniques, including substitution, integration by parts, trig integrals, trig substitution, and partial fractions
• Apply integration techniques to solve problems regarding volume, surface area, length of a curve, and other applications
• Understand sequences and series, including tests of convergence and divergence of series
• Work with power series and Taylor series and their basic properties
• Understand parameterized curves and polar coordinates.
• Topical Outline
• Review of Integration by Substitution
• Areas between Curves
• Volumes
• Volumes by Cylindrical Shells
• Average Value of a Function
• Integration by Parts
• Trigonometric Integrals
• Trigonometric Substitution
• Integration of Rational Functions by Partial Fractions
• Strategy for Integration
• Approximate Integration
• Improper Integrals
• Arc Length
• Area of a Surface of Revolution
• 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
• Curves defined by Parametric Equations
• Calculus with Parametric Curves
• Polar Coordinates
• Areas and Lengths in Polar Coordinates
• Conic Sections
• Conic Sections in Polar Coordinates