-
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