Master the core topics of Calculus II: advanced integration techniques including integration by parts, trigonometric substitution, and partial fractions; applications of integration such as arc length and surface area; infinite sequences and series with rigorous convergence tests; power series and Taylor series expansions; and parametric equations with polar coordinates.
Master advanced methods of integration: integration by parts, trigonometric integrals and substitutions, and partial fractions
Apply integration to compute volumes by shells, arc length, surface area, and physical applications
Understand infinite sequences and series, including geometric series and the divergence test
Master the ratio test, root test, and develop a systematic strategy for determining series convergence
Represent functions as infinite power series, construct Taylor and Maclaurin series, and determine intervals of convergence
Represent curves using parametric equations and polar coordinates, and apply calculus in these coordinate systems
A cumulative 20-question assessment covering integration techniques, applications of integration, sequences & series, convergence tests, power & Taylor series, and parametric & polar coordinates